2D Schroedinger eq. vs Bohr's model?

[arivero]

For low values of n, Bohr's model fails to reproduce the value of the square of angular momentum, and the repulsion angles

But Bohr model is basically a planar model... so the question should be, if we solve the hydrogen atom potential in a 2D equation, is it still different? The eigenvalues of angular momentum squared, in generical dimensions, are as L(L+d-2), are they?

 

[Dr. Courtney]

I seem to remember the quantum solutions to the 2-D hydrogen atom having energy levels that depend on (n - 1/2) rather than n.

 

[Dr. Courtney]

Some classic references:

http://academic.reed.edu/physics/fa...scellaneous Essays/2-Dimensional Hydrogen.pdf

https://www.uni-ulm.de/fileadmin/we..._SS2008/Eindimensionales_Wasserstoff_Atom.pdf

http://arxiv.org/pdf/math-ph/0205031v1.pdf

 

[arivero]

depend on (n - 1/2) rather than n.

Hmm I see. Probably related to Biederharn "Sommerfeld' puzzle"

Thanks for the references, going to read them.