Abstract
This paper illustrates the application of group theory to a quantum-mechanical three-dimensional quartic anharmonic oscillator with Oh symmetry. It is shown that group theory predicts the degeneracy of the energy levels and facilitates the application of perturbation theory and the Rayleigh–Ritz variational method as well as the interpretation of the results in terms of the symmetry of the solutions. We show how to obtain suitable symmetry-adapted basis sets.
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