Application of formula method for bound state problems in Schrödinger equation

Abstract

By using Formula method for bound state problems, we have obtained the approximate analytical solution of the radial Schrödinger equation for Varshni potential model. The energy eigenvalues and the corresponding eigenfunctions are calculated in closed forms. In the process, eigen values for a = b =1, a = −1, b = −2, and b = −1, a = −2 for 2p, 3p, 3d, 4p and 4f states with three different values of the potential range were generated using the Varshni potential. Special cases of the potential are equally studied. Some numerical results have been presented which showed a good agreement with previous results obtained from another method.

Keywords: Varshni potential, Schrödinger equation, Formula method, Bound state