QUANTUM-MECHANICS OF NONCENTRAL HARMONIC AND ANHARMONIC POTENTIALS IN 2-DIMENSIONS

With a view to obtaining an exact analytic solution of the Schrodinger wave equation for a variety of potentials we investigate further applications of an already suggested ansatz (Phys. Lett. 142A (1989) 57) for the eigenfunction. The problems related to noncentral harmonic and anharmonic potentials in two-dimensions are investigated. While the difficulties that arise in the study of these potentials are explicitly shown, several new potentials are suggested which admit an exact solution of the wave equation and sometimes at the cost of certain constraints on their parameters. The method is also applied to some other types of potentials; particularly, the cases of singular- and exponential-type central potentials in three-dimensions are discussed through the examples of the potential, V(r) = ar2 + br-2 + cr-6, and the Morse potential. © 1991.