NON RELATIVISTIC BOUND STATE SOLUTION OF THE SCHRODINGER EQUATION WITH SCREENED COULOMB POTENTIAL

Abstract

This study investigates the non-relativistic bound-state solutions of the Schrödinger equation for a particle interacting with the screened Coulomb (Yukawa) potential. The screened Coulomb potential modifies the classical Coulomb interaction by introducing an exponential screening parameter that accounts for environmental effects such as plasma shielding and many-body interactions. Due to the mathematical complexity introduced by the screening term, exact analytical solutions of the Schrödinger equation are difficult to obtain. Therefore, the Nikiforov–Uvarov (NU) method was employed to obtain approximate analytical expressions for the energy eigenvalues and corresponding wavefunctions. The radial Schrödinger equation was transformed into a hypergeometric-type differential equation suitable for the NU formalism. Numerical calculations of the energy eigenvalues were performed for different values of the radial quantum number, angular
momentum quantum number, and screening parameter. The results show that the screening
parameter significantly influences the bound-state energy spectrum, as increasing screening reduces the strength of the effective interaction. The study demonstrates the effectiveness of the Nikiforov–Uvarov method in solving quantum mechanical problems involving screened potentials.