Phys. Rev. A 79, 024101 (2009) [4 pages]State operator, constants of the motion, and Wigner functions: The two-dimensional isotropic harmonic oscillatorReceived 15 October 2008; revised 23 December 2008; published 4 February 2009 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. © 2009 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevA.79.024101
DOI:
10.1103/PhysRevA.79.024101
PACS:
03.65.Fd, 03.65.Ge, 03.65.Ca
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