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Bound state solutions with a linear combination of Yuakawa plus four-parameter diatomic potentials using path integral approach: Thermodynamic properties

Mohamed Améziane Sadoun, Redouane Zamoum, Abdellah Touati

Abstract

In this paper, we investigate the approximate analytical bound states with a linear combination of two diatomic molecule potentials, Yukawa and four parameters potentials, within the framework of the path integral formalism. With the help of an appropriate approximation to evaluate the centrifugal term, the energy spectrum and the normalized wave functions of the bound states are derived from the poles of Green's function and its residues. The partition function and other thermodynamic properties were obtained using the compact form of the energy equation.

Bound state solutions with a linear combination of Yuakawa plus four-parameter diatomic potentials using path integral approach: Thermodynamic properties

Abstract

In this paper, we investigate the approximate analytical bound states with a linear combination of two diatomic molecule potentials, Yukawa and four parameters potentials, within the framework of the path integral formalism. With the help of an appropriate approximation to evaluate the centrifugal term, the energy spectrum and the normalized wave functions of the bound states are derived from the poles of Green's function and its residues. The partition function and other thermodynamic properties were obtained using the compact form of the energy equation.
Paper Structure (12 sections, 58 equations, 5 figures, 2 tables)

This paper contains 12 sections, 58 equations, 5 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Path integral formalism
  3. Evaluation of the radial Green's function
  4. Energy spectrum and wave functions
  5. Thermodynamic properties
  6. Vibrational free energy
  7. Vibrational mean energy
  8. Vibrational heat capacity
  9. Vibrational entropy
  10. Resuls and Discussion
  11. Application to diatomic molecules
  12. Conclusion

Figures (5)

  • Figure 1: Variation of the energy against the screening parameter $\alpha$ for different quantum states: for $n$ at the left panel and for $l$ at the right panel.
  • Figure 2: Variation of the energy according to the values of the deformation parameter $q$ for different quantum states: for $n$ at the left panel and for $l$ at the right panel.
  • Figure 3: Variation of the energy as a function of the dissociation energy $D_e$ in the left panel and as a function of the depth of the potential well $V_0$ in the right panel, and for different quantum state $n$.
  • Figure 4: Partition function as a function of $\beta$, deformation parameter $q$ and quantum number $l$.
  • Figure 5: The variation of the energy spectrum and thermodynamic properties as a function of $q$ and $\beta$ respectively, for some diatomic molecules.