Cohen Leon
Department of Physics, Hunter College of the City University, New York, New York, 10065.
J Comput Chem. 2018 Jun 30;39(17):1059-1067. doi: 10.1002/jcc.24884. Epub 2017 Jul 27.
We formulate the standard quantum mechanical eigenvalue problem in quantum phase space. The equation obtained involves the c-function that corresponds to the quantum operator. We use the Wigner distribution for the phase space function. We argue that the phase space eigenvalue equation obtained has, in addition to the proper solutions, improper solutions. That is, solutions for which no wave function exists which could generate the distribution. We discuss the conditions for ascertaining whether a position momentum function is a proper phase space distribution. We call these conditions psi-representability conditions, and show that if these conditions are imposed, one extracts the correct phase space eigenfunctions. We also derive the phase space eigenvalue equation for arbitrary phase space distributions functions. © 2017 Wiley Periodicals, Inc.
我们在量子相空间中构建标准量子力学本征值问题。所得到的方程涉及与量子算符对应的c函数。我们将相空间函数用维格纳分布表示。我们认为所得到的相空间本征值方程除了有恰当解外，还有非恰当解。也就是说，不存在能产生该分布的波函数的解。我们讨论确定一个位置动量函数是否为恰当相空间分布的条件。我们将这些条件称为ψ可表示性条件，并表明如果施加这些条件，就能提取出正确的相空间本征函数。我们还推导了任意相空间分布函数的相空间本征值方程。© 2017威利期刊公司
