Schrodinger Quantization VS Bohr Quantization

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SUMMARY

The discussion compares the quantization of angular momentum in the Schrödinger theory and the Bohr model. Both theories utilize the principal quantum number, n, to determine energy levels, resulting in identical energy levels for hydrogen. However, the Bohr model is often mischaracterized as one-dimensional; it actually describes circular motion in three dimensions due to angular momentum conservation. In contrast, Schrödinger's theory fully incorporates three-dimensional wave mechanics, providing a more comprehensive understanding of angular momentum quantization.

PREREQUISITES
  • Understanding of quantum mechanics principles
  • Familiarity with the Bohr model of the atom
  • Knowledge of Schrödinger's wave equation
  • Basic concepts of angular momentum in physics
NEXT STEPS
  • Study the quantization rules for angular momentum in the Bohr model
  • Explore the implications of Schrödinger's wave mechanics on angular momentum
  • Investigate the differences in energy level calculations between the two models
  • Examine the historical context and development of quantum mechanics theories
USEFUL FOR

Students of quantum mechanics, physics educators, and anyone interested in the foundational theories of atomic structure and angular momentum quantization.

awat
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Homework Statement



What are the similarities and differences between the quantization of angular momentum in the Schrödinger theory and in the Bohr model?


Homework Equations



?

The Attempt at a Solution



Similarities:
-In both theories, the principal quantum #, n, determines the energy levels.
-Identical energy levels are determined for Hydrogen.

Differences:
-While the Bohr model was limited to one dimension, Schrödinger's thory accounts for all 3


I feel that these answers are very obvious and that I am missing the more fundamental points of angular momentum. Any insight?
 
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Actually the Bohr model is also 3D. it turns out that the motion of the electron is circular (one parameter = 1DOF), due to angular momentum conservation, because of the central potential.

What's the quantization rule for angular momentum in the Bohr model ? What about wave mechanics of Schrödinger ?
 

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