Exact Solution of Schrodinger Equation for Three Parameter Exponential-Type Potential

Student: Solomon Ojonugwa Moses (Project, 2025)
Department of Physics
Prince Abubakar Audu University, Anyigba

Abstract

ABSTRACT This study presents an exact analytical solution of the Schrödinger equation for a three-parameter exponential-type potential using the Parametric Nikiforov-Uvarov (PNU) method. The PNU method is an extension of the conventional Nikiforov-Uvarov technique, which simplifies the process of obtaining energy eigenvalues and corresponding wave functions for a wide range of potential models in quantum mechanics. By transforming the Schrödinger equation into a hypergeometric-type differential equation, the PNU method allows for a straightforward derivation of the solutions. The three-parameter exponential-type potential is examined, and the energy eigenvalues are computed for various quantum states. The results reveal a complex dependency of the energy levels on the quantum number, with distinct trends observed across different parameter sets. These findings provide valuable insights into the quantum behavior of systems described by exponential-type potentials. The study demonstrates the efficacy of the PNU method in solving the Schrödinger equation for complex potentials, offering a reliable and efficient approach for obtaining exact solutions in quantum mechanics. The results are expected to have implications for theoretical studies and practical applications involving similar potential models.

Keywords
exact solution schrodinger equation three parameter exponential-type potential
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