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

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 Schrödinger 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.

18 pages, 4 figures, 3 tables

References in corpus (25)

• Exact Solutions of the 2D Dunkl--Klein--Gordon Equation: The Coulomb Potential and the Klein--Gordon Oscillator
• $SU(1,1)$ solution for the Dunkl oscillator in two dimensions and its coherent states
• Dunkl-Klein-Gordon equation in three-dimensions: The Klein-Gordon oscillator and Coulomb Potential
• Algebraic approach for the one-dimensional Dirac-Dunkl oscillator
• Thermal Properties of Relativistic Dunkl Oscillators
• Dunkl-Graphene in constant magnetic field
• Exact solution of two dimensional Dunkl harmonic oscillator in Non-Commutative phase-space
• On the Path Integral Formulation of Wigner-Dunkl Quantum Mechanics
• Relativistic Solutions of Generalized-Dunkl Harmonic and Anharmonic Oscillators
• Landau levels for the $(2+1)$ Dunkl-Klein-Gordon oscillator
• Ideal Bose Gas and Blackbody Radiation in the Dunkl Formalism
• Dunkl-Pauli Equation in the Presence of a Magnetic Field
• The condensation of ideal Bose gas in a gravitational field in the framework of Dunkl-statistic
• Effect of the two-parameter generalized Dunkl derivative on the two-dimensional Schrödinger equation
• The Generalized Fokker-Planck Equation in terms of Dunkl-type Derivatives
• Dunkl-Schrödinger equation with time-dependent harmonic oscillator potential
• The Dunkl-Fokker-Planck Equation in $1+1$ Dimensions
• Superintegrability on the Dunkl oscillator model in three-Dimensional spaces of constant curvature
• Time-Dependent Dunkl-Schrödinger Equation with an Angular-Dependent Potential
• Dunkl-Schrodinger Equation in Higher Dimension
• On the Hydrogen Atom via Wigner-Heisenberg Algebra
• The Condensation of Ideal Dunkl-Bose Gas in Power-Law Traps
• A Path Integral Treatment of Time-dependent Dunkl Quantum Mechanics
• On Dunkl-Bose-Einstein Condensation in Harmonic Traps
• One-dimensional Dunkl Quantum Mechanics: A Path Integral Approach