Computer Algebra in Physics: The hidden SO(4) symmetry of the hydrogen atom

• URL: http://arxiv.org/abs/2006.12498v2
• Date: Fri, 29 Jan 2021 23:22:29 GMT
• Title: Computer Algebra in Physics: The hidden SO(4) symmetry of the hydrogen atom
• Authors: Pascal Szriftgiser, Edgardo S. Cheb-Terrab
• Abstract summary: We derive SO(4) symmetry and spectrum using a computer algebra system (CAS) It is an excellent model to test the current status of CAS concerning this kind of quantum-and-tensor-algebra computations.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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