Analytical Solutions to the <i>D</i> -Dimensional Schrödinger Equation with the Eckart Potential

Abstract

The analytical solutions to the Schrödinger equation with the Eckart potential in arbitrary dimension D is investigated by using the Nikiforov–Uvarov method, and the centrifugal term is treated approximatively with the scheme of Greene and Aldrich. The discrete spectrum is obtained and the wavefunction is expressed in terms of the Jacobi polynomial or the hypergeometric function. Some special cases of the Eckart potential are discussed for D=3, and the resulting energy equation agrees well with that obtained by other methods.