Bound and scattering states for a hyperbolic‐type potential in view of a new developed approximation

A new developed approximation is used to obtain the arbitrary l‐wave bound and scattering state solutions of Schrödinger equation for a particle in a hyperbolic‐type potential. For bound state, the energy eigenvalue equation and unnormalized wave functions in terms of Jacobi polynomials are achieved using the Nikiforov–Uvarov (NU) method. Besides, energy eigenvalues are calculated numerically for some states and compared with those given in the literature to check accuracy of our results. For scattering state, the wave function is found in terms of hypergeometric functions. Furthermore, scattering amplitude and phase shifts are achieved using scattering solutions. Also it is shown that the energy eigenvalue equation obtained from analytic property of scattering amplitude is same with one obtained using NU method. © 2015 Wiley Periodicals, Inc.