State operator, constants of the motion, and Wigner functions: The two-dimensional isotropic harmonic oscillator

Jens Peder Dahl, W. P. Schleich

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Abstract

For a closed quantum system the state operator must be a function of the Hamiltonian. When the state is degenerate, additional constants of the motion enter the play. But although it is the Weyl transform of the state operator, the Wigner function is not necessarily a function of the Weyl transforms of the constants of the motion. We derive conditions for which this is actually the case. The Wigner functions of the energy eigenstates of a two-dimensional isotropic harmonic oscillator serve as an important illustration.
Original languageEnglish
JournalPhysical Review A
Volume79
Issue number2
Pages (from-to)024101
ISSN2469-9926
DOIs
Publication statusPublished - 2009

Bibliographical note

Copyright 2009 American Physical Society

Keywords

  • harmonic oscillators
  • quantum theory
  • eigenvalues and eigenfunctions
  • transforms

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