Eigen-solutions and thermal properties of multi-parameter exponential potential

Area of Science:

• Quantum Mechanics
• Theoretical Chemistry
• Spectroscopy

Background:

• The modified multi-parameter exponential potential is crucial for understanding molecular interactions.
• Supersymmetric quantum mechanics (SUSY) offers a robust framework for solving quantum mechanical problems.
• Approximations for the centrifugal term are necessary for analytical solutions.

Purpose of the Study:

• To determine approximate eigen solutions for the modified multi-parameter exponential potential.
• To obtain the energy equation and normalized radial wave function.
• To investigate the thermodynamic properties of the potential for diatomic molecules.

Main Methods:

• Utilized supersymmetric quantum mechanics (SUSY) approach.
• Employed an improved Greene-Aldrich approximation for the centrifugal term.
• Calculated thermodynamic properties (mean energy, heat capacity, entropy, free energy) via the partition function.

Main Results:

• Derived analytical expressions for energy eigenvalues and wave functions.
• Demonstrated that the potential simplifies to known potentials (Rosen-Morse, Hellmann, Yukawa, Coulomb).
• Applied the method to diatomic molecules: CrH, TiH, and ScN, obtaining their thermodynamic properties.

Conclusions:

• The SUSY approach with the Greene-Aldrich approximation provides accurate solutions for the modified multi-parameter exponential potential.
• The derived solutions and thermodynamic properties are applicable to real diatomic molecular systems.
• Excellent agreement was found when comparing special cases with existing literature results, validating the method's accuracy.