Bound states of a more general exponential screened Coulomb potential

TL;DR

This paper develops an analytical approximation method to solve the Schrödinger equation for a generalized exponential screened Coulomb potential, providing explicit bound state energies and wave functions.

Contribution

It introduces a new approximation scheme for solving the Schrödinger equation with a more general exponential screened Coulomb potential, extending previous methods.

Findings

Derived analytical expressions for bound state energies of 1s, 2s, and 3s states.

Obtained the ground state wave function analytically up to second perturbation order.

Demonstrated the effectiveness of the approximation scheme for complex potentials.

Abstract

An alternative approximation scheme has been used in solving the Schrodinger equation to the more general case of exponential screened Coulomb potential, V(r)=-(a/r)\[1+(1+br)e^{-2br}]. The bound state energies of the 1s, $2s, and 3s-states, together with the ground state wave function are obtained analytically upto the second perturbation term.