ENERGY SPECTRUM AND SOME USEFUL EXPECTATION VALUES OF THE TIETZ-HULTHÉN POTENTIAL
Keywords:
Energy spectrum, SUSYQM, Tietz-Hulthén potential, Hellmann-Feynman theorem, expectation values
Abstract
In this paper, concept of supersymmetric quantum mechanics has been employed to derive expression for bound state energy eigenvalues of the Tietz-Hulthén potential, the corresponding equation for normalized radial eigenfunctions were deduced by ansatz solution technique. In dealing with the centrifugal term of the effective potential of the Schrödinger equation, a Pekeris-like approximation recipe is considered. By means of the expression for bound state energy eigenvalues and radial eigenfunctions, equations for expectation values of inverse separation-squared and kinetic energy of the Tietz-Hulthén potential were obtained from the Hellmann-Feynman theorem. Numerical values of bound state energy eigenvalues and expectation values of inverse separation-squared and kinetic energy the Tietz-Hulthén potential were computed at arbitrary principal and angular momentum quantum numbers. Results obtained for computed energy eigenvalues of Tietz-Hulthén potential corresponding to Z = 0 and V0 = 0 are in excellent agreement with available literature data for Tietz and Hulthén potentials respectively. Studies have also revealed that increase in parameter Z results in monotonic increase in the mean kinetic energy of the system. The results obtained in this work may find suitable applications in areas of physics such as: atomic physics, chemical physics, nuclear physics and solid state physics
References
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Xu, Y., He, S. & Jia, C.-S. (2010). Approximate analytical solutions of the Klein–Gordon equation with the Pöschl–Teller potential including the centrifugal term. Phys. Scr., 81, 045001. https://doi.org/10.1088/0031-8949/81/04/045001
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Chen, Z.-Y., Li, M. & Jia, C.-S. (2009). Approximate analytical solutions of the Schrödinger equation with the Manning–Rosen potential model. Mod. Phys. Lett. A, 24, 1863–1874 https://doi.org/10.1142/S0217732309030345
Dong, S.-H. & Cruz-Irisson, M. (2011). Energy spectrum for a modified Rosen-Morse potential solved by proper quantization rule and its thermodynamic properties. J. Math. Chem., 50, 881–892 https://doi.org/10.1007/s10910-011-9931-3
Eshghi, M., Sever, R. & Ikhdair, S. M. (2019). Thermal and optical properties of two molecular potentials. Eur. Phys. J, Plus, 134, 155 https://doi.org/10.1140/epjp/i2019-12634-x
Eyube, E.S., Jabil, Y.Y. & Umar, W. (2019a). Bound state solutions of Non-relativistic Schrödinger equation with Hellmann potential within the frameworks of generalized Pekeris approximation of the centrifugal term potential. J. NAMP., 52, 215
Eyube, E.S., Yerima, J.B. & Ahmed, A.D. (2021). J – state solutions and thermodynamic properties of the Tietz oscillator. Phys. Scr. 96, 055001 https://doi.org/10.1088/1402-4896/abe3be
Eyube, E.S., Sanda, A. & Jabil, Y.Y (2019b). ℓ-wave analytical solutions of Schrödinger equation with Tietz-Hua potential. Trans. NAMP., 10, 51
Eyube, E.S., Yabwa, D. & Yerima, J.B. (2019c). Bound state solutions of Non-relativistic Schrödinger equation with Hellmann potential within the frameworks of generalized Pekeris approximation of the centrifugal term potential. J. NAMP., 52, 215
Eyube, E.S., Ahmed, A.D. & Hussaini, M. (2020a). Vibrational energy levels and mean values of the deformed Hulthén plus shifted Tietz-Wei oscillator. NJP. 29, 168
Eyube, E. S., Ahmed, A. D. & Timtere, P. (2020b). Eigensolutions and expectation values of shifted-rotating Möbius squared oscillator. Eur. Phys. J. Plus, 135, 893 https://doi.org/10.1140/epjp/s13360-020-00915-6
Eyube, E.S., Rawen B.O. & Ibrahim N. (2021b). Approximate analytical solutions and mean energies of stationary Schrödinger equation for the general molecular potential. Chin. Phys. B https://doi.org/10.1088/1674-1056/abe371
Eyube, E.S., Hussaini, M. & Ahmed, A.D. (2020c). Vibrational partition function and approximate solutions of Schrödinger equation with improved Tietz potential plus generalized Hulthén potential. NJP. 29, 180
Hassanabadi, H., Yazarloo, B. H., Ikot, A. N., Salehi, N. & Zarrinkamr, S. (2013a). Exact analytical versus numerical solutions of Schrödinger equation for Hua plus modified Eckart potential. Indian J. Phys., 87, 1219–1223 https://doi.org/10.1007/s12648-013-0368-3
Hassanabadi, H., Yazarloo, B. H., Mahmoudieh, M. & Zarrinkamar, S. (2013b). Dirac equation under the Deng-Fan potential and the Hulthén potential as a tensor interaction via SUSYQM. Eur. Phys. J. Plus, 128, 111 https://doi.org/10.1140/epjp/i2013-13111-4
Horchani, R., Al-Aamri, H., Al-Khindi, N., Ikot, A.N., Okorie, U.S., Rampho, G.J. & Jelassi, H. (2021). Energy spectra and magnetic properties of diatomic molecules in the presence of magnetic and AB fields with the inversely quadratic Yukawa potential. Eur. Phys. J. D 75, 36 https://doi.org/10.1140/epjd/s10053-021-00038-2
Ikhdair, S. M. (2011). On the bound-state solutions of the Manning–Rosen potential including an improved approximation to the orbital centrifugal term. Phys. Scr., 83, 015010. https://doi.org/10.1088/0031-8949/83/01/015010
Ikhdair, S. M. (2009). An improved approximation scheme for the centrifugal term and the Hulthén potential. Eur. Phys. J. A, 39, 307–314. https://doi.org/10.1140/epja/i2008-10715-2
Ikhdair, S. M. & Sever, R. (2010). Approximate bound state solutions of Dirac equation with Hulthén potential including Coulomb-like tensor potential. Appl. Math. Comput., 216, 911–923 https://doi.org/10.1016/j.amc.2010.01.104
Ikot, A. N., Zarrinkamar, S., Ibanga, E. J., Maghsoodi, E. & Hassanabadi, H. (2014). Pseudospin symmetry of the Dirac equation for a Möbius square plus Mie type potential with a Coulomb-like tensor interaction via SUSYQM. Chinese Physics C, 38, 013101 https://doi.org/10.1088/1674-1137/38/1/013101
Jia, C.-S., Liu, J.-Y. & Wang, P.-Q. (2008). A new approximation scheme for the centrifugal term and the Hulthén potential. Phys. Lett. A, 372, 4779–4782 https://doi.org/10.1016/j.physleta.2008.05.030
Jia, C.-S., Chen, T. & Cui, L.-G. (2009). Approximate analytical solutions of the Dirac equation with the generalized Pöschl–Teller potential including the pseudo-centrifugal term. Phys. Lett. A, 373, 1621–1626. https://doi.org/10.1016/j.physleta.2009.03.006
Liu, J.-Y., Hu, X.-T. & Jia, C.-S. (2014). Molecular energies of the improved Rosen−Morse potential energy model. Can. J. Chem., 92, 40–44 10.1139/cjc-2013-0396
Lucha, W. & Schöberl, F. F. (1999). Solving The Schrödinger Equation for Bound States with Mathematica 3.0. Int. J. Mod. Phys. C, 10, 607–619 https://doi.org/10.1142/S0129183199000450
Meyur, S. & Debnath, S. (2009). Solution of the Schrödinger equation with Hulthén plus Manning-Rosen potential. Lat. Am. J. Phys. Educ., 3, 300–306
Nikoofard, H., Maghsoodi, E., Zarrinkamar, S., Farhadi, M. & Hassanabadi, H. (2013). The nonrelativistic Tietz potential. Turk. J. Phys., 37, 74–82 doi.org/10.3906/fiz- 1207 - 1
Sous, A. J. (2019). Asymptotic iteration method applied to new confining potentials. Pramana J. Phys., 93, 22 https://doi.org/10.1007/s12043-019-1782-7
Tsaur, G. & Wang, J. (2013). A universal Laplace-transform approach to solving Schrödinger equations for all known solvable models. Eur. J. Phys., 35, 015006. https://doi.org/10.1088/0143-0807/35/1/015006
Varshni, Y. P. (1990). Eigenenergies and oscillator strengths for the Hulthén potential. Phys. Rev. A, 41, 4682–4689 https://doi.org/10.1103/PhysRevA.41.4682
Wei, G.-F. & Dong, S.-H. (2008). Approximately analytical solutions of the Manning–Rosen potential with the spin–orbit coupling term and spin symmetry. Phys. Lett, A, 373, 49–53 https://doi.org/10.1016/j.physleta.2008.10.064
Xu, Y., He, S. & Jia, C.-S. (2010). Approximate analytical solutions of the Klein–Gordon equation with the Pöschl–Teller potential including the centrifugal term. Phys. Scr., 81, 045001. https://doi.org/10.1088/0031-8949/81/04/045001
Yahya, W. A. & Oyewumi, K. J. (2016). Thermodynamic properties and approximate solutions of the ℓ-state Pöschl–Teller-type potential. J. Assoc. Arab Univ. Basic Appl. Sci., 21, 53–58 https://doi.org/10.1016/j.jaubas.2015.04.001
Yanar, H., Taş, A., Salti, M. & Aydogdu, O. (2020). Ro-vibrational energies of CO molecule via improved generalized Pöschl–Teller potential and Pekeris-type approximation. Eur. Phys. J. Plus, 135, 292 https://doi.org/10.1140/epjp/s13360-020-00297-9
Published
2021-07-06
How to Cite
Bitrus, B. M., Wadata, U., Nwabueze, C. M., & Eyube, E. S. (2021). ENERGY SPECTRUM AND SOME USEFUL EXPECTATION VALUES OF THE TIETZ-HULTHÉN POTENTIAL. FUDMA JOURNAL OF SCIENCES, 5(2), 255 - 263. https://doi.org/10.33003/fjs-2021-0501-614
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Research Articles
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