2D Schroedinger eq. vs Bohr's model?

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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?
 
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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 said:
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.
 

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