Analytical Arbitrary-Wave Solutions of the Deformed Hyperbolic Eckart Potential by the Nikiforov–Uvarov Method

The arbitrary ?-wave solutions to the Schr?dinger equation for the deformed hyperbolic Eckart potential is investigated analytically by using the Nikiforov–Uvarov method. The centrifugal term is treated with the improved Greene and Aldrich approximation scheme. The wave functions are expressed in terms of the Jacobi polynomial or the hypergeometric function. The discrete spectrum is obtained and it is shown that the deformed hyperbolic Eckart potential is a shape-invariant potential and the bound state energy is independent of the deformation parameter q.