The Arbitrary l-state Solutions of the Hellmann Potential by Feynman Path Integral Approach

Abstract

In this study, we used the Path integral method to obtain the bound state solutions of the Hellmann potential. Firstly we analytically derived the radial kernel expression of the Hellmann potential using the approximation of the centrifugal term and space-time transformations. Then we calculated the exact energy spectrum and the normalized eigenfunction from the poles of the Green function and their residues. We expressed normalized wave functions in terms of Jacobi polynoms and Hypergeometric functions.