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Connection Between q-Deformed Anharmonic Oscillators and Quasi-Exactly Soluble Potentials

Dennis Bonatsos·C. Daskaloyannis·Harry A. Mavromatis
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Abstract

It is proved that quasi-exactly soluble potentials (QESPs) corresponding to an oscillator with harmonic, quartic and sextic terms, for which the $n+1$ lowest levels of a given parity can be determined exactly, may be approximated by WKB equivalent potentials corresponding to deformed anharmonic oscillators of SU$_q$(1,1) symmetry, which have been used for the description of vibrational spectra of diatomic molecules. This connection allows for the immediate approximate determination of all levels of the QESPs.

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Dennis Bonatsos, C. Daskaloyannis, Harry A. Mavromatis. 1995-10-21. Connection Between q-Deformed Anharmonic Oscillators and Quasi-Exactly Soluble Potentials. https://doi.org/10.1016/0375-9601(95)00036-3

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