Schrödinger’s Wave Mechanics

  • Alexander Komech

Abstract

In 1926, Schrödinger proposed an alternative wave theory of quantization by developing de Broglie’s wave particle duality. The Schrödinger theory also regards the Hamiltonian as an operator in a Hilbert space, and the stationary energies, as the corresponding eigenvalues.

The Schrödinger wave equation alone cannot be justified experimentally. One should complete the equation with the corresponding quantum observables: energy, momentum, angular momentum, charge and current, etc. A fundamental requirement for the introduction of the quantum observables is their agreement with the corresponding classical observables; this follows from the ‘quasiclassical asymptotics’.

Schrödinger showed that his theory is equivalent to the Heisenberg’s matrix theory. Moreover, both theories turn into the classical one as ħ→0: Heisenberg’s theory implies this correspondence directly, while for the Schrödinger theory, this follows from the quasiclassical asymptotics.

Keywords

Geometrical Optic Canonical Quantization Heisenberg Equation Quantum Observable Homogeneous Beam 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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