Exactly solvable schrödinger equation for a class of multiparameter exponential-type potentials

The solution to a spectral problem involving the Schrödinger equation for a particular class of multiparameter exponential-type potentials is presented. The proposal is based on the canonical transformation method applied to a general second-order differential equation, multiplied by a function g(x), to convert it into a Schrödinger-like equation. The treatment of multiparameter exponential-type potentials comes from the application of the transformed results to the hypergeometric equation under the assumption of a specific g(x). Besides presenting the explicit solutions and their spectral values, it is shown that the problem considered in this article unifies and generalizes several former studies. That is, the proposed exactly solvable multiparameter exponential-type potential can be straightforwardly applied to particular exponential potentials depending on the choice of the involved parameters as exemplified for the Hulthén potential and their isospectral partner. Moreover, depending on the function g(x), the proposal can be extended to find different exactly solvable potentials as well as to generate new potentials that could be useful in quantum chemical calculations.