Symbolic calculations of unitary transformations in quantum dynamics

Abstract The present paper deals with the development of a Mathematica package of programs for handling quantum mechanical equations involving commutators and unitary transformations. One program implements general commutators handling rules. Another evaluates a series of nested commutators representing a general unitary transformations. We apply these new symbolic routines to test-transformations, ranging from simple translations in both spatial and momentum spaces to transformations involving nonlin... Title of program: NCComAlgebra Catalogue Id: ADJL_v1_0 Nature of problem Computer algebra implementation of the definition of a commutator, of commutator handling rules. Symbolic evaluation of unitary transformations for use in quantum dynamical problems. Versions of this program held in the CPC repository in Mendeley Data ADJL_v1_0; NCComAlgebra; 10.1016/S0010-4655(98)00129-5 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018)

摘要 本论文阐述了一款用于处理含对易子（commutator）与幺正变换（unitary transformation）的量子力学方程的Mathematica程序包的开发工作。其中一款程序实现了通用对易子运算规则，另一款程序则用于求解表征一般幺正变换的一系列嵌套对易子序列。我们将这些新型符号化运算工具应用于各类测试变换，涵盖空间与动量空间的简单平移，乃至涉及非线性……
程序名称：NCComAlgebra
目录编号：ADJL_v1_0
问题属性：实现对易子定义与对易子运算规则的计算机代数方案，以及面向量子动力学问题的幺正变换符号化求解。
Mendeley数据的CPC程序库存储版本：ADJL_v1_0; NCComAlgebra; 10.1016/S0010-4655(98)00129-5
本程序源自贝尔法斯特女王大学维护的CPC程序库（1969-2018）