2002/04/15 by Hongtao Zhang, Hong-Tao Zhang, Zhang, Hong-Tao
Computer Science · Physics and Astronomy · #Computational Physics and Python Applications #Distributed and Parallel Computing Systems #FOS: Physical sciences #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/0204081
8 pages, Latex, no figures
arxiv created 2002/04/15 · openalex publication_date 2002/04/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.