The review of a new probability representation of quantum states is presented, where the states are described by conventional probability distribution functions. The invertible map of the probability distribution onto density operators in the Hilbert space is found using the introduced operators called a quantizer–dequantizer, which specify the invertible map of operators of quantum observables onto functions and a product of the operators onto an associative product (star product) of the functions. Examples of a quantum oscillator and a spin-1/2 particle are considered. The kinetic equations for probabilities, specifying the evolution of the states of a quantum system, which are equivalent to Schrödinger and von Neumann equations, are derived explicitly.

中文翻译：

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具有描述量子系统状态的概率分布的常规量子统计

提出了一种新的量子态概率表示形式的综述，其中量子态由常规概率分布函数描述。希尔伯特空间中密度算子在概率分布上的可逆映射可通过引入的称为量化器-去量化器的算子找到，该算子指定了量子可观算子在函数上的可逆映射，算子在关联产品上的乘积（星号）产品）的功能。考虑量子振荡器和自旋1/2粒子的例子。明确推导了概率动力学方程，该动力学方程指定了量子系统状态的演化，该动力学方程等效于Schrödinger和von Neumann方程。