In this worksheet, we derive the SO(4) symmetry of the hydrogen atom and its energy spectrum, without explicitly solving Schrodinger’s equation, using the Maple Physics package. While this problem is well known [4], [5], its solution involves several steps manipulating expressions with tensorial quantum operators, including 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 Computer Algebra Systems (CAS) concerning this kind of quantum-and-tensor-algebra computations and to showcase the CAS technique. The presentation also shows two alternative patterns of steps that can be used for systematically tackling more complicated symbolic problems of this kind.