Book Title: Multidisciplinary Research Nexus: Exploring Intersections of Knowledge
Editor: Prof. Amos R
Chapter: 8
DOI: https://doi.org/10.59646/559/8
Authors: Kaushal Purohit, Devansh Desai, Hiren Jagani, Vikrant Baxi
Abstract
The analytical and numerical solutions of quantum-mechanical wave equations for diverse potential models provide fundamental insight into the structure and dynamics of physical systems across multiple scientific disciplines. This chapter presents a comprehensive analysis of various exactly and approximately solvable potentials within the framework of the Schr¨odinger, Dirac, and Klein–Gordon equa- tions. Emphasis is placed on the application of the Nikiforov–Uvarov (NU) method, the parametric NU (pNU) method, the proper quantization rule (PQR), super- symmetric quantum mechanics (SUSYQM), the formula method, and the series expansion method (SEM). These analytical and computational tools are applied to screened cosine Kratzer, modified Yukawa–Kratzer, Hulthen–screened cosine Kratzer, and linear plus modified Yukawa potentials. The interdisciplinary rele- vance of these models is highlighted through their implications for molecular spec- troscopy, thermodynamics of nanostructures, and quark–antiquark bound states in particle physics. The results demonstrate the versatility of analytical eigensolutions in bridging quantum mechanics, material science, and nanotechnology.