| Topic: |
Science > Physics |
| User: |
"OsherD" |
| Date: |
26 Jan 2005 11:32:16 PM |
| Object: |
Quantum Hydrogen Atom and E = wLF |
From Osher Doctorow
COPYRIGHT NOTICE
Quantum Hydrogen Atom and E = wLF
Copyright By Owner Osher Doctorow Ph.D.
First Published 2005.
From Schiff (1955), for the quantum hydrogen atom:
1) V(r) = -Ze^2/r
2) E_n = -/E_n/
= -muZ^2 e^4/(2h^2 n^2)
where V(r) is potential energy, E_n nth energy eigenvalue, n =
1, 2, ... (n total quantum number), for any finite value of Z
where Z = 1 for hydrogen atom, Z = 2 for singly charged helium
ion, etc. Here we have:
3) (e^2Zmu/(2h^2 n^2)rV(r) = E_n
and setting L = r:
4) E_n = kLV(r) (k constant depending on n, Z, etc.)
We have:
5) F = -e^2/r^2 = (1/(rZ))V(r) = (1/(LZ))V(r)
Now L^2 F is a constant times E_n from (5) and (4). We wanted
E_n = wLF so what happens if w = r = kZL and so on? Notice
that if w = x + iy and y = 0, there's nothing to prevent x = r,
which is especially useful for the hydrogen atom. That is to
say, we choose the only non-angle coordinate along the radius.
Osher Doctorow
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| User: "OsherD" |
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| Title: Re: Quantum Hydrogen Atom and E = wLF |
27 Jan 2005 08:47:18 AM |
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To understand how infinitely many discrete values
occur and what they represent, consider the
difference between one-direction-at-a-time curvilinear
motion used in almost all physics and many-
directions-at-a-time motion which occurs in
expansion-contraction motion in cosmology, bio-
logy, condensation, etc. In the former, there is
either one equation as for example the Schrodinger
equation where one tends to lose sight of direction entirely or
simultaneous equations are unified via a
tensor but with one direction still implicit. In the
latter, I have argued and presented evidence for
several years that simultaneous Riccati Differential equations are used
for different directions, so that
infinitely many countable Riccati equations would
represent countably many directions simultan-
eously, although if symmetry applies one can use
the radius to express one equation unifying all
directions. So the countable eigenvalues which
QM finds represent energy E calculated in different
directions, countably many of them. One can
obtain uncountably many eigenvalues by developing
uncountably many Riccati equations, although
until that is done we have to be satisfied with
countably many. This also applies to the quantum
linear harmonic oscillator thread that I just began.
Osher Doctorow
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