Computer Algebra in Physics: The hidden SO(4) symmetry of the hydrogen atom
| Autor: | Szriftgiser, Pascal, Cheb-Terrab, Edgardo S. |
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| Rok vydání: | 2020 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.cpc.2021.108076 |
| Popis: | Pauli first noticed the hidden SO(4) symmetry for the Hydrogen atom in the early stages of quantum mechanics [1]. Departing from that symmetry, one can recover the spectrum of a spinless hydrogen atom and the degeneracy of its states without explicitly solving Schr\"odinger's equation [2]. In this paper, we derive that SO(4) symmetry and spectrum using a computer algebra system (CAS). While this problem is well known [3, 4], its solution involves several steps of manipulating expressions with tensorial quantum operators, simplifying them by taking into account a combination of commutator rules and Einstein's sum rule for repeated indices. Therefore, it is an excellent model to test the current status of CAS concerning this kind of quantum-and-tensor-algebra computations. Generally speaking, when capable, CAS can significantly help with manipulations that, like non-commutative tensor calculus subject to algebra rules, are tedious, time-consuming and error-prone. The presentation also shows a pattern of computer algebra operations that can be useful for systematically tackling more complicated symbolic problems of this kind. Comment: 28 pages, submitted for publication in Computer Physics Communications |
| Databáze: | arXiv |
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