Connection Between q-Deformed Anharmonic Oscillators and Quasi-Exactly Soluble Potentials
Dennis Bonatsos, C. Daskaloyannis, Harry A. Mavromatis
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 SUq(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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