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Algebraic solution of hydrogenic atom

  1. Dec 19, 2009 #1
    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.
  2. jcsd
  3. Dec 20, 2009 #2


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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: Dec 20, 2009
  4. Dec 20, 2009 #3


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    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.
  5. Dec 21, 2009 #4
    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!!.
  6. Dec 21, 2009 #5

    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.
  7. Jan 1, 2010 #6


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    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.
  8. Jan 1, 2010 #7


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  9. Jan 3, 2010 #8
    Thank you bigubau. I will look for this reference. K.
  10. Jan 3, 2010 #9
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