Approximate energies and thermal properties of a position-dependent mass charged particle under external magnetic fields

doi:10.1088/1674-1056/26/6/060302

Abstract

We solve the Schrödinger equation with a position-dependent mass (PDM) charged particle interacted via the superposition of the Morse-plus-Coulomb potentials and is under the influence of external magnetic and Aharonov-Bohm (AB) flux fields. The nonrelativistic bound state energies together with their wave functions are calculated for two spatially-dependent mass distribution functions. We also study the thermal quantities of such a system. Further, the canonical formalism is used to compute various thermodynamic variables for second choosing mass by using the Gibbs formalism. We give plots for energy states as a function of various physical parameters. The behavior of the internal energy, specific heat, and entropy as functions of temperature and mass density parameter in the inverse-square mass case for different values of magnetic field are shown.

Keywords: Schrödinger equation Morse-plus-Coulomb potentials position-dependent mass distribution functions perpendicular magnetic and Aharonov-Bohm flux fields

Received: 02 January 2017
Revised: 26 February 2017
Accepted manuscript online:

PACS:	03.65.Ge	(Solutions of wave equations: bound states)
	03.65.Ca	(Formalism)
	03.65.Db	(Functional analytical methods)

Corresponding Authors: M Eshghi
E-mail: eshgi54@gmail.com,m.eshghi@semnan.ac.ir

Cite this article:

M Eshghi, H Mehraban, S M Ikhdair Approximate energies and thermal properties of a position-dependent mass charged particle under external magnetic fields 2017 Chin. Phys. B 26 060302

[1]	Flugge S 1974 Practical Quantum Mechanics (Berlin, Heidelberg, New York: Springer-Verlag)
[2]	Eshghi M and Mehraban H 2016 Math. Meth. Aappl. Sci. 39 1599
[3]	Dong S H and Lozada-Cassou M 2004 Phys. Lett. A 330 168
[4]	Jia C S, Li Y, Sun Y and Sun L T 2003 Phys. Lett. A 311 115
[5]	Aydogdu O and Sever R 2010 Ann. Phys. 325 373
[6]	Chen G 2004 Phys. Lett. A 326 55
[7]	Ikhdair S M and Sever R 2007 J. Mol. Struc. THEOCHEM 806 155
[8]	Arda A and Sever R 2012 Commun. Theor. Phys. 58 27
[9]	Zhang M C, Sun G H and Dong S H 2010 Phys. Lett. A 374 704
[10]	Kestner N R and Sinanoglu O 1962 Phys. Rev. 128 2687
[11]	Stahlhofen A A 2004 J. Phys. A: Math. Gen. 37 10129
[12]	Karwowski J and Witek H A 2014 Theor. Chem. Acc. 133 1494
[13]	Greiner W 2001 Quantum Mechanics: an Introduction (Berlin: Spronger-Verlag)
[14]	Dong S H 2007 Factorization Method in Quantum Mechanics (Berlin: Springer)
[15]	Slavyanov S Y, Lay W and Seeger A 2000 Special Functions: A Unifield Theory Based on Singularities (New-York: Oxford University Press)
[16]	Ronveaux A 1995 Heun's Differential Equations (Oxford: Oxford University Press)
[17]	Eshghi M and Mehraban H 2017 C. R. Physique 18 47
[18]	Eshghi M, Mehraban H and Ikhdair S M 2016 Eur. Phys. J. A 52 201
[19]	Ikhdair S M, Falaye B J and Hamzavi M 2015 Ann. Phys. 353 282
[20]	Sharifi Z, Tajic F, Hamzavi M and Ikhdair S M 2015 Z. Naturf. A 70 499
[21]	Slater J C 1949 Phys. Rev. 76 1592
[22]	Ikhdair S M 2009 Chem. Phys. 361 9
[23]	Ikhdair S M and Sever R 2010 Appl. Math. Comp. 216 545
[24]	Rajbongshi H and Nimai Singh N 2013 J. Mod. Phys. 4 1540
[25]	Arda A and Sever R 2009 Chin. Phys. Lett. 26 090305
[26]	Arda A and Sever R 2010 Chin. Phys. Lett. 27 010106
[27]	Falaye B J, Serrano F A and Dong S H 2016 Phys. Lett. A 380 267
[28]	Jia C S, Wang P Q, Liu J Y and He S 2008 Int. J. Theor. Phys. 47 2513
[29]	Eshghi M, Hamzavi M and Ikhdair S M 2013 Chin. Phys. B 22 030303
[30]	Eshghi M and Mehraban H 2012 Few-Body Syst. 52 41
[31]	Eshghi M and Abdi M R 2013 Chin. Phys. C 37 053103
[32]	Panahi H and Bakhshi Z 2011 J. Phys. A: Math. Theor. 44 175304
[33]	Mustafa O 2008 Int. J. Theor. Phys. 47 1300
[34]	Mustafa O and Habib Mazaherimousavi S 2009 Phys. Lett. A 373 325
[35]	Chnha M S and Christiansen H R 2013 Commun. Theor. Phys. 60 642
[36]	Bahar M K and Yasuk F 2014 Can. J. Phys. 92 1565
[37]	Ikhdair S M, Hamzavi M and Sever R 2012 Physica B 407 4523
[38]	Bonatsos D, Georgoudis P E, Minkov N, Petrellis D and Quesne C 2013 Phys. Rev. C 88 034316
[39]	Yu J, Dong S H and Sun G H 2004 Phys. Lett. A 322 290
[40]	Dong S H and Lozada-Cassou M 2005 Phys. Lett. A 337 313
[41]	Jiang L, Yi L Z and Jia C S 2005 Phys. Lett. A 345 279
[42]	Jia C S, Li X P and Zhang L H 2012 Few-Body Syst. 52 11
[43]	Jia C S and de Souza Dutra A 2008 Ann. Phys. 323 566
[44]	Bonatsos D, Georgoudis P E, Lenis D, Minkov N and Quesne C 2010 Phys. Lett. B 683 264
[45]	Khordad R 2010 Sol. Stat. Sci. 12 1253
[46]	Yuce C 2006 Phys. Rev. A 74 062106
[47]	Ustoglu Unal V, Aksahin E and Aytekin O 2013 Physica E 47 103
[48]	Jia C S, Zhang L H and Wang C W 2017 Chem. Phys. Lett. 667 211
[49]	Strekalov M L 2007 Chem. Phys. Lett. 439 209
[50]	Toutounji M 2011 Int. J. Quantum Chem. 111 1885
[51]	Alhaidari A D 2004 Phys. Lett. A 72 322
[52]	Arias de Saavedra F, Boronat J, Polls A and Fabrocini A 1994 Phys. Rev. B 50 4248
[53]	Li Y M, Lu H M, Voskoboynikov O, Lee C P and Sze S M 2003 Surf. Sci. 811 532
[54]	Eshghi M and Mehraban H 2017 Eur. Phys. J Plus 132 121
[55]	Ju G X, Cai C Y, Xiang Y and Ren Z Z 2007 Commun. Theor. Phys. 47 1001
[56]	Eshghi M, hamzavi M and Ikhdair S M 2013 Chin. Phys. B 22 030303
[57]	Jia C S and de Souza Dutra A 2006 J. Phys. A: Math. Gen. 39 11877
[58]	Xu Y, Su H and Jia C S 2008 J. Phys. A: Math. Theor. 41 255302
[59]	Eshghi M and Ikhdair S M 2014 Chin. Phys. B 23 120304
[60]	Bagchi B, Gorain P, Quesne C and Roychoudhury R 2004 Mod. Phys. Lett. A 19 2765
[61]	Bordag M and Khusnutdinov N 1996 Class. Quantum Grav. 13 L41
[62]	Kristensson G 2010 Second Order Differential Equations, Special Functions and Their Classification (New York: Springer)
[63]	Zhang A P, Shi P, Ling Y W and Hua Z W 2011 Acta Phys. Pol. A 120 987
[64]	Patria R K 1972 Statistical Mechanics (Oxford: Pergamom Press)
[65]	Abramowitz M and Astegun I A 1972 Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (New York: Dover)

[1]	Efficient solver for time-dependent Schrödinger equation with interaction between atoms and strong laser field Sheng-Peng Zhou(周胜鹏), Ai-Hua Liu(刘爱华), Fang Liu(刘芳), Chun-Cheng Wang(王春成), Da-Jun Ding(丁大军). Chin. Phys. B, 2019, 28(8): 083101.
[2]	Dynamics of three nonisospectral nonlinear Schrödinger equations Abdselam Silem, Cheng Zhang(张成), Da-Jun Zhang(张大军). Chin. Phys. B, 2019, 28(2): 020202.
[3]	Quantum photodetachment of hydrogen negative ion in a harmonic potential subjected to static electric field Azmat Iqbal, Kiran Humayun, Sana Maqsood, Saba Jawaid, Afaq Ahmad, Amin Ur Rahman, Bakht Amin Bacha. Chin. Phys. B, 2019, 28(2): 023201.
[4]	Energy states of the Hulthen plus Coulomb-like potential with position-dependent mass function in external magnetic fields M Eshghi, R Sever, S M Ikhdair. Chin. Phys. B, 2018, 27(2): 020301.
[5]	Exact solitary wave solutions of a nonlinear Schrödinger equation model with saturable-like nonlinearities governing modulated waves in a discrete electrical lattice Serge Bruno Yamgoué, Guy Roger Deffo, Eric Tala-Tebue, François Beceau Pelap. Chin. Phys. B, 2018, 27(12): 126303.
[6]	Bound states resulting from interaction of the non-relativistic particles with the multiparameter potential Ahmet Taş, Ali Havare. Chin. Phys. B, 2017, 26(10): 100301.
[7]	Dynamics of cubic-quintic nonlinear Schrödinger equation with different parameters Wei Hua(花巍), Xue-Shen Liu(刘学深), Shi-Xing Liu(刘世兴). Chin. Phys. B, 2016, 25(5): 050202.
[8]	Nonautonomous solitary-wave solutions of the generalized nonautonomous cubic–quintic nonlinear Schrödinger equation with time- and space-modulated coefficients He Jun-Rong (何俊荣), Li Hua-Mei (李画眉). Chin. Phys. B, 2013, 22(4): 040310.
[9]	Multisymplectic implicit and explicit methods for Klein–Gordon–Schrödinger equations Cai Jia-Xiang (蔡加祥), Yang Bin (杨斌), Liang Hua (梁华). Chin. Phys. B, 2013, 22(3): 030209.
[10]	A new finite difference scheme for a dissipative cubic nonlinear Schr"odinger equation Zhang Rong-Pei(张荣培),Yu Xi-Jun(蔚喜军),and Zhao Guo-Zhong(赵国忠). Chin. Phys. B, 2011, 20(3): 030204.
[11]	Approximate solutions of Schrödinger equation for Eckart potential with centrifugal term F. Tacskin and G. Koccak. Chin. Phys. B, 2010, 19(9): 090314.
[12]	Bound states of the Schrödinger equation for the Pöschl–Teller double-ring-shaped Coulomb potential Lu Fa-Lin(陆法林) and Chen Chang-Yuan(陈昌远). Chin. Phys. B, 2010, 19(10): 100309.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Approximate energies and thermal properties of a position-dependent mass charged particle under external magnetic fields

Cite this article:

Online attention