On the q-deformed exponential-type potentials

In this work, both non-deformed and q-deformed exactly solvable multiparameter exponential-type potentials V^±(r) are obtained; V⁺(r= x) stands for one-dimensional potential and V^-(r) for the radial part of s-states used in the treatment of vibrational properties of diatomic molecules. As a first result, we show that non-deformed potentials arise from non-q-dependent parameters involved in V^±(r) and rather correspond to a class of q-shifted exponential-type potentials obtained from the Arai’s q-deformed hyperbolic functions. As a second result, by using q-dependent parameters in V^±(r) it is possible to obtain true q-deformed exponential-type potentials. As a useful application of these potentials, some examples of q-deformed exponential-type potentials are considered by means of a proper selection of the involved parameters. Our proposal is general and can be viewed as a unified treatment to the study of q-deformed exponential-type potentials with the advantage that it is not necessary to use a specialized method for solving the Schrödinger equation to each specific potential because many of them are obtained as particular cases of V^±(r). Furthermore, new q-deformed potentials used as interesting alternatives in quantum chemical applications can be derived.