Vibrational molecular and nuclear spectra in terms of quantum algebras

A generalized deformed oscillator giving the same spectrum as the Morse potential is con­ structed through the use of quantum algebraic techniques. The model of n coupled anharmonic oscillators of Iachello and Oss, suitable for the description of vibrational spectra of polyatomic molecules, is subsequently written in terms of such generalized deformed oscilla­tors. In addition to clarifying the relation of the model of Iachello and Oss to other models using coupled oscillators for the description of vibrational molecular spectra, the present formalism allows for the construction of a large class of exactly soluble models with no extra computational effort. As an example, the way of including a coupling of the Darling-Dennison type is shown. Nuclear models giving good descriptions of vibrational spectra are reviewed and the need of modifying the SUq(2) model in order to extend its region of applicability towards the vibrational limit is discussed.

Quasi-Exactly Soluble Potentials and Deformed Oscillators

It is proved that quasi-exactly soluble potentials 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 poten- tials 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 the levels of the same parity lying above the fewest n+1 known levels, as well as of all levels of the opposite parity. Such connections are not possible in the cases of the q-deformed oscillator, the Q-deformed oscillator, and the modified Pöschl-Teller potential with SU(1,1) symmetry.

WKB EQUIVALENT POTENTIALS FOR THE q-DEFORMED HARMONIC AND ANHARMONIC OSCILLATORS

WKB equivalent potentials ( WKB-EP) giving the same WKB spectrum as the q-deformed harmonic oscillator with symmetry SUq(2) are determined. The WKB-EP's of the anharmonic oscillator systems with Uq(2) or SUq(1,1) symmetries are also calculated.