NEW CLASS OF CONDITIONALLY EXACTLY SOLVABLE POTENTIALS IN QUANTUM-MECHANICS

Motivated by an idea of Dutra, we obtain a new class of one-dimensiona l conditionally exactly solvable potentials for which the entire spect ra can be obtained in an algebraic manner provided one of the potentia l parameters is assigned a fixed negative value. It is shown that usin g shape-invariant potentials as input, one may generate different clas ses of such potentials even in more than one dimension. We also illust rate that WKB and supersymmetry inspired WKB methods provide very good approximations for these potentials with the latter doing comparative ly better.