A scheme is presented by which Clebsch–Gordan coefficients can be determined by matrix diagonalization. The method uses Mathematica, a system for doing mathematics by computer, and shows one way matrix mechanics can be implemented in such a system. The result is a Mathematica package for angular momentum matrix mechanics. It is applied to a one‐electron atom in an external magnetic field to explore the competition between spin–orbit interaction and the separate interaction of the spin and orbital moments with the external field.

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