Generalized Evolution Equation of Wigner Function for an Arbitrary Linear Quantization

Abstract

The arbitrary linear quantization is considered for definition of Wigner function. The evolution equation of this function is derived with the use of inversion of linear quantization kernel. In general case the Moyal equation depends on the characteristic function of quantization. It is shown that only for Weyl quantization this equation does not consist the source of quasi-probability. The stationary solutions of Moyal equation are constructed for an arbitrary linear quantization of a harmonic oscillator. The case of anharmonic oscillator is presented as a practical example of quantum system model in the so-called post-newtonian approximation. This model exhibits the intersection effect between quantization dependences of Hamiltonian and Wigner function.