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(V4) Increasing Exclusion: The Pauli Exclusion Principle and Energy
Conservation for Bound Fermions Are Mutually Exclusive

INTRODUCTION
This article is intended to support two hypotheses
...
The ionization energies of the
simplest multi-electron system, helium, are used to illustrate the point
...

To emphasize: the failing is an inevitable consequence of assuming the Pauli Exclusion
Principle (PEP) as generally understood
...
) Second, we will show that the description of two electron systems based on a
new paradigm of quantum mechanics, Classical Quantum Mechanics (CQM), developed
by Randell Mills (1), but with a simple modification introduced herein, is consistent with
energy conservation
...
Extension to free electrons is left for future essays
...
First, we find it expedient to include a
description of the scientific process as it applies to physical sciences
...

Specifically, a novel classification scheme is presented to help ‘untangle’ the net of
quantum mechanics theories
...
Finally, there are the theories ‘between’ which are shown not to be
true quantum in their very nature, indeed, they do not even employ Hamiltonians
...

Once we show that ‘quantum’ is not even a coherent single theory, and that the
inclusion of the PEP in any quantum mechanics model makes the model inconsistent with
energy conservation, we argue it is scientifically rational, in fact scientifically obligatory,
to discuss alternatives to standard quantum theories
...
To wit: It is shown that a new theory
of quantum mechanics based solely on classical physics, particularly Maxwell’s equations
and Newton’s Laws, and arguably one postulate regarding the strength of the interaction
between two bound electrons, does give a totally satisfactory, algebraic, closed form,
model of helium photo ionization with no variable parameters
...


1

SCIENTIFIC PROCESS
In brief, physical science is a set of processes designed to produce an objective
and predictive description of nature
...
One set of processes is designed to measure and record
phenomenon in nature
...
Also, through
comparison/contrast with general observed patterns of nature, objective observations are
categorized
...
It has been repeated in countless labs and the quantities
associated with the process have been verified repeatedly (2-7)
...
The photo ionization of helium is a good example of a scientifically objective
observation as it is clearly a highly repeatable process that has been precisely quantified,
and belongs to a larger set of related processes, similarly repeatable and quantified
...
These theories are valuable in that they can be used
to predict behaviors quantitatively
...
Also, scientific theories should be self-consistent, and consistent with
theories that are known to be consistent with all observables over the proposed range of
validity (8)
...

Theories come and theories go
...
The
best seem to come as epiphanies and involve simple ideas
...
In contrast there is a simple
method for eliminating theories: scientific testing, the third category of scientific process
relevant to this paper
...
Scientific
testing is conceptually simple: A theory cannot be proved, but it can be disproved
...
At a minimum, a theory
shown inconsistent with a single objective scientific observation is no longer valid, or at
least not valid over some range (8)
...

The above section/lecture should not be necessary
...
Unfortunately, the author believes many in the
community are not aware that no theory is proven, hence questioning any theory is a
scientifically sound activity, whereas arguing against even the consideration of alternative
theories, as many scientists have in regard to quantum theory, is unscientific and
2

irrational
...
Although these attempts to create a planetary/solar
system model of electrons/atoms ultimately failed, generally because they could not
predict the correct g-factor (13), they indicate that many scientists have always
understood that the current quantum model is far from satisfactory and that alternatives
should be considered
...

However, no physicist succeeded in finding a means to explain the ‘quantum’ nature of
stable energy levels in atoms, discovered via spectroscopy (e
...
Balmer series), using
these laws (13)
...
In time it was realized that this new theory, SQQM, was
totally inconsistent with classical physics laws at size scales ‘less than h-bar’
...
, hence in violation of Newton’s Laws
...
At those positions in order to preserve the total binding energy, that is
the sum of the potential and kinetic energy, the electron is presumed to have negative
kinetic energy
...

The violations of Maxwell’s equations are equally clear
...
In a classical sense this is
accelerated motion, which by Maxwell’s equations should require the emission (jump
toward nucleus) or absorption (jump away from nucleus) of energy
...

To make SQQM match the older classical theories the community, under the
guidance of Bohr, adopted the notion of the ‘Correspondence Principle’ more than 70
years ago
...

Still, there are many who never were satisfied with this explanation
...
’
The above issues are well rehearsed even in basic quantum theory courses
...
g
...
In particular: the multi-electron wave
function multiplied by its complex conjugate, a single scaler value at every point in 3N
(N is the number of electrons) phase-space, has no physical meaning
...

Another issue is the notion that anything regarding SQQM is proven
...
A theory shown
to be consistent with all known phenomenon is still not proved, just shown to be ‘likely’
...
Although proving
a theory is difficult, disproving one is simple
...
Indeed, this is the rationale given for
restricting the domain of applicability of Newton’s Laws and Maxwell’s Equations to
scales ‘greater than h-bar’
...
It has not been proven that they do not, all we know is that earlier efforts
failed! Thus, the argument at the core of this manuscript, that a single epiphany regarding
the correct geometrical description of elementary particles ‘allows’ correct (i
...
matches
objective scientific observations) values to be obtained using classical laws of physics on
all scales, cannot be summarily rejected as ‘unscientific’
...
In our case we provide a first test of the CQM physical description of bound
electrons
...
Will the physics
community recognize the primacy of the scientific process and not be guided by the
weight of tradition? Will they even consider questioning SQQM?
The sections below amplify many of the themes introduced above
...
Discussions of standard quantum, including defenses of standard
quantum, must necessarily begin with the identification of the class of quantum theory at
issue
...
These three theories, it is
argued below, are distinct and incompatible
...
There are actually at least three categories of ‘parallel’ quantum
theories
...

It is often erroneously conflated with SQQM
...
In the DQM theory, electrons are quasi-independent
particles that independently occupy (hydrogen like) ‘orbitals’ and have energies/spins and
other properties associated with the orbital they occupy
...
Each electron in a
multielectron system has a particular energy, associated with the quantum level it
occupies
...
The total spin of the system is the sum of the ‘spins’ of the
individual electrons
...
One important feature of DQM is that in the
language of DQM the PEP actually has meaning
...
More below
...
In any event,
we show below that in DQM either PEP or energy conservation must be incorrect
...

DQM also can explain phenomena such as XPS data from multi-electron atoms in
which it is clear that there are a multitude of ionization energies
...
Since its description of an atom indicates that electrons occupy
specific energy levels, it is consistent with the supposition that atoms at lower energies
(inner orbitals) can be ‘knocked-out’ of the atom (ionized) with a bolt of the correct
energy
...

Is DQM a valid physics theory (8)? As shown below, DQM cannot even produce an
energy balance consistent with photo ionization of helium, thus clearly DQM cannot be
considered a valid scientific model
...
)
Deposing DQM- Postulate: If quantum theory cannot explain photo ionization of
helium, then it is not a valid scientific model for any bound electrons
...

The DQM model of the photo ionization process for atoms is that a photon with
sufficient energy is absorbed by a bound (atomic) electron and hence ‘frees’ the electron
...
6 eV is required to ‘free’ an electron, that is bring it to a state in which it no
longer feels any force from its original nucleus
...

A second aspect of the model of relevance is the postulate that for all two electron
atoms in their ground state, the two electrons are identical in all respects, except for their
spin direction/spin quantum number
...
For helium the energy of both electrons in the DQM model is approximately
-24
...
The energy assignment of
24
...
In the DQM model the magnitude of the ionization energy and
the magnitude of the energy of the electron that is being ionized are equal, just as it is the
case for one electron systems
...
5 eV does not come necessarily from

5

a direct quantitative theory (and DQM as defined here is not quantitative), but rather from
objective scientific observation (14) of the ionization process (See Figure 1)
...
1- Classic Energy Level Diagram for Helium
...
5 eV, what are their energies? (From Ref
...
The measured value of ionization for the
electron in He+ is -54
...
Although it is not generally explicitly stated, in virtually any standard
text (15-17), it is an inescapable implication of the model, and the only interpretation
consistent with energy level diagrams (see Figure 1) and the PEP
...
7, to
-54
...
There is no ‘scale’ at which this general principle
does not apply
...
Thus, one concludes that the nice physical picture of
the atom at the heart of DQM is not valid, and hence DQM is not a scientific theory
...
Remarkably, there is no need for math any more complex than basic
algebra to disprove DQM
...

During/after ionization the electron that is not ionized falls in energy from -24
...
4 eV
...
0 eV) + hν (+24
...
4 eV) + e- (0 eV); ΔHrxn= -29
...
(Incidentally, the identification of the measured ionization energy, 24
...
) The nearly 30 eV
unaccounted for is an enormous energy
...
2 eV /H atom, and this is associated with a lot of
sensible heat
...
S
...
) Moreover, it is clear the 1
...
In precisely the same fashion the 29
...

2
...
4 to -24
...
5 eV
of energy is released as a photon
...


He+ (-54
...
4 eV) + hν (+24
...
7 eV (2)

3
...
5) is -49
...
In contrast, for ionized
helium, the total energy of the free electron (0 eV) and the one bound electron is -54
...
Clearly ionized helium is in a lower energy state than helium
...


He (-49
...
4 eV) + e- (0 eV); ΔHrxn= -5
...
Energy and energy change are state properties
...
If
two objects are ‘identical’ or ‘indistinguishable’ they must have the same state properties
...
in New Mexico (10,
600 ft) to my front yard (5200 ft
...

Most physicists conflate SQQM and DQM and attempt to save DQM because they
perceive a threat to SQQM in the failure of DQM
...
As we shall see, they are wrong
...
These arguments, actually proposed ‘modifications’ to DQM, are considered
below
...
This category of modifications always postulates a release of energy never
previously observed during photo ionization
...
Second are the ‘stored’ energy models
...

Each category of answer is examined below
...
The patent office will not issue patents for perpetual motion
machines, yet the missed release model of helium photo ionization can be shown to be
equivalent to perpetual motion
...
Helium gas
is placed in a chamber with perfect mirrors
...
7 eV light from a laser is
added
...
In consequence, in these models, there is an
increase in the effective nuclear charge to a full +2 on the remaining electron
...
This is the ‘missed
release’ of energy, ‘missed’ as it has never been observed
...
This process is known to release the same amount of
energy as required for ionization, about 25 eV of energy! Clearly, this model again
violates the energy balance
...
No

8

fuel is burned, yet a net of almost 30 eV of ‘free’ energy is generated for each photon of
25 eV put into the system
...

The proposed ‘missed emission’ process can be written as two steps
...
However, as in the co-ordinate
system of the original atom momentum must be conserved, the electron, being almost
8000 times lighter than the ion, will have virtually all of the released energy
...

The ‘stored energy’ models all suffer from a lack of precision and quantification
...
How is the mass reconverted to energy during electron attachment? If the
energy is postulated to be stored in ‘fields’ the question is: What fields? Such a model
must be quantified, or it simply has no credibility
...
Warning I: This modified version is not found in the literature (e
...
14-17)
...
In respect to its consistency with an
energy balance the modified model is superior, however the modified model arguably
contains some metaphysics as it is not possible to compare the computed electron energy
values by any direct process
...

‘Abridged’ /‘schematic’ energy levels for all of the possible new models of helium
are illustrated in Figure 2
...
This is postulated to be a
process in which the energy released as the unionized electrons fall to there
postionization levels, the so-called ‘relaxation energy’, help ‘boost’ the ionized electron
9

out of the atom
...
In the ‘NON INTERACTING’
model the two electrons do not interact, and the ‘unexcited’ electron remains at its initial
energy level until ionization
...
5
eV (agrees with total observed electron energy of -79 eV), ii) None of the energy levels
of excited states are the same as in the ‘Standard Model’, iii) spacings between energy
levels are the same as in Figure 1, iv) no energy level corresponds to -24
...
In the ‘INITIAL DROP’ model, the electrons also do not interact, but the
‘unexcited’ electron falls to its final energy state under any and all excitation processes
...
4 eV, into the excited/ionized electron
...
In this model, the excited state energy levels of the
‘excited/ionized’ electron match those of the ‘STANDARD MODEL’ and there is no
large energy gap between excited states and the vacuum
...
The total energy of each electron is -39
...
For example, there could be a
(repulsive) total ‘bond’ energy of +10 eV, and each electron could be bonded to the
nucleus with an energy of -44
...
As the two electrons are identical, it is rational to
assign half of the ‘bond’ energy to each electron
...
5, as shown
...
) With each photon adsorption/excitation process there is a concomitant drop in
the energy of the unexcited electron
...
Other notable features of this model: All of
the excited states are at lower energies than those given in the ‘Standard Model’, and all
of the energy spacings between excited energy levels are larger than those of the standard
DQM model
...
That is, the energy required for ionization in the standard model is -24
...
Thus, there is no
accounting for the energy lost when the ‘unionized’ electron falls nearly 30 eV in energy
following the first ionization
...
That
energy, plus the input energy of 24
...
5
eV to the vacuum level
...

Given present information it is impossible to tell which, if any, is correct
...
5 eV, and none provide ANY information regarding the energy state of the
‘unexcited/unionized’ electron during the excitation process
...
In all of the above
novel (‘Non-Interacting’, ‘Initial Drop’, ‘Staged Excitation’) abridged/schematic models of helium, both
electrons in their ground state are at -39
...
In contrast, in the ‘Standard Model’, both electrons are
initially at -24
...
1 or any
text) and the PEP
...
First, one electron is ‘excited’, and the
other electron, according to the particular model, either remains at its initial energy level, or drops to a
lower energy
...
The ‘unexcited’
electron in all cases is found at -54
...
Finally, it is notable that in the Standard Model
the energy for both the excitation and ionization step (a net of 24
...
In contrast, for the other models some of the energy comes from photon adsorption (a net of
24
...
5 eV to its final value of
54
...
7 eV)
...
5 eV
...
7 to -54
...
Hence, there is approximately 30 eV of energy ‘lost to
the universe’ during the ionization process as it is described in the Standard Model
...
As applied to atoms and ions SQQM does produce a model of
photo ionization of helium that is consistent with energy conservation, but it must ‘give
up’ all the physical content of DQM, in fact all physical meaning, in order to do so
...
Thus,
the arguments given below, particularly those regarding the inherent inconsistency of the
Pauli Exclusion Principle and Energy Conservation, as per the title of the manuscript, are
distinct from those employed in the DQM section
...

In SQQM applied to multi-electron systems, there are no ‘individual electrons’
...
In SQQM one develops a single ‘wave function’, from a single Hamiltonian,
not a number of Hamiltonians, that ‘number’ being set equal to the number of electrons
...
The Hamiltonian is intended to express all the energies arising from forces
...
For two electron
systems, the Hamiltonian is written in non-operator form (18):

p12
H=

p22

Ze2

Ze2

e2

+
!
!
+
2m 2m
r1
r2
| r1 !r2 |

(6)

Where p is the momentum, Z the nuclear charge and m is the reduced mass
...
One adds an additional kinetic and
nuclear electrostatic term for each electron, and the number of two electron repulsive

15

terms is one less than the number of electrons
...
In particular for a two
electron system the wave function is most easily expressed as a product-sum of ‘single
particle’ wave functions and has this general form:
1
!=["1(A)"2(B)±"1(B)"2(A)]
(7)
2
Where the subscripts represent the different ‘single particle’ wave functions (φ), and the
letters in parentheses are the electron identifiers
...
A
minus sign is correct if the spins are parallel and positive if they are anti- parallel, to
insure total antisymmetry of the wavefunction
...
That is, if the electrons
are interchanged, the wave function is not changed
...
In other
words, the bound electrons of an atom are sort of ‘one big electron’, hence describable by
one big Hamiltonian
...

That this answer is correct is found from a consideration of three issues: normalization
(phase space), computation of electron-electron interaction (real space), and examination
of the values of the wave function ‘mapped’ from phase space into real space
...
Indeed, it is clear that even the
mathematics employed in the first two standard processes are inconsistent
...

Another violation of the requirement of consistency is the nature of the wave function
...
For single electron wave
functions each point in real space has a single value and that value has a clear (?)
meaning: The probability that the electron will be at that point
...
As a
consequence, multi-electron wave functions cannot be graphed
...
Of particular concern is the use of 3N (N is the number of electrons) ‘phase
space’ to make the value of this function integrated over all ‘space’ equal one
...
Examination of Eq
...
Indeed, the value for the Slater determinant
antisymmetric wave function (18) for any number of electrons is one
...
Two of these terms integrate to zero because the
wave functions are orthonormal in both 3D phase spaces
...
It is notable
that the number of dimensions required for integration/normalization increases with the
number of electrons
...

It might be reasonable to argue that the ‘phase space’ approach is acceptable if it were
employed consistently
...
Indeed, the last term in the multi-electron Hamiltonian
(Eq
...
(This in itself is odd
...
For example, we
show below how two giants of quantum mechanics suggested means to understand and
compute this interaction that are fundamentally flawed
...
6),
where r (r=r1-r2) is the distance between the electrons, in real space
...
Early in the development of SQQM,
methods to evaluate this integral containing the very apparent singularity were offered
...
However, as we show
below, they are clearly not correct
...
(20) suggested the
following equality could be used, and would lead to a finite value of the repulsive energy
1

! m=+n

="
ri, j

n=0

4# r
"
m=$n

m

m*

Y (%&)Y (%& )
2n+1r>n+1

n

i

i

n

j

(9)

j

where rij is the “distance between the two particles” and “r> be the greater of ri and rj and
r< be the lesser”
...
Indeed, consider that r< is at the origin, and r> is any point but the origin
...
Yet, it is clear that 1/rij in this case is not
zero
...
(21), took an alternative approach to evaluation of the integral with
the singularity
...
It begins with an assertion: The
integral representing the electrostatic repulsion between two electrons is equivalent to,
“the mutual electrostatic energy of two spherically symmetric distributions of electricity
with density functions e-r1 and e-r2”, and he proposes to integrate this over real space
...
Even if this assertion is accepted as
true, it is quite clear that such charge distributions would have infinite energy as there
would be non-zero overlap of charge at all points in space
...
g
...
There may be a mathematical
rationalization for the final expressions, however, there is clearly no physical explanation
...

How is the difficulty of the singularity in real space avoided? The approach
generally taken is to propose that electron motion is correlated
...

Those who insist that the multi-electron wave function is ‘physical’ indicate that
the wave function is really defined by this correlation
...
Thus, for a two electron system the
value of the wave function at any point in space (R1) is the probability that one electron is
at R1 and the second electron is at R2
...
But, there is some value for every
geometry
...
The wave function
at this point must also be a measure of the probability that one electron is at R1 and the
second at R4, etc
...
, etc
...
This is because if one electron is at this point, there are an infinite
number of positions that the other electron can be found, some more probable than others
...
This is not only
‘ungraphable’, it is not a physically plausible interpretation
...
For every position Electron 1 takes in its ‘phase space’, there is a
matching probability distribution, encompassing every point in the ‘phase space’ of
Electron 2
...
) Since Electron 1 can be an infinite
number of positions, there are an infinite number of Electron 2 distributions in Electron 2
phase space
...
What

18

about the element lead, for which the electron ‘phase space’ has 246 dimensions? At a
minimum, it is clear that the multi-electron wave function does not have a ‘physical
meaning’ even remotely similar to that of the one electron wave function
...

Is there any other possible physical meaning to the multi-electron wave function?
The first difficulty is attempting any type of mapping of the fully anti-symmetric 3N
dimensional wave function into three dimensions (see above discussion of
normalization)
...
For example, if it were the sum of the probabilities of various electrons
occupying a position in space, then the normalized value of the wave function would
equal the total number of electrons, yet as discussed above it is always one
...
Indeed, the
normalized probability of any one electron occupying a particular position is less than
one
...

The above arguments lead to the following conclusion: The multi-electron wave function
has no physical meaning
...
It is
interesting to note in this regard that even the most thorough discussions of the physical
meaning of quantum theory only discuss the one electron case (13)
...
It is not
plausible in the multi-electron case
...
Thus, the multi-electron
wave function can be considered a description of a group ‘average’ behavior, or perhaps
is better understood as the behavior of one big electron with a total charge equal to that of
the number of electrons in the wave function
...
It is the sum of the energy of all the electrons
...

This non-intuitive nature of SQQM, the remarkable limitations of the theory are
widely understood
...
Thus, for example, in the NIST tables the excitation
energies of helium are listed relative to the ground state (23)
...
Also, in careful
computations of the helium energy, no single electron values are provided for either the
ground state electrons, nor the ‘excited electron’
...
SQQM, as applied to multi-electron systems, is
not consistent with the notion of multiple energy states, one for each electron in the atom
...
It is clear that in SQQM that if one were to provide the electron energies for

19

multielectron systems, they could not be equal to the measured ionization energies, or the
‘perpetual motion’ conundrums expressed in Equations 1-5 would apply to SQQM just as
they do for DQM
...
All energy level diagrams for electrons, molecules, etc
...
And exactly where is phase space?
This analysis of the ‘meaning’ of a multi-electron wave function leads to an
additional puzzle regarding physical understanding of the Pauli Exclusion Principle
...
In SQQM there are no independent identifiable electrons, there is only
one orbital, one energy, one average radius, for any number of electrons
...
They all occupy the one orbital
...
Discussing PEP in relation to SQQM is as meaningful as a
discussion of the shape of red or the temperature of a triangle
...
That is, it can produce an expectation value for
energy and radius and in a manner of speaking, spin
...
There is absolutely no means to separate electrons and speak of the energy,
the orbital, etc
...
After all, there is only one Hamiltonian and it
produces one wave function, and that yields one energy
...
In the case of helium, this methodology correctly yields a total electron
energy equal to the sum of the two measured ionization energies, approximately -79 eV
...
5 eV? No
...
So, is this result really
consistent with the known ionization energies? Yes, but a second calculation must be
performed
...
Hence, it is always necessary to
make two calculations, one for a system of N electrons and one for a system of N-1
electrons
...
So, the approximate ionization energy is computed to be:
Eion= -54 eV- (-79eV)= 25 eV

(10)

in agreement with experiment
...
Can it produce the multiple ionization energies

20

measured with x-ray photoelectron spectroscopy (XPS) etc? Not directly, as the only
energy value it provides is for the total system of electrons and since it is organized to
indicate the electrons in an atom are indistinguishable
...


THE HYBRID MODELS: DESCRIPTIVE/QUANTITATIVE QUANTUM MODELS
(D/Q)As DQM has no quantitative content (e
...
can’t close an energy balance) and as
SQQM cannot even begin to explain many well known physical phenomenon (e
...

multiple ionization energies in multi-electron systems) there is a natural tendency to
invent models that are a bit of both
...
Hence, scientists search relentlessly for a quantum
theory in which energy level diagrams are meaningful, a world in which measured
ionization values agree with computed energy levels and a totally three dimensional
world
...

Simple or naïve models are not satisfactory
...
g
...
This can easily be shown to be wrong
...
It is clear that this is not true
just by examining the expressions derived from the multiplications of the wave
function(s) and their complex conjugates
...
In the ‘naïve’ one electron ‘interpretation’:

Etot= !i <φ1(A)|Hi|φ1(A)>

(11)

where the Hamiltonians in the above expression are some type of ‘effective’
Hamiltonians, and the sum is over the total number of electrons in the system
...
11 and Eq
...
Moreover, simply using
single particle wave functions derived from perturbation theory it is easy to show that for
helium Eq
...
12 yields better
than 95% (25)
...

Note,
single particle wave functions, derived from perturbation theory, lead to notions like
‘effective nuclear charge’, and ‘look’ like ‘hydrogen orbitals’, but from nuclei with
reduced ‘effective nuclear charge’
...
In fact, the ‘best’ basis set of orbitals by definition is the set
that produces the lowest total system energy, not the set composed of hydrogen-like
orbitals (25,26)
...

The naïve
approach outlined above does not work, but it does indicate some necessary elements of
any ‘theory’ that produces both the ‘descriptive’ elements of DQM and the quantitative
elements of SQQM
...
Solving a
set of these equations leads to ‘eigenfunctions’ and ‘eigenvalues’ the former are then
associated with orbitals and the latter with orbital energy levels
...
11, as well as the best single electron wave
functions (basis set) to use in these operator based quantitative quantum theories
...

Or, if they are resolved, as is sometimes the case for models of molecular orbital
energies, the computed energy levels and the measured ionization energies don’t match
...

This
inability of the Hartree-Fock and other ab initio methods (which all contain ad hoc
hypotheses) to properly account for relaxation, to obtain energy level sequences in
agreement with known sequences, etc
...
Perhaps the most famous critics
are J
...
Slater (Slater determinant) and his students (27-29)
...
methods…of quantum chemistry
...
…Unfortunately, this assumption ignore the orbital
relaxation that generally accompanies ionization
...
large in many
systems so …Koopmans’ lead to inaccurate electron binding energies…
...
carry out…energy calculations

22

for the neutral system and the ion, (this) requires one to subtract two very large total
energies to obtain a small energy difference
...
Hence, they felt empowered to
create a competing computational method with no pretenses
...
In the end the symmetric solutions generated in each region
are forced to ‘match’ at region boundaries
...

However, it often provides energy levels closer to measured ionization energies, (in the
correct order) than do any of the so called ab initio theories
...
It is based on empirical studies
showing that removing half an electron (creating a ‘transition state’) yields something
close to the measured ionization energy
...
’ And
he points out that there is no correlation between the order of the orbital energy levels and
those observed
...
For example, atomic helium (notably there is
no work in the literature of helium in which energy levels are computed consistent with
an accounting of relaxation energy) clearly should have a ‘computed’ ground state for the
two electrons of -39
...
This energy is necessarily far lower than the measured ionization energy
of approximately -24
...
As we discuss below, all earlier
computations of helium report only the total system energy, ignoring the fact that there
computations directly indicate that the two electrons in the ground state must have an
energy of -39
...
Another issue: the starting point for computing energy levels using a
Hartree Fock approach during excitation
...
That is, both the excited electron and the ‘unexcited’
electron levels must be computed
...

There is always a presumption involved in matching measured values (e
...
-24
...
g
...
5)
...

None of the ab intio or other computational methods are to be confused with SQQM
...

Instead, employing a variety of assumptions, ab initio methods treat a multi-electron
system as composed of individual electrons with distinct energies
...
There are sets of operator equations, but these are
not Hamiltonians
...
This leads to a set of ‘orbitals’ each with a distinct
energy, and in the final analysis the ‘orbitals’ generated are presumed (by adoption of the
PEP) to be doubly occupied by spin paired electrons and the eigenvalues are presumed to
be the energies of these electrons
...

23

That is, the ‘single electron’ Hamiltonian methodologies are a means to create a middle,
‘quantitative’, ground between DQM and SQQM
...

In addition to the earlier described ‘relaxation energy’ problem there are many other
fundamental problems with attempting to make a theory that is somewhat in the middle
of SQQM and DQM
...
For example,
in the Hartree-Fock method (26) the operator equations (not Hamiltonians!) include two
types of integrals that both represent the energetics of interactions between ‘distinct
electrons’: Coulombic repulsion integrals that require the electrons to be independent
entities with charge distributions that are ‘decreed’ to be fully described by ‘single
particle wave function x single particle wave function*’, and a second type of repulsive
integral for which the underlying basis is ‘correlated motion’ of point particles
...
The final form of the
equations that must be solved are worth contemplating as even for this simple system it
shows all of the deviations of this approach from true SQQM
...
The probability distribution is
treated as a charge distribution
...
The two electrons are clearly distinct in character
...

There are clearly at least three major inconsistencies with SQQM inherent in this
approach: i) The electrons are treated as independent (against the basic assumption of
SQQM) particles
...
And iii), in order to compute the magnitude of both
types of repulsive interactions the wave functions, which in SQQM theory are probability
distributions, are treated as charge distributions
...

A fourth ‘inconsistency’ regarding the use of the Hartree Fock method applies
specifically to helium
...
The method historically used to compute the energy
levels of the electrons as well as the total energy of all the electrons, explicitly assuming

24

the PEP
...
e
...

The first term are the diagonal elements of the final, fully diagonalized, set of equations
...
g
...
Equation 16 clearly
shows that for helium the H-F method leads to the conclusion that in the ground state the
energy of each electron has an energy of one-half the total energy, or each electron is
bound at about -39
...
Interestingly, in those relatively recent cases in which the H-F
method has been applied to helium, only the total energy of the ground state (very close
to the measured value) is explicitly reported (33,34)
...

As shown later this clearly does not work for helium
...
Thus, computations are complex as they must be done iteratively until the
final wave function set employed in computing the Hamiltonians is nearly identical to the
‘estimated’ set of the previous iteration
...
iii) There is no term in SQQM Hamiltonians (Eq
...

D/Q
type computational methodologies are so often presented as ‘quantum theory’ that it is
easy to get confused and begin to ‘buy’ the notion that they are fundamental theory
...
Yet, they are based on ‘multiple operators’ (not
Hamiltonians), rather than a single Hamiltonian and generate multiple ‘orbitals’ each
with a distinct energy
...
Or perhaps the term ‘ab initio’ implies that all forces are considered? In that case
why is there no magnetic interaction term? These D/Q methods, which come in
innumerable variations, are employed because there is no choice
...

Koopmans’ theorem is the basis for ‘teasing out’ individual orbital energies from ab
intio calculations, including Hartree-Fock
...
g
...
The energy of the new,
N-1, wave function can then be calculated and the energy so calculated is the ‘energy
level’ of the removed electron, or:

25

EN -E N-1= E removed orbital

(17)

Moreover, Koopman’s theory requires that the total energy be the sum of all the orbital
energies! This clearly does not apply to our standard example, helium! In the helium
case Equation 17 becomes:

EN -E N-1= -79eV-(-54
...
Clearly, employing this method returns us to the list of
conundrums, including the perpetual motion conundrum, discussed in the section on
DQM, above
...

To be specific, Koopman’s theory is not consistent with energy conservation for all
two electron systems
...
That is, an ‘excellent’ result
would be achieved if the Hartree Fock method, or any other D/S computation method,
predicted a first ionization energy precisely equal to that measured experimentally
...
Precisely the same objections raised repeatedly,
including the ‘perpetual motion’ objection, again indicate that the method provides
energy levels not consistent with a closed energy balance, and yields a total energy value
for the two electron system totally inconsistent with the total energy obtained using any
‘total’ wave function computation
...
Thus, the performance of any pseudo one-electron method is assessed
generally by comparing computed energy level spacings with measured energy level
spacing
...

Are the failures of Koopmans’ theory to achieve energy self-consistency for helium
unique or the rule? It is the rule, as shown below, demonstrating once again that SQQM
really says nothing about individual electrons in multi-electron systems
...
This is inevitable because it is an experimental
fact for atoms that the second ionization energies are always higher than first ionization

26

energies
...
It is always far lower than
that! The system ‘relaxes’, or at least does so theoretically, to a lower energy
...

For all of the alkali earth elements the second ionization energy is nearly twice the
first
...
Assume one of these
electrons is ionized
...
Where does the energy ‘go’ when
the s-electron that is not ionized falls to a lower state? Can’t we capture that energy and
thereby solve the energy crisis? From whence comes the energy to bring that electron
‘back’ to its atomic state during electron capture? After all, if a precise amount of energy
is required to ionize an atom, then exactly the same amount should be released when the
atom recaptures the ionized electron and returns to its original configuration
...
Happily, in the real world energy is not lost or gained during
ionization or electron capture
...
Hence, this model leads to
the absurd conclusion that alkali metal atoms should spontaneously ionize
...
There are never two ionization energies in a row for any
atom that are the same
...
This is done, in an empirical fashion, by assuming that ‘relaxation energy’ is
part of the energy that contributes the ionization process
...
For example, the binding energy computed
using this approach is necessarily greater (see Figure 2) than the measured ionization
energies
...
First, the
‘boost energy’ from relaxation is always made assuming that the second ionization
energy matches the true energy state of the relaxed electron after ionization
...
In short the
nesting of ‘energy boost’ corrections is not considered
...
As pointed out by
Slater and Johnson, the (molecular) calculations often predict the re-ordering of energy

27

levels (27-29)
...

Just as ‘-39
...
Too
many assumptions, combined with no direct substantiating measurements, puts a theory
in the realm of metaphysics
...
The scientific method demands such a clear correlation
...

Third, there appears to be no need to consider relaxation ‘boost’ when inner electrons are
directly ionized
...
Why is ‘boost’ only a
consideration for the ionization of the outermost electron? Finally, to make the entire
complex web of proposed energy levels work with energy conservation and the PEP,
invariably all sorts of variable parameters are introduced in the calculations
...
e
...
generally yield
results closer to reality than SQQM
...
These computational approaches are in fact distinct theories
e
...
see above discussion of some features of SCF - Xα)
...
However, as distinct
theories they are not proper subjects of this essay
...

There are at least three categories of quantum theory
...
For each the ‘meaning’ of the PEP is different
...

An analysis of DQM, as it currently is described in the literature, and its
relationship to measured ionization energies, in particular helium, clearly shows that the
model predicts infinite energy can be obtained via a process of ionization, and subsequent
electron capture
...
This is clearly not consistent with energy conservation
...
And a simple energy balance show the model predicts helium
should spontaneously ionize in order to attain minimum energy
...

The only means, and this is not done in the literature, to bring an energy balance
and PEP into alignment for the DQM model is to assume the relaxation energy ‘boosts’
the ionization process
...
In particular, for two electron systems, in both
DQM and D/Q methods, the ground state energies must be exactly one-half the total
energy of the electron system
...
5 eV, about 15 ev less
than the measured first ionization energy
...
This requirement also brings up a host of questions
regarding the levels occupied by both electrons, not just the higher energy electron,
during the excitation process (see Figure 2)
...

Precisely the same objections listed above for DQM, apply to all D/Q methods
...
In fact, as discussed, this objection applies to any (and that is all!) atomic
systems in which the second ionization energy is greater than the first
...
And one final objection: D/Q models are not based on
Shrodinger’s equation
...

5
...
All the electrons are
indistinguishable
...
There is only one orbital, and all
the indistinguishable electrons are in it
...
Yet, SQQM is a very limited model, capable only of
computing total properties for multi-electron systems such as total energy, average
radius, etc
...
Absurd
conclusions are inevitable when the method is misrepresented as a means to provide
information about individual electrons in the multi-electron system
...

The truth is the SQQM model cannot be employed or ‘manipulated’ to provide data
regarding energy states, etc
...
This
inability to yield individual electron energies is not a minor issue
...

Finally, multi-electron SQQM is not acceptable as physics at all because it is not a
‘physical’ model, unless 3N phase space is to be considered physical
...
In fact, it is an inconsistent mathematical construct
...
The new theory should: 1) be consistent with all classical laws of physics at all
29

scales, 2) lead to quantitative computations that close all energy balances, 3) be
quantitatively consistent with the observation that in all multi-electron systems (e
...

atoms) distinguishable electrons are found in distinct sharply defined energy levels, 4)
provide a clear value of the angular momentum of each electron in the multi-electron
system, and 5) provide predictions directly (not indirectly) comparable to measured data
...
One is offered below
...
Mills overcomes all of the inherent difficulties of SQQM and DQM
...
This work also leads to the conclusion, and this is the
modification to CQM offered herein, that in order to close energy balances the Pauli
Exclusion Principle must be amended
...

Each electron is an individual particle with its own energy, magnetic moment, angular
momentum and size
...
There is no uncertainty
principle
...
e
...
There is no ‘phase space’
...
However, unlike DQM, this is a
quantitative theory
...

And unlike SQQM the fundamental equations employed to compute energy levels are
simple algebraic, Newtonian force balances
...
It is explicit that each electron has a precise angular momentum
...
A new
exclusion principle is postulated, based on the notion that electrons are actually physical
objects: No two electrons can occupy the same space at the same time
...

CQM of Two Electron Systems- The CQM model, developed previously entirely by Dr
...
These bubbles of zero thickness charge
(‘orbitsphere’) are not solutions to a wave equation
...

However, for helium and other two electron atoms in the ground state there is no orbital
angular momentum on either orbitsphere
...
) It is simply postulated
that these bubbles will have properties consistent with all the valid scientific observations
regarding bound electrons including the right quantized energy levels, the correct
magnetic moment (determined with Maxwell’s Laws) and the correct g-factor (angular
momentum determined using standard mechanics)
...
Most of the
above has already been thoroughly demonstrated and vetted in the reviewed literature
(37)
...
It is also clearly
shown that they will not radiate
...
Indeed, it is well known that currents in
superconductors, for example in magnets formed in loops, do not radiate
...
All that is required is that the model be
consistent with all objective scientific observations
...

In this paper we do not have the ambition or need to repeat the arguments made for
the success of the orbitsphere in producing quantitative results in precise agreement with
objective scientific observations about angular momentum, magnetic moment, g-factor
etc
...
The goal of this paper is simpler: To show that two electrons,
each assumed to be simply a spherical shell of charge of ‘zero’ thickness (an
‘orbitsphere’), that obeys Newton’s Laws and Maxwell’s equations, will provide a
solution to the above energy balance conundrum, while yielding quantum energy levels
precisely equal to measured ionization energies
...
These readers are urged to take the
following principled pledge of the honest skeptic: I will expend effort studying the CQM
model of the bound electron (i
...
orbitsphere), if and only if it can be shown the
orbitsphere model provides quantitative predictions for two electron atoms more
consistent with objective scientific observations, including energy conservation, than
SQQM
...

The legitimacy of efforts to find physical models for electrons/atoms is verified by the
fact that others (9-12) have attempted to find physical models of the electron
...
Indeed, one
remarkable, new, epiphany is added in the CQM model: the electron is a spherical shell
of charge surrounding the nucleus
...

CQM Model of the Helium Atom: In this model the atom is built in two stages from its
constituent parts
...
) In the first step a single electron/orbitsphere is ‘added’ to a
31

nucleus consisting of two protons, and one or two neutrons to create a He+ ion
...
It is
included for clarity
...
A helium atom is the product of this second electron addition
...
(Mills accepts the PEP
...
) For both steps,
the arguments below only concern computation of stable final state properties, not the
mechanism of the process
...
Clearly, it obeys standard orbital mechanics
...
In essence this is a very simple statement of Newtonian
mechanics: The centripetal force must equal the central force, and the central force is the
standard form of the electrostatic interaction between opposite charges
...
As the loops are all
great circles, each has the same radius
...
These overlapping and crossing rings are
woven to produce a vector projected net angular momentum consistent with experimental
measurements, as described elsewhere (1,37)
...
Thus, it may be correct to say: In CQM one
aspect of elementary particle behavior is postulated that in a classical physics sense is
‘unphysical’
...
Another required postulate of
CQM that the scaler sum (not the vector sum) of the angular momentums of all the rings
is h-bar:

=!r"mring = mevr

(21)

Determining the vector sum of the angular momentum from the rings is a more complex
geometric computation and is carried out elsewhere (1, 37)
...
20 into
Eq
...

Given this definition of Bohr radius:

4!" 2
a0 = 2 0

(24) 

e me

33

A very simple formula for the radius of the first electron in any one electron system is
obtained:

a0
r=

(25)
Z

This is significant as the energy of any object bound by a central force with inverse
square strength can be obtained from standard mechanics once the mass, radius and
angular momentum are determined
...
And the total binding energy will be the sum of kinetic and potential energies
...
(Note: it is
a simple matter to determine independently the potential and kinetic energy of the
orbitsphere, add them together, and obtain the same result
...
For example, terms
not included in the energy balance include ‘self-interaction’
...
Instead, the infinite self-interaction of point particles is
swept away in a mathematical vortex known as ‘renormalization’
...
First, as
the orbitsphere is a perfect conductor, it has no field inside
...
Hence, there is no interaction between charge and an
internal field
...
Inside the orbitsphere there is no field, outside there is a well defined
field, equivalent to that produced from a single charge at the center of the orbitsphere
...
This is in fact a standard
postulate of E&M
...
Alternatively, symmetry indicates there can be no
field in the plane of a sphere
...
The net result is that at any single point, symmetry shows that the
fields must cancel
...

There are small corrections that lead to even greater accuracy
...
As the number of protons increases, the radius decreases and the velocity
increases in order to maintain h-bar of angular momentum
...
This and other small corrections are discussed
in detail elsewhere (1)
...
Comparison with experimental values is excellent
...
26)

EXPERIMENTAL
IONIZATION
ENERGY, eV

(Eq
...
00

13
...
59

He+

0
...
42

54
...
333

122
...
45

Be3+

0
...
69

217
...
200

340
...
22

C5+

0
...
81

489
...
143

666
...
03

35

O7+

0
...
77

871
...
g
...
Again, simply algebraic force balances are all that are required
...
e
...
In the CQM model, photons do not
mysteriously disappear upon capture as they do in standard physics, their energy
converted to a higher potential for an electron
...
In this essay
the minimum number of CQM concepts required to produce a resolution to the issue of
closing the energy balance are introduced
...

Step 2: In the second step, an atom is formed when a free electron is captured by the ion
created in Step 1
...
That is, as the single
electron on the ion is spherically symmetric, it creates a field equivalent to that of a point
electron at its center
...
As noted earlier it creates no field inside itself
...
In other words, the orbitsphere field cancels one
proton field outside of itself
...

A force balance is once again employed to determine the stable radius
...
) However, in this
case the force balance should have two terms, one for the net one proton central field and
one from the magnetic interaction
...
19
...
To wit, it is postulated that the magnetic force between any two
’nested’ orbitspheres, in which neither has orbital angular momentum, in any atom (of
which two electron atoms are a subset), is described with this equation:
2

Fmag = 3 s(s+1)

(27) r Zme

36

where r is the radius of the electron being acted on and s, the spin quantum number, is
1/2
...
In the full development of CQM, available
elsewhere, it is argued that this term is derived from the standard Lorentz force (1)
...
However, the expression given is acceptable as a postulate as it
has a simple algebraic form, uses only the most standard constants (Plank’s constant,
mass of an electron) and has no adjustable parameters
...
For those who must debate, please
recall: Postulates are at the heart of all physics
...

Clearly the outer electron feels two forces
...
(As noted above
the fields at the outer electron arising from the inner electron and one proton, both
mathematically represented by point charges at the center of the atom, cancel
...
In sum, this leads to the following force
balance for the ground state:

mv2

2

e2

Ftot = = 2 (Z #1)+ 3 s(s+1) (28) r 4!"0r r Zme
This can be re-written, using Eq
...
24):
1
r =a0[

s(s+1)
!

(Z !1)

]

(30)

Z(Z !1)

This simple algebraic equation, derived from a straightforward two term force balance,
will be shown to provide energies consistent with measurements of ionization energies, to
better than two percent accuracy, for all measured two electron atoms
...

Computing the energy of this second electron is not quite as simple as for the first,
because in this case the central forces are not inverse square
...
The energy
balance for the system is:

ΔEtot = ΔEpot + ΔE kinetic + ΔE magnetic

(31)

where Epot is the electric potential energy
...
Thus, the change in the magnetic energy is determined from an
integration of Eq
...
Hence:

1
-ΔEkin = 22
2 mer

(34)

Thus the total energy change of the outer electron during ionization, that is the energy
input to bring the outer electron from the bound state to the free state is:

38



Eion= ΔEtot= (Z !1)e2 / 4"#0r + 1 1 22 s(s+1) 2 Z mer
 

1 2

2

(35)

2 mer

It should be noted that this equation explicitly shows that the kinetic energy, inherent in
any physical object in a stable orbit, is ‘re-deployed’ such that it contributes to the
ionization process
...
30) is substituted in Equation 35 it
can be shown:

- ½ ΔEPot= ΔEKin + ΔEMag

(36)

It is interesting to reflect on the qualitative ‘mechanics’ of this equation
...
In
the presence of an added central force (e
...
magnetic) the velocity required to maintain
the object in stable orbit at any particular radius should be larger, hence the magnitude of
the kinetic energy larger
...
35
...
36 can be re-written:

Eion = ½ ΔEPot= (Z !1)e2 / 8"#0r

(37)

Can two extremely simple one-dimensional formulas really quantitatively predict all the
known ionization energies of two electron atoms? That is, can the simple formula for
ionization energy with no adjustable parameters, derived from a simple algebraic energy
balance, Eq
...
30, derived from a one
dimensional force balance also with no adjustable parameters, using only NIST values for
physical constants really predict all of the known ionization energies for two electron
atoms? The answer, as seen in Table II, is a yes
...
As Z increases, the ions become smaller (literally!), and the
relative error decreases to a small fraction of one percent
...

MEASURED
IONIZATION
CQM COMPUTED ENERGY
IONIZATION
Z RADIUS

ENERGY

From CRC Relative
Tables

BOHR RADIUS UNITS* Calculated**, eV
2 0
...
9965

Error***

eV
24
...
024016757

3 0
...
50902

75
...
011486488

4 0
...
289

153
...
015542863

5 0
...
295

259
...
015113253

6 0
...
519

392
...
013854068

7 0
...
958

552
...
012473378

8 0
...
61

739
...
011254041

9 0
...
474

953
...
010871755

10 0
...
552 1195
...
008967339
11 0
...
84

1465
...
007998657

12 0
...
34 1761
...
007114576
13 0
...
0537 2085
...
006267414

14 0
...
977
15 0
...
63 -0
...
1124 2816
...
004686838

40

16 0
...
459

3223
...
003932961

17 0
...
0178 3658
...
003142472
* Eqs 24 and 30, **Eq
...
Some small corrections are probably required
...
Indeed, in Mills’s model a ‘magnetic energy of pairing’ is computed that
dramatically improves the agreement with data (1, chapter 6), however, the origin of this
correction is not clear to the present author
...
’ And the cliché ignores
the fact that in the first part of this essay it was demonstrated that standard quantum
theory is fundamentally wrong
...
In fact, there exists not a single D/Q computation for helium in which
the only energy consistent with an energy balance, the PEP and the known ionization
energies, that is -39
...
In contrast, in the modified CQM model, described above, the ‘inner
electron’ energy is virtually the same as that given in Table I
...

Isn’t there some experimental data that proves the Pauli Exclusion Principle?
Note first that the entire notion of a ‘proof’ is a misunderstanding in physics
...
It is not possible to prove it
...
Thus, the failure of the Pauli Exclusion Principle to
be consistent with energy conservation, according to any standard paradigm, or with the
predictions of CQM, is reason for doubt
...
g
...
5 eV)
...
g
...
Hence, it is clear that any D/Q or DQM model that
assumes the PEP must also assume ‘boost’
...
There is no ‘proof’ of it
...
There is no experimental support for this belief
...
And we
note that contrary to standard quantum theory, this observation of fact, and its prediction
by CQM theory, does provide consistency with energy conservation in the universe
...
For example, all two-electron entities in a zero spin state are Bosons according
to CQM theory
...
The
objects have no net angular momentum
...
If the magnetic moment of these
bosons aligns with an applied field, as required for a species to produce an electron
paramagnetic resonance (EPR) effect, this means that there is a magnetic moment
...
Thus a contradiction in classical physics, the basis of the CQM theory,
arises for any magnitude magnetic alignment with an applied field for a Boson
...
Hence, there is absolutely no basis for arguing
that the absence of an EPR signal indicates that the two electrons are ‘identical’
...

It is also clear from the most recent studies of the ionization of helium that no
data contrary to CQM exists (2-7)
...
Moreover, neither the
observation that there is no time lag between the ionization of the two electrons in a
‘double ionization’ event or the finding that the total energy required for this process is
about 79 eV is contrary to the predictions of CQM theory
...
Moreover, these models apparently predict that there should be a time lag
between first and second ionization events
...
Only after it occupies its new state can a
second ionization, requiring a higher energy, occur
...
How do SQQM and CQM models of
the energy levels in excited helium compare? Once again CQM provides simple algebraic
formulas that provide close computational matches for every single energy levels of
excited states
...
Once again, standard quantum provides a few energies that match a few
measured values using convoluted, complex mathematics and questionable physics
...
Indeed, to obtain
the correct energy levels for excited helium CQM implicitly accepts the postulate put
forth here that helium in the ground state contains electrons at very different energies
...

The inner electron force balance is the same as that for a one electron helium ion with a

42

small correction due to the screened magnetic interaction with the outer electron
...
5 Bohr radii with an
energy of approximately -54
...
The excited electron,
initially at an energy of approximately -24 eV and a radius of approximately 0
...

Is the existence of an electron in helium at -54 eV and a radii of 0
...
6) presented in an earlier chapter? No
...
567 eV
...
Thus, if the model of excitation is to be forced into consistency with the
current CQM model of the ground state two electron systems, the excitation model of a
later chapter must be modified to explain two simultaneous phenomenon: drop in energy
(nearly 30 eV!) and radius of the inner electron, and the simultaneous promotion of the
outer electron to an excited state (<25 eV in all cases)
...
The values for energy and radii computed in the
CQM model of excitation are virtually identical to those of the inner unexcited electron in
the ground state helium
...
In contrast the two electron excited state and ground state models in
the current version of CQM are not consistent with each other
...

The above paragraph may be better understood if presented in a different manner
...
(In the Mills book, the first excited state has the two electrons with parallel spins
...
That is precisely the one described for
the ground state in this manuscript: two electrons with an attractive magnetic interaction,
that is with anti-parallel spins
...

In a sense, in the Mills text there are two versions of the ground state for helium, one
completed in the text, the one that requires a mysterious ‘application’ of the PEP (1, Ch
...
That treatment is unacceptable for two reasons
...
Second, that treatment of the ground state
requires the two electrons to be at the same place at the same time, leading to the
electrostatic repulsive infinity of energy (singularity) that mars all forms of quantum

43

physics of bound electrons, as discussed above
...
9)
...
Thus, the modification of CQM promoted in this essay is the only means
to save CQM from the energy balance conundrum found in any system required to
‘perform’ according to the PEP
...
Only simple
algebraic force balances are required
...
Angular
momentum is explicitly preserved
...
Only four
constants are required
...

Standard Quantum Model of Excited States- Denizens of the standard physics world
are almost universally surprised to discover that standard physics doesn’t offer a simple
model of excited helium
...
Surely, helium is well solved
...
The newest plead a shortage of supercomputer time
...
(Imagine if gravity or electrostatic interactions were allowed a
term that could be optimized for each two body interaction
...


SUMMARY
Numerous arguments are made in this essay regarding flaws in standard quantum
theory as applied to atoms and ions, and an equal number are made in support of a new
theory (although limited in this essay to the range of bound electrons), Classical Quantum
Mechanics
...
For example, it is demonstrated that if two electrons are in an
identical state/energy level prior to ionization, and that if the electron of the pair not
ionized truly relaxes into lower energy states following ionization, the very process of
ionization would generate energy, yes increase the energy in the universe without any
concomitant mass loss
...

44

The addition of the ‘boost’ concept allows the PEP and an energy balance to be in
harmony
...

First, it requires that the computed energy levels not match any experimentally measured
value
...
5 eV, clearly very different from the first ionization
energy of -24
...
4 eV
...
Not even a ‘talking model’ of
the energy levels of the ‘unexcited’ electron currently exists
...

It is postulated herein that electron energy levels do not relax (not significantly)
following ionization
...
In fact, there is no
experimental evidence of either relaxation or boost
...

The energy balance failures of DQM are generally ignored, or are conflated with
process steps, such as change in screening constant following ionization, which are
irrelevant to computation of an energy balance (44)
...
The nature of the particular process of
change is not relevant to this computation
...

The only ‘category’ of standard quantum modeling for which the PEP does not
require the existence of energy levels that don’t match ionization energies is SQQM
...
Discussions
regarding the application of PEP to SQQM are equivalent to arguing regarding the shape
of red
...
It only provides the total electron system energy
...
It is inconsistent with basic
spectroscopy (e
...
multiple ionization energies for multi-electron atoms), Maxwell’s
equations, Newton’s Laws, the existence of spin, requires renormalization of self-energy,
and fails the self-consistency requirement of valid scientific theories
...
It even requires a new force (‘correlation energy’), a
corresponding set of optimized variable parameters, and fails to account for obviously
existing magnetic interactions between electrons
...
There is no 3-D wave! At best there are waves in 3N (N is
the number of electrons) phase space
...

Mills is consistent with Maxwell’s Equations, Newton’s Laws and spectroscopy
...
Magnetic moments arise from moving charge, as per the Maxwell
equations
...
There

45

is no ‘uncertainty’
...
Specifically , it is shown that the modified
CQM theory predicts very accurately that in two electron systems in the ground state the
two electrons have dramatically different energies
...

Many physicists will proclaim that the PEP has been experimentally validated
...
Do not accept an interpretation of the data
...


46



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Title: Pauli Exclusion Principle
Description: exam questions with complete answer and explanation

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