论文标题
Wigner在量子力学中的功能，其最小长度尺度是由普遍不确定性原理产生的
Wigner functions in quantum mechanics with a minimum length scale arising from generalized uncertainty principle
论文作者
论文摘要
在本文中，在量子力学的情况下，由于使用了广义不确定性原理（GUP），因此在量子力学的情况下概括了Wigner功能的概念。我们介绍了GUP之后的这种理论的相空间公式，并表明Weyl Transform和Wigner函数确实满足了标准量子力学中的某些已知特性。我们利用广义的Wigner函数来计算量子谐波振荡器的哈密顿量的相位平均值满足变形的Heisenberg代数。还表明，在这种理论中，某些量子机械算子的平均值可能限制了指定海森贝格代数变形程度的变形参数的值。呈现的所有结果都是针对纯状态的。结果可以推广到混合状态。
In this paper we generalize the concept of Wigner function in the case of quantum mechanics with a minimum length scale arising due to the application of a generalized uncertainty principle (GUP). We present the phase space formulation of such theories following GUP and show that the Weyl transform and the Wigner function does satisfy some of their known properties in standard quantum mechanics. We utilise the generalized Wigner function to calculate the phase space average of the Hamiltonian of a quantum harmonic oscillator satisfying deformed Heisenberg algebra. It is also shown that averages of certain quantum mechanical operators in such theories may restrict the value of the deformation parameter specifying the degree of deformation of Heisenberg algebra. All the results presented are for pure states. The results can be generalized for mixed states.
