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The Eigenvalue Problem

  • Alexander Komech

Abstract

The eigenvalue problem for the Hydrogen atom was solved by Schrödinger in 1926.

The solution relies on the separation of variables which is possible due to the spherical symmetry of the Schrödinger equation. The angular functions are chosen to be the spherical functions which are the eigenfunctions of the spherical Laplacian. The spherical functions are constructed by an analysis of the Lie algebra of the rotation group \(\operatorname{SO}(3)\). The radial functions are obtained solving the radial differential equation applying the Sommerfeld method of factorization.

Bibliography

  1. 145.
    R. Newton, Quantum Physics (Springer, New York, 2002) Google Scholar
  2. 164.
    M.A. Shubin, Pseudodifferential Operators and Spectral Theory (Springer, Berlin, 2001) Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Alexander Komech
    • 1
  1. 1.Faculty of MathematicsUniversity of ViennaViennaAustria

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