I have read enough of Mills' book on CQM to have found the answer to my own questions.
What follows are my observations and an analysis leading to conclusion #2. It won't be easy to follow, but if you've studied quantum mechanics even just a little bit, and if you go and look in Mills' book (following the links I provide), the conclusion in #2 above is inescapable.
On page 24 of the current online version of the Introduction to Mills' book, when discussing the principle quantum, n, for the solution to the Schrödinger equation, Mills states:
Contrary to Mills' statement, the mathematics intrinsic to the solution of the Schrödinger equation in 3-D spherical coordinates for a hydrogen atom requires that n be an integer. This arises because the separation of variables technique used in arriving at the solution employs a product of independent functions, one of those being a radial function. The solution for the radial function is an infinite series involving Laguerre functions. Mathematically speaking, n is just the number of each term in the series. When terms are numbered, integers are used to number them. That's the way we count. Thus, for strictly mathematical reasons, n has to be an integer.
The number, n, is subsequently interpreted to have a physical meaning. This is an underlying "weakness" of all mathematical models; i.e., mathematical terms are interpreted to have a physical meaning. In fact, Mill's spends quite a bit of time articulating the weaknesses of the QM mathematical model (i.e., the Schrödinger equation). Apparently, Mills has a blind spot here, i.e., the heart of Mills' CQM model for a hydrogen atom (or any one-elctron atom) is a mathematical model with its own underlying weaknesses.
On page 26 of the current online version of the Introduction, when discussing the principle quantum, n, for his CQM solution to the classic wave equation, Mills states:
The nonradiative state of atomic hydrogen, which is historically called the "ground state" forms the basis of the boundary condition of CQM to solve the wave equation. The solutions for electron states having principal energy levels corresponding to integers and corresponding to n = 1 reveal the mechanism of the corresponding transitions.
Let me explain.
Mills' solution to the classic wave equation is found on pages 41-50 of Chapter 1 - The One Electron Atom On p. 43 he states:
where rn is an allowed radius. This function defines the charge density on a spherical shell of a fixed radius, not yet determined, and Eq. (1.1) becomes the two-dimensional wave equation plus time with separable time and angular functions. Given time harmonic motion with angular velocity, ωn, and a radial delta function, the relationship between an allowed radius and the electron wavelength is given by
where the integer subscript n here and in Eq. (1.3) is determined during photon absorption as given in the Excited States of the One-Electron Atom (Quantization) section. It is shown in this section that the force balance between the electric fields of the electron and proton plus any resonantly absorbed photons gives the result that rn = nr1 wherein n is an integer in an excited state.
The remaining details to Mills' solution can also be found in Chapter 1. It is more than a little interesting to note that on p. 44 Mills inserts a bolded section that is obviously part of an attempt to mislead the reader regarding possible values of n. That statement reads:
Following the trail on the mysterious fractional values for the principle quantum number, n, on page 136 in Chapter 2 - Excited States of the One-Electron Atom (Quantization), without any explanation, Mills' states:
Chasing down the last lead on the possibility of a fractional value for the principle quantum number, n, we again follow Mills' direction and go to Chapter 5 - Hydrino TheoryÂBlackLight Process. On page 246, Mills states:
That is it! Just a couple statements out of nowhere to the effect that the principle quantum number, n, can take on the fraction values n = 1/2, 1/3, 1/4, Â 1/137. These statements are just plain untrue! These statements in no way overcome the requirement that n is an integer arising from the series solution to the radial function.
The only thing I can think of is I pulled the html coded post in an out of MS Word to spell/grammar check etc. Maybe MS Word scambled some of the html code.
Anyway, sorry about the formating problems.
For those whose eyes glaze over in this mathematical analysis, a bit of history : physicists couldn't quite understand why the negatively charged electron didn't just spiral into the positively charged nucleus(unlike charges attract, like charges repel, as in the coulomb force of a fissioning U235 nucleus). Then came the 2 reasons : the electron travels at the c limit at the Bohr Radius(.5 angstrom)and the perimeter of the orbit is one matter wavelength. Thus it's difficult for delacoert and others to get past the Bohr Radius in their thinking. As to "infinity" : n/0=n why? Simple : division is repetitive subtraction. n/0 = n-0-0-0-...until the world wears flat and hell glaciates..-0-0-0-...=n. You see, n/0=n-0=n because infinity is NO THING, just as zero is NO THING. Only pharisees, the pied piper types...infer that infinity is some THING and their(PT Barnum's)suckers suck that nonsense right up....give them a radish and knife and ask that they carve it up into an infinite salad by slicing zero pieces off... Dr Mills is a true genius and his re-examination of the Rydberg Equation is where this all started; like all great scientists of the past, he took a critical look at accepted theory(something we all should do with "givens"). The proof of hydrinos(24 smaller orbits of the electron)is found in the solar spectrum : UV lines right where his theory predicts them(helium was discovered in much the same way). And if shrinking the hydrogen atom(80% of the universe is hydrogen)down to smaller sizes is a natural solar-burning process then the di-hydrino H2 atom explains the "dark matter" conundrum : stellar-burning "pollution", where is the EPA on that one? Dr Mills' hydrino development work has been fought tooth and nail by big oil and futurists. His hydrino compound patent(electric batteries with 500 times the energy density of your lead acid battery)was denied in federal court on these same specious Bohr Radius grounds with big oil behind the curtains of course. Futurists fight it because : if WATER(the hydrogen therein)has 37 times the heat-density of an equal weight of gasoline then : where does the WASTE HEAT go when everyone in the whole world(7 billion people)is cranking out GIGAWATTS of hydrino-heat? If you think global warming is bad now... Bottom line : the movie CHAIN REACTION.