New class of conditionally exactly solvable potentials in quantum mechanics

Motivated by an idea of Dutra (1993), we obtain a new class of one-dimensional conditionally exactly solvable potentials for which the entire spectra can be obtained in an algebraic manner provided one of the potential parameters is assigned a fixed negative value. It is shown that using shape-invariant potentials as input, one may generate different classes of such potentials even in more than one dimension. We also illustrate that WKB and supersymmetry inspired WKB methods provide very good approximations for these potentials with the latter doing comparatively better.