Abstract
In deformation quantization, static Wigner functions obey functional *-genvalue equation, which is equivalent to time-independent Schrödinger equation in Hilbert space operator formalism of quantum mechanics. This equivalence is proved mostly for Hamiltonian with form Ĥ = (1/2)p̂2 + V(x̂) [D. Fairlie, Proc. Camb. Phil. Soc. 60 (1964) 581]. In this note we generalize this proof to a very general Hamiltonian Ĥ(x̂, p̂) and give examples to support it.
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