Spectral and Thermal Analysis of the Morse Potential within the Dunkl Formalism: Analytical Approximations and Applications

TL;DR

This paper explores the quantum behavior of particles in the Morse potential using Dunkl calculus, revealing how symmetry deformation affects energy spectra and thermodynamic properties in molecular systems.

Contribution

It introduces a novel application of Dunkl formalism to the Morse potential, providing analytical solutions and thermodynamic analysis for diatomic molecules.

Findings

Dunkl parameters modify vibrational energy levels.

Thermal properties are significantly affected by Dunkl deformation.

Analytical solutions are obtained using Pekeris approximation.

Abstract

In this work, we investigate the quantum dynamics of a particle subject to the Morse potential within the framework of Dunkl quantum mechanics. By employing the Dunkl derivative operator, which introduces reflection symmetry, we construct a deformed Schr\"odinger equation and obtain exact analytical solutions using the Pekeris approximation. The resulting energy spectrum and wavefunctions reveal how Dunkl parameters alter the effective potential and vibrational states. The model is applied to several diatomic molecules, including H$_2$, HCl, and I$_2$, illustrating the impact of symmetry deformation on energy spectra. We also compute thermodynamic functions, including the partition function, free energy, internal energy, entropy, and specific heat. The analysis shows that the Dunkl deformation induces distinct thermal behavior and offers a tunable approach to molecular modeling. These results highlight the potential of the Dunkl formalism as a useful tool for extending conventional quantum models and for exploring symmetry-deformed systems in molecular physics and quantum thermodynamics.