Polynomial Solutions of the Schrödinger Equation for the “Deformed” Hyperbolic Potentials by Nikiforov–Uvarov Method

Abstract

In this study, the bound state energy eigenvalues and the corresponding wave functions of the deformed Poschl–Teller and Hyperbolic Kratzer-like potentials have been obtained by the Nikiforov–Uvarov method using the deformed hyperbolic functions (sinhq (x) ≡ ½(ex – qe-x), coshq (x) ≡ ½(ex + qe-x), sechq (x) ≡ 1/coshq (x) and tanhq (x) ≡ sinhq (x)/coshq (x)) that were introduced for the first time by Arai [J. Math. Anal. Appl. 158, 63 (1991)]. It is also observed that, the energy eigenvalues of these new type deformed hyperbolic potentials bring up the criteria for the shape invariance of the potentials according to the deformation parameter q.