Schrödinger’s Wave Mechanics

  • Alexander Komech


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.


Geometrical Optic Canonical Quantization Heisenberg Equation Quantum Observable Homogeneous Beam 
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© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

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

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