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Heisenberg’s Matrix Mechanics

  • Alexander Komech

Abstract

The quantum selection rule and its generalizations are capable of predicting energies of the stationary orbits; however they should be obtained in a more general framework of a universal theory, which could provide the intensities of spectral lines, scattering cross sections, etc.

Such a dynamical theory has been discovered first by Heisenberg in 1925 by developing Bohr’s correspondence principle. The Heisenberg ‘matrix mechanics’ serves as a tool for extending the quantum selection rule ( 1.55) to arbitrary quantum systems, independently of the periodicity of trajectories of the corresponding classical models. The stationary energies appear to be the eigenvalues of the matrix Hamiltonian.

All equations and predictions of the Heisenberg theory turn into the classical one as ħ→0; this agrees with the Bohr Correspondence Principle.

Heisenberg’s theory, as was developed immediately by Born, Jordan, Pauli and others, is capable of producing the Hydrogen spectra, the selection rules and intensities of spectral lines, the quantization of the Maxwell field, etc. Up to now, Heisenberg’s theory serves as the ground for the quantum electrodynamics and for modern quantum field theory.

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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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