2D Schroedinger eq. vs Bohr's model?

  • Context: Graduate 
  • Thread starter Thread starter arivero
  • Start date Start date
  • Tags Tags
    2d Model
Click For Summary

Discussion Overview

The discussion centers around the comparison between the 2D Schrödinger equation and Bohr's model in the context of the hydrogen atom. Participants explore the implications of solving the hydrogen atom potential in a two-dimensional framework, particularly focusing on angular momentum and energy levels.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant notes that Bohr's model fails to accurately reproduce the square of angular momentum and the repulsion angles for low values of n, suggesting a limitation of the model.
  • Another participant recalls that quantum solutions for the 2D hydrogen atom yield energy levels that depend on (n - 1/2) instead of n, indicating a potential difference in behavior compared to the 3D case.
  • References are provided by a participant to support the discussion, including academic papers that may contain relevant analyses of the 2D hydrogen atom.
  • A later reply connects the observation about energy levels to Biederharn's "Sommerfeld puzzle," hinting at deeper theoretical implications.

Areas of Agreement / Disagreement

Participants express differing views on the implications of the 2D Schrödinger equation compared to Bohr's model, particularly regarding angular momentum and energy levels. The discussion remains unresolved with multiple competing perspectives presented.

Contextual Notes

There are limitations related to the assumptions made in the models discussed, particularly regarding the dimensionality of the systems and the definitions of angular momentum in different contexts. The mathematical steps leading to the conclusions about energy levels are not fully resolved.

arivero
Gold Member
Messages
3,485
Reaction score
188
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?
 
Physics news on Phys.org
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.
 

Similar threads

Undergrad How to turn model of Schrödinger's Equation 2D?
  • · Replies 6 ·
Replies
6
Views
3K
Rutherford model of atom and Bohr model
  • · Replies 1 ·
Replies
1
Views
2K
Graduate The Hydrogen Atom (Schrodinger vs original Bohr theory)
  • · Replies 1 ·
Replies
1
Views
7K
Graduate Bohr Model missing momentum question
  • · Replies 8 ·
Replies
8
Views
3K
Bohr-Sommerfeld model question "Old" Quantum Theory
  • · Replies 8 ·
Replies
8
Views
3K
Graduate Renormalizability conditions for a real scalar field in d dimensions
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Angular momentum and the hydrogenic atom
  • · Replies 5 ·
Replies
5
Views
3K
Why did Bohr's model work for 1 electron systems?
  • · Replies 7 ·
Replies
7
Views
8K
Angular momentum of hydrogen atom with Schrodinger Equation
  • · Replies 8 ·
Replies
8
Views
4K
Schrodinger Quantization VS Bohr Quantization
  • · Replies 1 ·
Replies
1
Views
8K