一类相空间中的准几率分布函数系

定义了一类相空间中的准几率分布函数系，这个准几率分布函数系直接建立在具有更加广泛意义的量子相空间Schr?dinger方程解的基础之上，其中定义_α=αp-i?q和_α=(1-α)q+i?p.发现了两个有趣的关系.(1)建立的量子相空间Schr?dinger方程的解实际上是对函数φ(λ)exp［i(1-α)qp］做窗口Fourier变换.(2)这个窗口函数g(λ)起着选择窗口形式的作用，而且不同的窗口对应着不同的分布函数.当g(λ)是一个代表Gauss窗的Gauss函数的时候，准几率分布函数就是一个类似于Husimi的分布函数f^HL_α(q,p)；当g(λ)是一个表示椭圆的复函数时，准几率分布函数就是一个椭圆分布函数f^E_α(q,p)；再在g(λ)为复函数的基础上附加α=0，就可得到标准序分布函数f^S(q,p)、反标准序分布函数f^AS(q,p)和Wigner分布函数f^W(q,p)，此时g(λ)表示高度为1/12π?而长度为λ的矩形窗. 关键词： 窗口Fourier变换 相空间 Wigner分布函数

A family quasi-distribution function representation in phase space

A family quasi-distribution function representation is defined in this article. This family quasi-distribution function representation is constructed from the family wave function of the Schrdinger equation in phase space in which the definitions of the operators are _α=αp-i?q and _α=(1-α)q+i?p. Two interesting relationships are found. The first one is that the family wave function of the Schrdinger equation in phase space is a “Window” Fourier transform of the function φ(λ)exp［i(1-α)qp/?］. The second one is that different choices of the window functions result in different distribution functions. When the window function g(λ) is a Gaussian function the distribution function is the Husimi-like distribution function. When the window function g(λ) is a plural function representing an ellipse, the quasi-distribution function is the Ellipse distribution function; and finally when the plural function g(λ) is supplemented with the additional condition α=0, it will result in the standard ordering, anti-standard ordering distribution function and Wigner function. In this case g(λ) is a function depieting a rectangular window with width λ and height 1/12π?.
Keywords： “Window” Fourier transform phase space Wigner function