Re: Another student question

[John Mallinckrodt <ajmallinckro@CSUPomona.Edu>]

On Mon, 17 Nov 1997, Jim Riley wrote:

> ...  For the ground state of the
> H atom the Bohr model assumes an angular momentem of hbar.  In the
> Schrodinger solution the angular momentum is given by L square = (l)(l+1)h
> bar and the z component of the angular momentum by Lz=m hbar.  But m must be
> less than or equal to l and l must be less than n.  For the ground state of
> the hydrogen atom n = 1 , l=m=o.  It has no (orbital) angular momentum, so
> Bohr's initial postulate by which he calculated the energy of the various
> levels in the hydrogen atom was wrong.  Why does he get the right answer?
> Luck I guess.  

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."

I'd be surprised if there really wasn't *some* level on which the
mathematics could be understood to be similar enough to require the same
answers.  But I'd still be interested in hearing others speculate on
whether or not the underlying models themselves share similarities which
might be expected to yield this otherwise surprising result.

If it really was just "dumb luck" I think it might have been *very*
fortunate dumb luck, for without the success of the Bohr Model in
explaining the spectrum of hydrogen, it occurs to me to wonder if the
early development of quantum mechanics might have been dealt a significant
setback.

I've already told Martha that I think she should submit this item to the
Q&A section of AJP.  Any AJP editors lurking out there?

John
-----------------------------------------------------------------
 A. John Mallinckrodt      http://www.intranet.csupomona.edu/~ajm
 Professor of Physics    mailto:ajmallinckro@csupomona.edu
 Physics Department       voice:909-869-4054
 Cal Poly Pomona            fax:909-869-5090
 Pomona, CA 91768-4031   office:Building 8, Room 223