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.

翻译：Pauli首先注意到在量子力学[1]的早期阶段氢原子隐藏的SO(4)对称性[1]。脱离这一对称性,人们可以在不明确解决Schr\'doninger的等式[2]的情况下,恢复无脊氢原子的频谱及其状态的退化。在本文中,我们推断SO(4)对称性和频谱使用计算机代数系统(CAS)是众所周知的。虽然这个问题是[3,4],但其解决办法涉及与抗量操作员调控表达的几步步骤,通过将通电规则与爱因斯坦对重复指数的总规则结合起来来简化这些表达方式。因此,这是一个极好的模型,可以测试关于这种量子和十倍数值的计算的化学文摘社现状。一般而言,当能力强时,CAS可以极大地帮助操纵,这些操纵与受升数规则约束的非交配制的高压微积微积分,是乏味、耗时和易出错的。演示还展示了计算机代数操作模式模式,能够系统解决更为复杂的象征性的问题。