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Re: Another student question



John Mallinckrodt <ajmallinckro@CSUPomona.Edu> wrote:

I think Martha's question about the surprising agreement of the
Schrodinger and Bohr models of the hydrogen atom is a *really* good one.
I've waited to accumulate some evidence for this statement and I think I
now have it: It doesn't seem that anyone around here, myself included, can
give an answer any more compelling than the one that Jim has
provided--"luck."

Right now I'd have to go along with that, too. Perhaps one could put
together a chain of connections between Bohr's assumption and
Schroedinger's model, something like this:

1. Bohr's assumption gives the same result as de Broglie's (?)
assumption that the quantization is due to "fitting" an integral number of
de Broglie wavelengths of the electron around the circumference of a
circular orbit (and thereby preventing destructive interference).

2. de Broglie's assumption is reminiscent of the way we actually
derive the azimuthal part of the psi-function for the hydrogen atom.

3. The maximum value of the azimuthal quantum number (m) for a
particular "orbital" quantum number (l) is just l.

4. The value of l influences which radial functions are possible,
which in turn determines the expectation value of the energy.

But this is such a tortuous chain of logic that it might as well be
"luck".

--
Jon Bell <jtbell@presby.edu> Presbyterian College
Dept. of Physics and Computer Science Clinton, South Carolina USA