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 language | English |
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Journal | Physical Review A |
Volume | 79 |
Issue number | 2 |
Pages (from-to) | 024101 |
ISSN | 2469-9926 |
DOIs | |
Publication status | Published - 2009 |
Bibliographical note
Copyright 2009 American Physical SocietyKeywords
- harmonic oscillators
- quantum theory
- eigenvalues and eigenfunctions
- transforms