Frishberg Carol, Cohen Leon
Department of Chemistry, Ramapo College of New Jersey, 505 Ramapo Valley Rd, Mahwah, New Jersey, 07430.
Department of Physics, Hunter College of the City University, New York, New York, 10065.
J Comput Chem. 2018 Jun 30;39(17):1068-1075. doi: 10.1002/jcc.24883. Epub 2017 Jul 27.
The phase space formulation of quantum mechanics is equivalent to standard quantum mechanics where averages are calculated by way of phase space integration as in the case of classical statistical mechanics. We derive the quantum hierarchy equations, often called the contracted Schrödinger equation, in the phase space representation of quantum mechanics which involves quasi-distributions of position and momentum. We use the Wigner distribution for the phase space function and the Moyal phase space eigenvalue formulation to derive the hierarchy. We show that the hierarchy equations in the position, momentum, and position-momentum representations are very similar in structure. © 2017 Wiley Periodicals, Inc.
量子力学的相空间表述等同于标准量子力学，其中平均值的计算方式与经典统计力学中一样，是通过相空间积分来进行的。我们在量子力学的相空间表示中推导了量子层级方程，该方程通常被称为收缩薛定谔方程，它涉及位置和动量的准分布。我们使用维格纳分布作为相空间函数，并采用莫亚尔相空间本征值表述来推导该层级方程。我们表明，位置、动量以及位置 - 动量表示中的层级方程在结构上非常相似。© 2017威利期刊公司。
