CONNECTION BETWEEN Q-DEFORMED ANHARMONIC-OSCILLATORS AND QUASI-EXACTLY SOLUBLE POTENTIALS

It is proved that quasi-exactly soluble potentials (QESPs) correspondi ng 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 defo rmed anharmonic oscillators of SUq(1,1) symmetry, which have been used for the description of vibrational spectra of diatomic molecules. Thi s connection allows for the immediate approximate determination of all levels of the QESPs.