Approximate solutions and thermodynamic properties of a potential model

Authors

  • C. A. Onate
  • B. B. Deji-Jinadu Bowen University
  • O. O. Ajani

DOI:

https://doi.org/10.31349/RevMexFis.72.011703

Keywords:

Bound State, Therma property, Enthalpy, Gibbs free energy, Entropy

Abstract

The solution of the radial Schrödinger equation for a Pὃschl-Teller type of potential with two main parameters is obtained via the supersymmetric approach. The energy equation and its corresponding wave function are obtained explicitly. The energy equation obtained was used to calculate the partition function via the Poisson summation formula. The calculated partition was used to studied the enthalpy, Gibbs free energy and entropy of the system. The result obtained showed that the two parameters have the same effect on the energy of the system but different effects on the thermodynamic properties. It was also shown that the rise in temperature of the system only increases enthalpy but decreases partition function, Gibbs free energy an entropy.

References

S. A. Moses, J.P. Covey, M.T. Miecnikowski, B. Yan, B. Gadway, J. Ye and D.S. Jin. Creation of a low-entropy quantum gas of polar molecules in an optical lattice. Science 350 (2015) 659-662. https://doi.org/10.1126/science.aac6400

N.P. Stadie, M. Murialdo, C.C. Ahn and B. Fultz. Anomalous isosteric enthalpy of adsorption of methane on zeolitetemplated carbon supporting information. J. Am. Chem. Soc. 135 (2013) 990-993. https://doi.org/10.1021/ja307076t

D.E. Otten, P.R. Shaffer, P.L. Geissler and R.J. Saykally. Elucidating the mechanism of selective ion adsorption to the liquid water surface. Proc. Natl. Acad. Sci. USA 109 (2012) 701-705. https://doi.org/10.1073/pnas.1209307109

T. Zhang, G.S. Ellis, S.C. Ruppel, K. Milliken and R. Yang. Effect of organic-matter type and thermal maturity on methane adsorption in shale-gas systems. Org. Geochem 47 (2012) 120-131 https://doi.org/10.1016/j.orggeochem.2012.03.012

G. Feng, S. Yu, T. Wang and Z. Zhang. Discussion on the weak equivalence principle for a Schwarzschild gravitational field based on the light-clock model. Ann. Phys. 473 (2025) 169903. https://doi.org/10.1016/j.aop.2024.169903

N.M. Yunus, M.I.A. Mutalib, Z. Man, M.A. Bustam and T. Murugesan. Solubility of CO2 in pyridinium based ionic liquids. Chem. Eng. J. 189 (2012) 94-100. https://doi.org/10.1016/j.cej.2012.02.033

I. Yahiatne, S. Hennig and T. Huser. Optical fluctuation microscopy based on calculating local entropy values. Chem. Phys. Lett. 587 (2013) 1-6. https://doi.org/10.1016/j.cplett.2013.09.039

C.A. Onate and J.O. Ojonubah. Relativistic and nonrelativistic solutions of the generalized Poschl-Teller and hyperbolical potentials with some thermodynamic properties. Int. J. Mod. Phys. E 24 (2015) 1550020. https://doi.org/10.1142/S0218301315500202

M. S¸ime¸k and Z. Yalc¸in. Generalized Poschl-teller potential. J. Math. Chem. 16 (1994) 211-215 https://doi.org/10.1007/BF01169207

U. C. da Silva, C. F.S. Pereira and A. A. Lima. Renormalization group and spectra of the generalized Poschl-Teller potential. Ann. Phys. 460 (2024) 169549. https://doi.org/10.1016/j.aop.2023.169549

Y. You, F-L. Lu, D-S. Sun, C-Y. Chen and S-H. Dong. Solutions of the Second Poschl-Teller Potential Solved by an Improved Scheme to the Centrifugal Term. FewBody Syst. 54 (2013) 2125-2132. https://doi.org/10.1007/s00601-013-0725-y

C.A. Onate. Bound state solutions of the Schrodinger equation with second Poschl-Teller like potential model and the vibrational partition function, mean energy and mean free energy. Chin. J. Phys. 54 (2016) 165-174. https://doi.org/10.1016/j.cjph.2016.04.001

P. Sahoo and U. Laha. Phase shift and cross section analysis of nucleon-nucleon and nucleon-nucleus scattering using second Poschl-Teller potential. Can. J. Phys. 101 (2023) 441-52. https://doi.org/10.1139/cjp-2022-0317

M. Miranda, S-H. Sun, S-H. Dong. The solution of the second Poschl- Teller like potential by Nikiforov-Uvarov method. Int. J. Mod. Phys. E 19 (2010) 123-129. https://doi.org/10.1142/S0218301310014704

W-C. Qiang and S-H. Dong. Analytical approximations to the l-wave solutions of the Klein-Gordon equation for a second Poschl-Teller like potential. Phys Lett A 372 (2008) 4789. https://doi.org/10.1016/j.physleta.2008.05.020

J.M. Martinez-Espinosa, R.E. Balderas-Navarro and S-H. Dong. On the solutions of the Schrodinger equation with 2nd Poschl-Teller potentials. Results in Phys. 58 (2024) 107455. https://doi.org/10.1016/j.rinp.2024.107455

R. Horchani, H. Jelassi, A.N. Ikot, U.S. Okorie. Rotation vibration spectrum of potassium molecules via the improved generalized Poschl-Teller oscillator. Int. J. Quant. Chem. 121 (2021) https://doi.org/10.1002/qua.26558

H. Yanar, A. Tas¸, M. Salti and O. Aydogdu. Ro-vibrational energies of CO molecule via improved generalized Poschl-Teller potential and Pekeris-type approximation. Eur. Phys. J. Plus 135 (2020) 292. https://doi.org/10.1140/epjp/s13360-020-00297-9

C-S. Jia, L-H. Zhang and X-L. Peng. Improved Poschl-Teller potential energy model for diatomic molecules. Int. J. Quant. Chem. 117 (2017) e25383 https://doi.org/10.1002/qua.25383

P. Senn. The modified Poschl-Teller Oscillator. J. Chem. Educ. 63 (1986) 75. https://doi.org/10.1021/ed063p75

S. Dong, Q. Fang, B.J. Falaye, G-H. Sun, C. Yañez-Marquez and S-H. Dong. Exact solutions to solitonic profile mass Schrodinger problem with a modified Poschl-Teller potential. Mod. Phys. Lett. A 31 (2016) 1650017. https://doi.org/10.1142/S0217732316500176

A. Suparmi, O.R. Pamungkas and C. Cari. Analytical solution of the proca equation for the modified posch teller potential. J. Phys. Conf. Ser. 1153 (2019) 012102. https://doi.org/10.1088/1742-6596/1153/1/012102

C.A. Onate, I.B. Okon, U.E. Vincent, E.S. Eyube and E. Omugbe. Pure-vibrational spectrum of diatomic molecules using an improved Poschl-Teller potential. Chem. Phys. 566 (2023) 111770. https://doi.org/10.1016/j.chemphys.2022.111770

B.J. Falaye. Energy spectrum for trigonometric Poschl-Teller potential. Can. J. Phys. 90 (2012) 1259-65. https://doi.org/10.1139/p2012-103

C. Edet, P. Amadi, U. Okorie, A. Tas, A.N. Ikot and G. Rampho. Solutions of Schrodinger equation and thermal properties of generalized trigonometric Poschl-Teller potential. Rev. Mex. Fis. 66 (2020) 824-839. https://doi.org/10.31349/RevMexFis.66.824

S.M. Ikhdair and B.J. Falaye. Approximate analytical solutions to relativistic and nonrelativistic Poschl-Teller potential with its thermodynamic properties. Chem. Phys. 421 (2013) 84-95. https://doi.org/10.1016/j.chemphys.2013.05.021

D. Agboola. Solutions to the modified Poschl-Teller potential in D-dimensions. Chin. Phys. Lett. 27 (2010) 040301. https://doi.org/10.1088/0256-307X/27/4/040301

G. Arora, A. Singh, A.V. Bandhu. A neural network approach for solution of the Schrodinger equation for a particle in the Poschl-Teller potential. Can. J. Phys. 99 (2021) 728. https://doi.org/10.1139/cjp-2021-0006

C. Tezcan, R. Sever, A General Approach for the exact Solution of the Schrodinger equation, Int. J. Theor. Phys. 48 (2009) 337. https://doi.org/10.1007/s10773-008-9806-y

F. Cooper, A. Khare and U. Sukhatme. Supersymmetry and quantum mechanics. Phys. Rep. 251 (1995) 267. https://doi.org/10.1016/0370-1573(94)00080-M

E. Witten. Dynamical breaking of supersymmetry. Nucl. Phys. B 185 (1981) 513. https://doi.org/10.1016/0550-3213(81)90006-7

G.F. Wei and S-H. Dong. Pseudospin symmetry in the relativistic Manning-Rosen potential including a Pekeristype approximation to the pseudo-centrifugal term. Phys. Lett. B 686 (2010) 288. https://doi.org/10.1016/j.physletb.2010.02.070

C.A. Onate and M.C. Onyeaju. Fisher information of a vector potential for time-dependent Feinberg-Horodecki equation. Int. J. Quantum Chem. 2020 (2020) e26543. https://doi.org/10.1002/qua.26543

F. Cooper and B. Freeman. Aspects of supersymmetric quantum mechanics. Ann. Phys. 146 (1983) 262. https://doi.org/10.1016/0003-4916(83)90034-9

C.C. Jia, T. Chen, S. He. Bound state solutions of the Klein Gordon equation with the improved expression of the Manning Rosen potential energy model. Phys. Lett. A 377 (2013) 682-686. https://doi.org/10.1016/j.physleta.2013.01.016

Y. Wu, Y. Jin, Y. Liu, and G. Lyu. (2025). Quantum teleportation of incomplete multi-quantum systems. Physica Scripta, 100(2) (2025) 25253. https://doi.org/10.1088/1402-4896/adab68

C. A. Onate, O. Adedewe, O. Ikubanni, and D. B. Olanrewaju. Spectral and thermodynamic properties of a particle in multiparameter exponential-type radial potential. Fiz. Nizk. Temp. 50 (2024) 1301-1312. https://doi.org/10.1063/10.0034371

H. Hassanabadi, E. Maghsoodi, S. Zarrinkamar. Relativistic symmetries of Dirac equation and the Tietz potential. Eur. Phys. J. Plus 127 (2012) 1-14. https://doi.org/10.1140/epjp/i2012-12001-7

H. Hassanabadi, E. Maghsoodi, S. Zarrinkamar and H. Rahimov. An approximate solution of the Dirac equation for hyperbolic scalar and vector potentials and a Coulomb tensor interaction by SUSYQM. Mod. Phys. Lett. 26 (2011) 2703-2718. https://doi.org/10.1142/S0217732311037091

E. Maghsoodi, H. Hassanabadi and O. Aydogu, Dirac particles in the presence of the Yukawa potential plus tensor interaction in SUSYQM framework. Phys. Scr. 86 (2012) 015005. https://doi.org/10.1088/0031-8949/86/01/015005

E. Maghsoodi, H. Hassanabadi and S. Zarrinkamar. Spectrum of Dirac equation under Deng-Fan scalar and vector potentials. Few-Body Syst. 53 (2012) 525-538. https://doi.org/10.1007/s00601-012-0452-9

G-H. Liu, Q-C. Ding, C-W. Wang, C-S. Jia. Unified non-fitting explicit formulation of thermodynamic properties for five compounds, J. Mol. Struct. 1294 (2023), 136543. https://doi.org/10.1016/j.molstruc.2023.136543

C-S. Jia, J. Li, Y-S. Liu, X-L. Peng, X. Jia, L-H. Zhang, R. Jiang, X-P. Li, J-Y. Liu, Y-L. Zhao. Predictions of thermodynamic properties for hydrogen sulfide, J. Mol. Liq, 315 (2020) 113751. https://doi.org/10.1016/j.molliq.2020.113751

R. Khordad, A. Ghanbari. Theoretical prediction of thermodynamic functions of TiC: Morse ring-shaped potential. Journal of Low Temp. Phys. 199 (2020) 1198-1210. https://doi.org/10.1007/s10909-020-02368-8

R. Jiang, C-S Jia, Y-Q. Wang, X-L. Peng, L-H. Zhang. Prediction of Gibbs free energy for the gases Cl2, Br2, and HCl, Chem. Phys. Lett. 726 (2019) 83. https://doi.org/10.1016/j.cplett.2019.04.040

R. Khordad, A. Ghanbari. Analytical calculations of thermodynamic functions of lithium dimer using modified Tietz and Badawi-Bessis-Bessis potentials. Comput. Theor. Chem. 1155 (2019) 1-8. https://doi.org/10.1016/j.comptc.2019.03.001

X. Tian, R. Xun, T. Chang, and J. Yu. (2025). Distribution function of thermal ripples in h-BN, graphene and MoS2. Phys. Lett. A, 550 (2025) 130597. https://doi.org/10.1016/j.physleta.2025.130597

M.L. Strekalov. An accurate closed-form expression for the partition function of Morse oscillators Chem. Phys. Lett. 439 (2007)

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Published

2026-01-01

How to Cite

[1]
C. Onate, B. Deji-jinadu, and O. Ajani, “Approximate solutions and thermodynamic properties of a potential model”, Rev. Mex. Fís., vol. 72, no. 1 Jan-Feb, pp. 011703 1–, Jan. 2026.

Issue

Vol. 72 No. 1 Jan-Feb (2026): Revista Mexicana de Física

Section

17 Thermodynamics and Statistical Physics

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Copyright (c) 2026 C. A. Onate, B. B. Deji-Jinadu, O. O. Ajani

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