Numerical solution of Schrödinger equation with screened Kratzer Eckart potential via finite difference method

Abstract

The numerical solution to the time-independent Schrödinger equation (TISE) for hydrogen-related diatomic molecules was obtained using the finite difference method (FDM) for the Screened-Kratzer-Eckart Potential (SKEP) system. With the SKEP, the study explores the quantum behaviour of molecular systems by discretising the TISE and solving the resulting eigenvalue problem. MATLAB was employed to implement the numerical scheme, generating the energy eigenvalues and corresponding  eigenfunctions. The results obtained demonstrate consistency with theoretical expectations and existing analytical models, validating the effectiveness of the finite difference approach. This study contributes to the understanding of molecular quantum systems and offers a computational framework applicable to a wide range of quantum mechanical problems involving complex potentials.