For an arbitrary linear combination of quantizations, the kernel of the inverse operator is constructed. An equation for the evolution of the Wigner function for an arbitrary linear quantization is derived and it is shown that only for Weyl quantization this equation does not contain a source of quasi-probability. Stationary solutions for the Wigner function of a harmonic oscillator are constructed, depending on the characteristic function of the quantization rule. In the general case of Hermitian linear quantization these solutions are real but not positive. We found the representation of Weyl quantization in the form of the limit of a sequence of linear Hermitian quantizations, such that for each element of this sequence the stationary solution of the Moyal equation is positive.

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关于任意线性量化的moyal方程的推广

对于量化的任意线性组合，构造逆算子的核。推导了用于任意线性量化的 Wigner 函数的演化方程，并且表明仅对于 Weyl 量化，该方程不包含准概率源。根据量化规则的特征函数，构造谐波振荡器的 Wigner 函数的平稳解。在 Hermitian 线性量化的一般情况下，这些解是实数但不是正数。我们发现外尔量化的表示形式为一系列线性厄米量化序列的极限，因此对于该序列的每个元素，莫亚尔方程的平稳解是正的。