As a powerful tool in scientific computation, Mathematica offers us algebraic computation, but it does not provide functions to directly calculate commutators in quantum mechanics. Different from present software packets to deal with noncommutative algebra, such as NCAlgebra and NCComAlgebra, one simple method of calculating the commutator in quantum mechanics is put forward and is demonstrated by an example calculating SO(4) dynamical symmetry in 3 dimensions Coulomb potential. This method does not need to develop software packets but rather to directly write program in Mathematica. It is based on the connection between commutator in quantum mechanics and Poisson bracket in classical mechanics to perform calculations. Both the length and the running time of this example are very short, which demonstrates that this method is simple and effective in scientific research. Moreover, this method is used to calculate any commutator in Hamilton system in principle. In the end some deficiencies and applications are discussed.
Weighted Nested Commutators for Scalable Counterdiabatic State Preparation
Instituto de Ciencia de Materiales de Madrid ICMM-CSIC（马德里材料科学研究所）；Departamento de Física Teórica de la Materia Condensada, Universidad Autónoma de Madrid（马德里自治大学凝聚态物理理论系）；Joint Quantum Institute and Joint Center for Quantum Information and Computer Science, NIST/University of Maryland（马里兰大学/美国国家标准与技术研究院联合量子研究所和联合量子信息与计算科学中心）
Explicit error bounds with commutator scaling for time-dependent product and multi-product formulas
The University of Tokyo（东京大学）；RIKEN Center for Quantum Computing (RQC)（理化学研究所量子计算中心）；ZEN University（禅大学）；Hokkaido University（北海道大学）；Osaka University（大阪大学）
QCommute: a tool for symbolic computation of nested commutators in quantum many-body spin-1/2 systems
Skolkovo Institute of Science and Technology（斯科尔科沃科学与技术学院）；Steklov Mathematical Institute of Russian Academy of Sciences（俄罗斯科学院斯捷克洛夫数学研究所）；HSE University（高等经济学院）；Moscow State University, Faculty of Physics（莫斯科大学物理系）
