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Chin. Phys. B, 2017, Vol. 26(6): 060301    DOI: 10.1088/1674-1056/26/6/060301
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Solvability of a class of PT-symmetric non-Hermitian Hamiltonians: Bethe ansatz method

M Baradaran, H Panahi
Department of Physics, University of Guilan, Rasht 41635-1914, Iran
Abstract  We use the Bethe ansatz method to investigate the Schrödinger equation for a class of PT-symmetric non-Hermitian Hamiltonians. Elementary exact solutions for the eigenvalues and the corresponding wave functions are obtained in terms of the roots of a set of algebraic equations. Also, it is shown that the problems possess sl(2) hidden symmetry and then the exact solutions of the problems are obtained by employing the representation theory of sl(2) Lie algebra. It is found that the results of the two methods are the same.
Keywords:  PT-symmetry      Bethe ansatz method      Lie algebraic approach      quasi-exactly solvable  
Received:  18 November 2016      Revised:  09 February 2017      Published:  05 June 2017
PACS:  03.65.-w (Quantum mechanics)  
  03.65.Db (Functional analytical methods)  
  03.65.Fd (Algebraic methods)  
  03.65.Ge (Solutions of wave equations: bound states)  
Corresponding Authors:  H Panahi     E-mail:  t-panahi@guilan.ac.ir

Cite this article: 

M Baradaran, H Panahi Solvability of a class of PT-symmetric non-Hermitian Hamiltonians: Bethe ansatz method 2017 Chin. Phys. B 26 060301

[1] Bohr A and Mottelson B R 1969 Nuclear Structure (New York: Benjamin)
[2] Rüter C E, Makris K G, El-Ganainy R, Christodoulides D N, Segev M and Kip D 2010 Nat. Phys. 6 192
[3] Feinberg J and Zee A 1999 Phys. Rev. E 59 6433
[4] Bender C M and Boettcher S 1998 Phys. Rev. Lett. 80 5243
[5] Bender C M and Boettcher S 1998 J. Phys. A: Math. Gen. 31 L273
[6] Bender C M and Milton K A 1998 Phys. Rev. D 57 3595
[7] Bender C M, Dunne G V and Meisinger P N 1999 Phys. Lett. A 252 272
[8] Cannata F, Junker G and Trost J 1998 Phys. Lett. A 246 219
[9] Cannata F, Ioffe M, Roychoudhury R and Roy P 2001 Phys. Lett. A 281 305
[10] Znojil M 1999 Phys. Lett. A 259 220
[11] Znojil M 2000 J. Phys. A: Math. Gen. 33 L61
[12] Bagchi B and Roychoudhury R 2000 J. Phys. A: Math. Gen. 33 L1
[13] Bagchi B, Cannata F and Quesne C 2000 Phys. Lett. A 269 79
[14] Khare A and Mandal B P 2000 Phys. Lett. A 272 53
[15] Lévai G and Znojil M 2001 Mod. Phys. Lett. A 16 1973
[16] Lévai G and Znojil M 2002 J. Phys. A: Math. Gen. 35 8793
[17] Mostafazadeh A 2003 J. Phys. A: Math. Gen. 36 7081
[18] Mostafazadeh A 2002 J. Math. Phys. 43 205
[19] Buslaev V and Grecchi V 1993 J. Phys. A: Math. Gen. 26 5541
[20] Caliceti E, Graffi S and Maioli M 1980 Commun. Math. Phys. 75 51
[21] Yesiltas O, Simsek M, Sever R and Tezcan C 2003 Phys. Scripta 67 472
[22] Bagchi B and Quesne C 2000 Phys. Lett. A 273 285
[23] Qiang W C, Sun G H and Dong S H 2012 Annalen der Physik 524 360
[24] Özer O and Aslan V 2008 Cent. Eur. J. Phys. 6 879
[25] Özer O 2008 Chin. Phys. Lett. 25 3111
[26] Bagchi B and Quesne, C 2002 Phys. Lett. A 300 18
[27] Berkdemir A, Berkdemir C and Sever R 2006 Mod. Phys. Lett. A 21 2087
[28] Dorey P, Dunning C and Tateo R 2001 J. Phys. A: Math. Gen. 34 L391
[29] Znojil M 2002 arXiv: 0209062v1 [hep-th]
[30] Andrianov A, Ioffe M, Cannata F and Dedonder J P 1999 Int. J. Mod. Phys. A 14 2675
[31] Bender C M, Milton K A and Savage V M 2000 Phys. Rev. D 62 085001
[32] Itzykson C and Drouffe J M 1989 Statistical field theory (Cambridge: Cambridge University Press)
[33] Bender C M, Brody D C and Jones H F 2004 Phys. Rev. D 70 025001
[34] Znojil M 1999 J. Phys. A: Math. Gen. 32 4563
[35] Bagchi B, Mallik S, Quesne C and Roychoudhury R 2001 Phys. Lett. A 289 34
[36] Khare A and Mandal B P 2009 Pramana 73 387
[37] Infed L and Hull T E 1951 Rev. Mod. Phys. 23 21
[38] Lévai G 1992 J. Phys. A: Math. Gen. 25 L521
[39] Cooper F, Khare A and Sukhatme U 1995 Phys. Rep. 251 267
[40] Dong S H 2007 Factorization Method in Quantum Mechanics (Netherlands: Springer)
[41] Dong S H 2011 Wave equations in higher dimensions (New York: Springer)
[42] Dong S H 2000 Int. J. Theor. Phys. 39 1119
[43] Suparmi A, Cari C and Deta U A 2014 Chin. Phys. B 23 090304
[44] Falaye B J, Oyewumi K J and Abbas M 2013 Chin. Phys. B 22 0110301
[45] Ortakaya S 2012 Chin. Phys. B 21 070303
[46] Hassanabadi H, Yazarloo B H and Liang-Liang L U 2012 Chin. Phys. Lett. 29 020303
[47] Hassanabadi S, Ghominejad M, Zarrinkamar S and Hassanabadi H 2013 Chin. Phys. B 22 060303
[48] Ikot A N, Hassanabadi H, Obong H P, Chad Umoren Y E, Isonguyo C N and Yazarloo B H 2014 Chin. Phys. B 23 120303
[49] Turbiner A V 1988 Commun. Math. Phys. 118 467
[50] González-López A, Kamran N and Olver P J 1993 Commun. Math. Phys. 153 117
[51] González-López A, Kamran N and Olver P J 1994 Commun. Math. Phys. 159 503
[52] Shifman M A 1989 Int. J. Mod. Phys. A 4 2897
[53] Panahi H and Baradaran M 2016 Adv. High Energy Phys. 2016, Article ID 8710604
[54] Panahi H and Baradaran M 2013 Eur. Phys. J. Plus 128 1
[55] Panahi H, Zarrinkamar S and Baradaran M 2015 Chin. Phys. B 24 060301
[56] Ushveridze A G 1994 Quasi-exactly Solvable Models in Quantum Mechanics (Bristol: IOP)
[57] Zhang Y Z 2012 J. Phys. A: Math. Theor. 45 065206
[58] Chiang C M and Ho C L 2001 Phys. Rev. A 63 062105
[59] Chiang C M and Ho C L 2002 J. Math. Phys. 43 43
[60] Ho C L 2006 Ann. Phys. 321 2170
[61] Bagchi B, Quesne C and Roychoudhury R 2008 J. Phys. A: Math. Theor. 41 022001
[62] Lévai G and Znojil M 2000 J. Phys. A: Math. Gen. 33 7165
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