2D Schroedinger eq. vs Bohr's model?

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Bohr's model struggles to accurately represent the square of angular momentum and repulsion angles for low quantum numbers (n). The discussion suggests that solving the hydrogen atom potential using a 2D Schrödinger equation may yield different results compared to Bohr's planar model. It is noted that the eigenvalues of angular momentum squared in various dimensions follow a specific formula. Quantum solutions for the 2D hydrogen atom reportedly show energy levels that depend on (n - 1/2) instead of n. The conversation highlights the need for further exploration of these concepts through referenced academic materials.
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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.
 

Thread 'Two equivalent statements of time reversal symmetric Hamiltonian'

Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?
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