Exact Solutions of Effective Mass Dirac Equation with Non-PT-Symmetric and Non-Hermitian Exponential-type Potentials
Altug Arda1, Ramazan Sever2
1Department of Physics Education, Hacettepe University, 06800, Ankara, Turkey2Department of Physics, Middle East Technical University, 06800, Ankara,Turkey
Exact Solutions of Effective Mass Dirac Equation with Non-PT-Symmetric and Non-Hermitian Exponential-type Potentials
Altug Arda1, Ramazan Sever2
1Department of Physics Education, Hacettepe University, 06800, Ankara, Turkey2Department of Physics, Middle East Technical University, 06800, Ankara,Turkey
摘要By using a two-component approach to the one-dimensional effective mass Dirac equation, bound states are investigated under the effect of two new non-PT-symmetric and non-Hermitian exponential type potentials. It is observed that the Dirac equation can be mapped into a Schrödinger-like equation by rescaling one of the two Dirac wave functions in the case of the position-dependent mass. The energy levels and the corresponding Dirac eigenfunctions are found analytically.
Abstract：By using a two-component approach to the one-dimensional effective mass Dirac equation, bound states are investigated under the effect of two new non-PT-symmetric and non-Hermitian exponential type potentials. It is observed that the Dirac equation can be mapped into a Schrödinger-like equation by rescaling one of the two Dirac wave functions in the case of the position-dependent mass. The energy levels and the corresponding Dirac eigenfunctions are found analytically.
Altug Arda;Ramazan Sever. Exact Solutions of Effective Mass Dirac Equation with Non-PT-Symmetric and Non-Hermitian Exponential-type Potentials[J]. 中国物理快报, 2009, 26(9): 90305-090305.
Altug Arda, Ramazan Sever. Exact Solutions of Effective Mass Dirac Equation with Non-PT-Symmetric and Non-Hermitian Exponential-type Potentials. Chin. Phys. Lett., 2009, 26(9): 90305-090305.
[1] Bender C M and Boettcher S 1998 Phys. Rev. Lett. 80 5243 [arXiv:physics/9712001]. [2] Fernandez F M, Guardiola R, Ros J and Znojil M 1998 J. Phys. A: Math. Gen. 31 10105 [3] Cannata F, Junker G and Trost J 1998 Phys. Lett. A 246 219 [arXiv:quant-ph/9805085]. [4] Bender C M, Boettcher S and Meisinger P 1999 J. Math.Phys. 40 2201 [arXiv:quant-ph/9809072] [5] Bender C M, Dunne G V and Meisinger P 1999 Phys.Lett. A 252 272 [6] Khare A and Mandal B P 2000 Phys. Lett. A 27253 [arXiv:quant-ph/0006126] [7] Znojil M, Cannata F, Bagchi B and Roychoudhury R 2000 Phys. Lett. B 483 284 [arXiv:hep-th/0003277] [8] Mostafazadeh A 2002 J. Math. Phys. 43 205 [9] L\'{evai G and Znojil M 2000 J. Phys. A: Math. Gen. 33 7165 [10] Znojil M 2005 J. Math. Phys. 46 062109 [11] Bagchi B and Quesne C 2002 Phys. Lett. A 30018 [12] Jia C S, Zeng X L and Sun L T 2002 Phys. Lett. A 294 185 [13] Jia C S, Li S C, Li Y and Sun L T 2002 Phys. Lett.A 300 115 [14] Jia C S, Sun Y and Li Y 2002 Phys. Lett. A 305 231 [15] Jia C S, Yi L Z, Zhao X Q, Liu J Y and Sun L T 2005 Mod. Phys. Lett. A 20 1753 [16] Bender C M, Brody D C and Jones H F 2004 Phys. Rev.Lett. 93 251601 [17] Bender C M, Jones H F and Rivers R J 2005 Phys.Lett. B 625 333 [18] Bender C M, Brody D C, Chen J H, Jones H F, Milton K Aand Ogilvie M C 2006 Phys. Rev. D 74 025016 [19] Deb R N, Khare A and Roy B D 2003 Phys. Lett. A 307 215 Baye D, L\'{evai G and Sparenberg J M 1996 Nucl.Phys. A 599 435 [20] Ahmed Z 2000 Phys. Lett. A 273 343 [21] Huang F J, Qi R, Li Y D and Liu W M 2007 Europhys.Lett. 79 10004 [22] Fu Y P, Wang D, Li Y D and Liu W M 2007 J. Phys.:Cond. Matt. 19 496220 [23] Jiang Z F, Li R D, Zhang S C and Liu W M 2005 Phys.Rev. B 72 045201 [24] Sheng C T, Feng L H, Jie M, Quan Z S and Gui Z S 2003 Chin. Phys. Lett. 20 358 [25] You G J, Jie M and Xin X F 2003 Chin. Phys. Lett. 20 602 [26] Jia C S, Wang P Q, Liu J Y and He S 2007 Int. J.Theor. Phys. doi: 10.1007/s10773-008-9685-2 [27] Jiang L, Yi L Z and Jia C S 2005 Phys. Lett. A 345 279 [28] Jia C S, Yi L Z and Sun Y 2008 J. Math. Chem. 43 435 [29] Bagchi B, Quesne C and Roychoudhury R 2005 J. Phys.A 38 L647 [30] Roy B and Roy P 2005 J. Phys. A 38 11019 [31] Mustafa O and Mazharimousavi S H 2007 Int. J. Theor.Phys. doi: 10.1007/s10773-007-9470-7 [32] Tezcan C and Sever R 2007 Int. J. Theor. Phys. doi:10.1007/s10773-007-9589-6 [33] Jia C S and Dutra A S 2006 Int. J. Theor. Phys. 39 11877 [34] Mustafa O and Mazharimousavi S H 2007 J. Phys. A 40 863 [35] Jia C S, Liu J Y, Wong P Q and Che C S 2007 Phys.Lett. A 369 274 [36] Jia C S and Dutra A S 2007 Ann. Phys.doi:10.1016/j. aop.2007.04.007 [37] Serra L and Lipparini E 1997 Europhys. Lett. 40 667 [38] Von Roos O 1983 Phys. Rev. B 27 7547 [39] de Saavedra F A, Boronat J, Polls A and Fabrocini A 1994 Phys. Rev. B 50 4248 [40] Kennedy P 2005 J. Phys. A 35 689 [arXiv:hep-th/ 0107170] [41] Fl\"uge S 1971 Practical Quantum Mechanics I$\!$I(Berlin: Springer) [42] Nikiforov A F and Uvarov V B 1988 Special Functionsof Mathematical Physics (Basel: Birkhauser) [43] de Castro A S and Hott M 2007 Phys. Lett. A 342 53 [44] Wong C W 1991 Introduction to MathematicalPhysics-Methods and Concepts (Oxford: Oxford University) [45] Costa L C, Prudenter F V, Acioli P H, Neto J J S andVianna J D M 1990 J. Phys. B 32 2461
2009, Vol. 26 
