A quantum condition on phase-space distribution functions is introduced based on the probability for the quasimomentum k and quasicoordinate q. This condition is complementary to the conditions on the momentum p and the coordinate x. It is shown that the Wigner distribution does not satisfy this condition, and it is the Rihaczek function that obeys it. An equality is established for sums on the Wigner and the Rihaczek distributions. Linear dependences of phase-space distribution functions are derived based on the zeros of the kq functions.

• Received 28 August 1991

DOI:https://doi.org/10.1103/PhysRevA.45.3540