Solutions of Schrodinger equation and thermal properties of generalized trigonometric Poschl-Teller potential.

C. O. Edet, P. O. Amadi, U. S. Okorie, A. Tas, A. N. Ikot, G. Rampho

Abstract


Analytical solutions of the Schrödinger equation for the generalized trigonometric Pöschl–Teller potential by using an appropriate approximation to the centrifugal term within the framework of the Functional Analysis Approach have been considered. Using the energy equation obtained, the partition function was calculated and other relevant thermodynamic properties. More so, we use the concept of the superstatistics to also evaluate the thermodynamics properties of the system. It is noted that the well-known normal statistics results are recovered in the absence of the deformation parameter and this is displayed graphically for the clarity of our results. We also obtain analytic forms for the energy eigenvalues and the bound state eigenfunction solutions are obtained in terms of the hypergeometric functions. The numerical energy spectra for different values of the principal and orbital quantum numbers are obtained. To show the accuracy of our results, we discuss some special cases by adjusting some potential parameters and also compute the numerical eigenvalue of the trigonometric Pöschl–Teller potential for comparison sake. However, it was found out that our results agree excellently with the results obtained via other methods


Keywords


trigonometric Pöschl–Teller potential; factorization method; Superstatistics; Schrodinger Equation

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S. Dong, G. H. Sun, B.J. Falaye and S. H. Dong. Eur. Phys. J. Plus 131 (2016) 176

Q. Dong, G. H. Sun, J. Jing, S. H. Dong. Phys. Lett. A 383 (2019)270

S. Dong, G. H. Sun, B.J. Falaye and S. H. Dong. Int. J. Mod Phys E. 22 (2013) 1350036

A. N. Ikot, H. P. Obong, T. M. Abbey, S. Zare, M. Ghafourian and H. Hassanabadi Few-Body Syst. (2016). DOI 10.1007/s00601-016-1111-3

A. N. Ikot, E. Maghsoodi, A. D. Antia, H. Hassanabadi and S. Zarrinkamar Arab J Sci Eng.(2015) DOI 10.1007/s13369-015-1602-4.

C O Edet , K. O Okorie, H Louis and N A Nzeata-Ibe. Indian J Phys (2019). https://doi.org/10.1007/s12648-019-01467-x

C O Edet, U. S. Okorie , A T Ngiangia and A N Ikot. Indian J Phys (2019) https://doi.org/10.1007/s12648-019-01477-9

Jia C S, Guo P and Peng X L J. Phys. A: Math. Gen. 39 (2006) 7737

A. N. Ikot, S. Zarrinkamar, B. H. Yazarloo, and H. Hassanabadi. Chin. Phys. B 23 (2014) 100306

B. J. Falaye. Cent. Eur. J. Phys. 10 (2012) 960

H. Hassanabadi, B.H. Yazarloo, S. Zarrinkamar, and H. Rahimov. Commun. Theor. Phys. 57 (2012) 339

W. A. Yahya, B. J. Falaye, O. J. Oluwadare and K. J. Oyewumi. Intl. J. of Mod. Phys E 22 (2013) 1350062

K.J. Oyewumi, B.J. Falaye, C.A. Onate, O.J. Oluwadare and W.A. Yahya. Mol. Phys, 112, (2014), 127.

H. Boukabcha, M. Hachama and A. Diaf. Appl. Math. Comput. 321 (2018) 121

R Khordad and B Mirhosseini. Pramana J. Phys. 85 (2015) 723

H. Nikoofard, E. Maghsoodi, S. Zarrinkamar, M. Farhadi, H.Hassanabadi. Turk J Phys 37 (2013) 74

W.A. Yahya, K. Issa, B.J. Falaye, and K.J. Oyewumi. Can. J. Chem. 92 (2014) 215

H. M. Tang, G. C. Liang, L. H. Zhang, F. Zhao, and C. S. Jia. Can. J. Chem. 92 (2014) 201

R L Greene, C Aldrich, Phys. Rev. A 14, (1976) 2363.

W C Qiang, K Li and W L Chen, J. Phys. A: Math. Theor. 42 (2009) 205306

H. Fakhri and J. Sadeghi, Mod Phys Lett A, 19 (2004) 615

C. N. Isonguyo, I. B. Okon, A. N. Ikot, and H. Hassanabadi, Bull. Kor. Chem. Soc. 35 (2014) 3443

A. Arai, J. Math. Anal. Appl., 158 (1991) 63.

A. N. Ikot, B. H. Yazarloo, E. Maghsoodi, S. Zarrinkamar, and H. Hassanabadi, J. Assoc. Arab Uni. Basic Appl. Sci., (2014). https://doi.org/10.1016/j.jaubas.2014.03.005

C. O. Edet, P. O Okoi and S. O Chima, Rev. Bras. Ens. Fis. 42, (2020) 1

A. N. Ikot, A. D. Antia, L. E. Akpabio, and A. J. Obu, J. Vect. Rel. , 6 (2011) 65.

C.O. Edet and P.O. Okoi,Rev. Mex. Fis. 65 (2019) 333.

B.J. Falaye. Few-Body Syst.53 (2012) 557.

H. Çiftçi, R.L. Hall, N. Saad, J. Phys. A Math Gen. 36 (2003) 11807

H. Çiftçi, R.L. Hall, N. Saad, Phys. Lett. A 340 (2005) 388.

F. Chafa, A. Chouchaoui, M. Hachemane, and F.Z. Ighezou. Ann. Phys. 322 (2007) 1034.

A. N. Ikot · L. E. Akpabio and A. D. Antia. Arab J Sci Eng 37 (2012) 217

A. Diaf and A. Chouchaoui. Phys. Scr. 84 (2011) 015004

A. Khodja, F. Benamira, and L. Guechi J. Math Phys 59 (2018) 042108

S.H. Dong, Factorization Method in Quantum Mechanics (Springer, New York, 2007)

U. S. Okorie, A. N. Ikot, C.O.Edet, I.O.Akpan, R.Sever and R. Rampho J. Phys. Commun. 3 (2019) 095015

B.J. Falaye, S.M. Ikhdair, M. Hamzavi, Few Body Sys. 56 (2015) 63

S. H. Dong and A. Gonzalez-Cisneros, Ann. Phys. (N.Y.) 323 (2008) 1136

X.Y. Gu, S.H. Dong, and Z.Q. Ma. J. Phys. A: Math. Theor. 42 (2009) 035303.

S.M. Ikhdair and J. Abu-Hasna.. Phys. Scr. 83 (2011) 025002.

B. J. Falaye, S. M. Ikhdair and M. Hamzavi J Theor Appl Phys 9 (2015) 151

S.H. Dong, D. Morales, and J. Garcia-Ravelo. Int. J. Mod. Phys. E, 16 (2007) 189.

W.C. Qiang and S.H. Dong. Europhys. Lett. 89 (2010) 10003

B.J. Falaye, S.M. Ikhdair, M. Hamzavi, J. Math. Chem. 53 (2015) 1325.

S.H. Dong and M. Cruz-Irisson. J. Math. Chem. 50 (2012) 881.

O.J. Oluwadare, and K.J. Oyewumi, Eur. Phys. J. Plus 133 (2018) 422.

X.Y. Gu and S.H. Dong. J. Math. Chem. 49 (2011) 2053.

F.A. Serrano, X.Y. Gu, and S.H. Dong. J. Math. Phys. 51 (2010) 082103.

M. Hamzavi and A.A. Rajabi. Commun. Theor. Phys. 55 (2011) 35

G. Pöschl and E. Teller. Z. Phys. 83 (1933) 143

X.W. Liu, G.F. Wei, X.W. Cao, and H.G. Bai. Int. J. Theor. Phys. 49 (2010) 343

M.C. Zhang and Z.B. Wang. Acta Phys. Sinica, 55 (2006) 0525

M. Hamzavi, A. A. Rajabi, and M. Amirfakhrian Z. Naturforsch. 68a (2013) 524

N. Candemir Intl J. Mod Phys E 21 (2012) 1250060

M. Hamzavi and A. A. Rajabi. Adv. High Energy Phys 2013 (2013) 196986. http://dx.doi.org/10.1155/2013/196986

M. Hamzavi and A.A. Rajabi. Int. J. Quantum Chem. 112 (2012)1592

M. Hamzavi and S.M. Ikhdair. Mol. Phys 110 (2012) 3031

A N Ikot, E O Chukwuocha, M C Onyeaju, C A Onate, B I Ita. and M E Udoh. Pramana – J. Phys. 90 (2018) 22

X-Q Song, C-W Wang and C-S Jia, Chem Phy Lett 673 (2017) 50

A N Ikot, W Azogor, U S Okorie, F E Bazuaye, M C Onjeaju, C A Onate and E O Chukwuocha (2019) Indian J Phys. https://doi.org/10.1007/s12648-019-01375-0

G Herzberg, Molecular spectra and molecular structure II, Infared and Raman spectra of polyatomic molecules (Van Nostrand, New York, 1945)

A N Ikot, B C Lutfuoglu, M I Ngwueke, M E Udoh, S Zare and H Hassanabadi, Eur. Phys. J. Plus 131 (2016) 419

H J Korsch, J. Phys. A: Math. Gen. 12 (1979) 1521

G. Wilk and Z. Wlodarczyk, Phys. Rev. Lett. 84 (2000) 2770.

H. Touchette and C. Beck, Phys. Rev. E 71, (2005) 016131.

C. Beck and E. G. D. Cohen, Physica A 322(2003) 267.

D. Bonatsos and C. Daskaloyannis, Prog. Part. Nucl. Phys. 43, (1999) 537.

M. Chaichian, D. Ellinas and P. Kulish, Chem. Phys. Lett. 302 (1999).

S. Sargolzaeipor, H. Hassanabadi and A. Boumali, Int. J. Geom. Methods Mod. Phys. 14(2017) 1750112.

S. Sargolzaeipor, H. Hassanabadi and W. S. Chung, J. Korean Phys. Soc. 70, (2017) 557.

C. Beck, Phys. Rev. Lett. 87, 180601 (2001)

C. Tsallis and A. M. C. Souza, Phys. Rev. E 67, (2003)026106.

C. Beck, Continuum Mech. Thermodyn. 16, (2004) 293.

C. Tsallis, J. Stat. Phys. 52, (1988) 479.

S. Sargolzaeipor, H. Hassanabadiand W. S. Chung, Mod. Phys Lett A.33, (2018) 1850060

B J Falaye. Can. J. Phys. 91 (2013) 365




DOI: https://doi.org/10.31349/RevMexFis.66.824

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