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arXiv · 1501.00975

Group theoretical analysis of a quantum-mechanical three-dimensional quartic anharmonic oscillator

Francisco M. Fernández
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Abstract

This paper illustrates the application of group theory to a quantum-mechanical three-dimensional quartic anharmonic oscillator with $O_{h}$ 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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Francisco M. Fernández. 2015-01-05. Group theoretical analysis of a quantum-mechanical three-dimensional quartic anharmonic oscillator. https://doi.org/10.1016/j.aop.2015.02.029

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