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

C A Onate1, I B Okon2, M C Onyeaju3

  • 1Department of Physical Sciences, Reedemer's University, Ede, Nigeria.

Heliyon
|September 13, 2022
PubMed
Summary

We solved the modified multi-parameter exponential potential using supersymmetric quantum mechanics (SUSY) and an approximation for the centrifugal term. This approach yielded energy solutions and thermodynamic properties for diatomic molecules like CrH, TiH, and ScN.

Keywords:
Eigen-solutionsPotential modelSchrödinger equationSupersymmetric quantum mechanics approachThermodynamic properties

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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.