Algebraic solution of hydrogenic atom

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Discussion Overview

The discussion centers around the algebraic solution of the hydrogen atom, exploring historical methods and references related to quantum mechanics. Participants examine the contributions of various physicists and models leading up to the quantum mechanical treatment of the hydrogen atom.

Discussion Character

  • Historical
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant notes that the hydrogen atom was solved algebraically, referencing methods similar to those used for the harmonic oscillator.
  • Another participant claims that Wolfgang Pauli provided an algebraic solution in 1925, citing a specific book by Kurt Gottfried as a reference.
  • Some participants express skepticism about the existence of a model that achieved quantum mechanical results prior to Schrödinger, emphasizing the Bohr and Bohr-Sommerfeld models as earlier attempts.
  • There is a mention of the Bohr model being ad-hoc and the Bohr-Sommerfeld approach involving analytical mechanics rather than algebraic methods.
  • A later reply suggests that a better account of the algebraic solution can be found in Biedenharn's work on angular momentum, indicating additional resources for further reading.
  • Participants share links to Wikipedia articles that provide further context on the quantum mechanics of the hydrogen atom.

Areas of Agreement / Disagreement

Participants express differing views on the historical development of the algebraic solution to the hydrogen atom, with some asserting that no model achieved quantum results before Schrödinger, while others highlight Pauli's contributions. The discussion remains unresolved regarding the completeness and accuracy of the historical claims.

Contextual Notes

There are limitations in the discussion regarding the clarity of definitions and the specific contributions of various models and physicists. Some assumptions about the nature of the solutions and their historical context are not fully explored.

kowalski
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I've read that the hydrogen atom was solved by means of algebraic methods (similar to creation and annihilation operator for the harmonic oscillator) even before the works of Heisenberg and Schroedinger.

Could you give me some information and/or references about this issue?.

Thanks, Kowalski.
 
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It was actually solved algebraically in 1925 by Wolfgang Pauli. See the pages 235 up to 244 of Kurt Gottfried's book on QM (2nd edition, 2003).
 
Last edited:
There was the Bohr and Bohr-Sommerfeld models. But there was no model that got the QM result prior to Schrödinger, I'm almost certain.
 
bigubau said:
It was actually solved algebraically in 1925 by Wolfgang Pauli. See the pages 235 up to 244 of Kurt Gottfried's book on QM (2nd edition, 2003).

Thank you very much, bigubau!. I will look for this book by Gottfried in the library as soon as possible. Probably he citates the original (Pauli paper) reference. Thanks!.
 
alxm said:
There was the Bohr and Bohr-Sommerfeld models. But there was no model that got the QM result prior to Schrödinger, I'm almost certain.


Bohr was an ad-hoc model (with rules for producing desired known results) ; and Sommerfeld-Ishiwara applied more general ideas (extremizing the Action integral associated to the problem) based on analytical mechanics.(Not algebraic but analytical calculus--calculus of variations).

I think the good answer is bigubau's, about Pauli (algebraic) solution --1925.
 
A better account on the algebraic solution for the H-atom can be found in Biedenharn's "Theory of angular momentum", Vol 1, Chapter 7, dection 4. A detailed bibliography can be found at the end of the section.
 
bigubau said:
A better account on the algebraic solution for the H-atom can be found in Biedenharn's "Theory of angular momentum", Vol 1, Chapter 7, dection 4. A detailed bibliography can be found at the end of the section.

Thank you bigubau. I will look for this reference. K.
 

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