The usual quantum mechanics based on Schrödinger picture wave functions can be reformulated using a different distribution which behaves in some aspects more like a probability distribution, except that it is negative for some points in phase space.
The original article:
See also:
Wikipedia: Wigner quasiprobability distribution
C. Zachos, D. Fairlie, T. Curtright, Quantum mechanics in phase space: an overview with selected papers, World Sci. 2005.
Giuseppe Dito, Francisco J. Turrubiates, The damped harmonic oscillator in deformation quantization, Physics Letters A352:4–5 (2006) 309–316 doi
B. Belchev, M.A. Walton, On Wigner functions and a damped star product in dissipative phase-space quantum mechanics, Annals of Physics 324 (2009) 670–681
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