Molecular Physics

Analytical solutions of Klein–Gordon equation and non-relativistic molecular systems

C. A. Onate, B. B. Deji-Jinadu, O. O. Ajani

Published Apr 17, 2025• 1 citation

Abstract

This study examined the relativistic Klein–Gordon equation and highlighted the characteristics of positive and negative energies. Positive energies correspond to real particles, as they exhibit stable motion forward in time, while negative energies correspond to non-real systems due to antiparticles, highlighting the understanding of particles in relativistic quantum theory. The system’s stability is more pronounced at small screening parameters as the creation of particles (indicated by negative energies) also enlarged. The study further explores the contributions of component potentials in an interacting potential, with a focus on the Pöschl–Teller and symmetric trigonometric Rosen–Morse potentials. The duality of positive and negative energy solutions exemplifies the symmetry between matter and antimatter. The solution of the Schrödinger equation with the same potential is also studied and applied to diatomic models, specifically Cl2, Br2, I2, K2, N2 and F2, comparing analytic results with tested data for various quantum states. The analytic results demonstrate excellent agreement with experimental results, with deviations attributed to experimental methods or theoretical model limitations. The study underscores the reliability of the proposed analytic methods for predicting molecular properties.

DOI: 10.1080/00268976.2025.2491735

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