PT-invariant periodic potentials with a finite number of band gaps

Journal of Mathematical Physics

Volumn 46, Issue 8, 2005, Pages

  Khare, Avinash ^a   Sukhatme, Uday ^b  

^a INSTITUTE OF PHYSICS   (India)

^b UNIVERSITY AT BUFFALO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 24344506578     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2000207     Document Type: Article

References (37)

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12. C. M. Bender and S. Boettcher, J. Phys. A 0305-4470 10.1088/0305-4470/31/ 14/001 31, L273 (1998); C. M. Bender, S. Boettcher, and P. N. Meisinger, J. Math. Phys. 0022-2488 40, 2210 (1999); F. M. Fernandez, R. Guardiola, J. Ros, and M. Znojil, J. Phys. A 0305-4470 10.1088/0305-4470/32/17/303 32, 3105 (1999); M. Znojil, J. Phys. A 0305-4470 10.1088/0305-4470/32/24/318 32, 4563 (1999); M. Znojil, Phys. Lett. A 0375-9601 10.1016/S0375-9601(99)00805-1 264, 108 (1999); F. Cannata, G. Junker, and J. Trost, Phys. Lett. A 0375-9601 10.1016/S0375-9601(98)00517-9 246, 219 (1998); B. Bagchi and R. Roy-Choudhury, J. Phys. A 0305-4470 10.1088/0305-4470/33/1/101 33, L1 (2000); P. Dorey, C. Dunning, and R. Tateo, J. Phys. A 0305-4470 10.1088/0305-4470/34/28/102 34, L391 (2001); P. Dorey, C. Dunning, and R. Tateo, J. Phys. A 0305-4470 10.1088/0305-4470/34/28/305 34, 5679 (2001); A. Khare and B. P. Mandal, Phys. Lett. A 0375-9601 10.1016/S0375-9601(00)00409-6 272, 53 (2000); G. Levai and M. Znojil, J. Phys. A 0305-4470 10.1088/0305-4470/33/40/313 33, 7165 (2000); B. Bagchi and C. Quesne, Phys. Lett. A 0375-9601 10.1016/S0375-9601(02)00689-8 300, 18 (2002); A. Mostafazadeh, J. Math. Phys. 0022-2488 10.1063/1.1418246 43, 205 (2003); A. Mostafazadeh, J. Math. Phys. 0022-2488 10.1063/1.1461427 43, 2814 (2003); A. Mostafazadeh, J. Math. Phys. 0022-2488 10.1063/1.1489072 43, 3944 (2003); Z. Ahmad, Phys. Lett. A 0375-9601 10.1016/S0375-9601(01)00622-3 290, 19 (2001); R. N. Deb, A. Khare, and B. Dutta Roy, Phys. Lett. A 307, 215 (2003).
13. C. M. Bender and S. Boettcher, J. Phys. A 0305-4470 10.1088/0305-4470/31/ 14/001 31, L273 (1998); C. M. Bender, S. Boettcher, and P. N. Meisinger, J. Math. Phys. 0022-2488 40, 2210 (1999); F. M. Fernandez, R. Guardiola, J. Ros, and M. Znojil, J. Phys. A 0305-4470 10.1088/0305-4470/32/17/303 32, 3105 (1999); M. Znojil, J. Phys. A 0305-4470 10.1088/0305-4470/32/24/318 32, 4563 (1999); M. Znojil, Phys. Lett. A 0375-9601 10.1016/S0375-9601(99)00805-1 264, 108 (1999); F. Cannata, G. Junker, and J. Trost, Phys. Lett. A 0375-9601 10.1016/S0375-9601(98)00517-9 246, 219 (1998); B. Bagchi and R. Roy-Choudhury, J. Phys. A 0305-4470 10.1088/0305-4470/33/1/101 33, L1 (2000); P. Dorey, C. Dunning, and R. Tateo, J. Phys. A 0305-4470 10.1088/0305-4470/34/28/102 34, L391 (2001); P. Dorey, C. Dunning, and R. Tateo, J. Phys. A 0305-4470 10.1088/0305-4470/34/28/305 34, 5679 (2001); A. Khare and B. P. Mandal, Phys. Lett. A 0375-9601 10.1016/S0375-9601(00)00409-6 272, 53 (2000); G. Levai and M. Znojil, J. Phys. A 0305-4470 10.1088/0305-4470/33/40/313 33, 7165 (2000); B. Bagchi and C. Quesne, Phys. Lett. A 0375-9601 10.1016/S0375-9601(02)00689-8 300, 18 (2002); A. Mostafazadeh, J. Math. Phys. 0022-2488 10.1063/1.1418246 43, 205 (2003); A. Mostafazadeh, J. Math. Phys. 0022-2488 10.1063/1.1461427 43, 2814 (2003); A. Mostafazadeh, J. Math. Phys. 0022-2488 10.1063/1.1489072 43, 3944 (2003); Z. Ahmad, Phys. Lett. A 0375-9601 10.1016/S0375-9601(01)00622-3 290, 19 (2001); R. N. Deb, A. Khare, and B. Dutta Roy, Phys. Lett. A 307, 215 (2003).
14. C. M. Bender and S. Boettcher, J. Phys. A 0305-4470 10.1088/0305-4470/31/ 14/001 31, L273 (1998); C. M. Bender, S. Boettcher, and P. N. Meisinger, J. Math. Phys. 0022-2488 40, 2210 (1999); F. M. Fernandez, R. Guardiola, J. Ros, and M. Znojil, J. Phys. A 0305-4470 10.1088/0305-4470/32/17/303 32, 3105 (1999); M. Znojil, J. Phys. A 0305-4470 10.1088/0305-4470/32/24/318 32, 4563 (1999); M. Znojil, Phys. Lett. A 0375-9601 10.1016/S0375-9601(99)00805-1 264, 108 (1999); F. Cannata, G. Junker, and J. Trost, Phys. Lett. A 0375-9601 10.1016/S0375-9601(98)00517-9 246, 219 (1998); B. Bagchi and R. Roy-Choudhury, J. Phys. A 0305-4470 10.1088/0305-4470/33/1/101 33, L1 (2000); P. Dorey, C. Dunning, and R. Tateo, J. Phys. A 0305-4470 10.1088/0305-4470/34/28/102 34, L391 (2001); P. Dorey, C. Dunning, and R. Tateo, J. Phys. A 0305-4470 10.1088/0305-4470/34/28/305 34, 5679 (2001); A. Khare and B. P. Mandal, Phys. Lett. A 0375-9601 10.1016/S0375-9601(00)00409-6 272, 53 (2000); G. Levai and M. Znojil, J. Phys. A 0305-4470 10.1088/0305-4470/33/40/313 33, 7165 (2000); B. Bagchi and C. Quesne, Phys. Lett. A 0375-9601 10.1016/S0375-9601(02)00689-8 300, 18 (2002); A. Mostafazadeh, J. Math. Phys. 0022-2488 10.1063/1.1418246 43, 205 (2003); A. Mostafazadeh, J. Math. Phys. 0022-2488 10.1063/1.1461427 43, 2814 (2003); A. Mostafazadeh, J. Math. Phys. 0022-2488 10.1063/1.1489072 43, 3944 (2003); Z. Ahmad, Phys. Lett. A 0375-9601 10.1016/S0375-9601(01)00622-3 290, 19 (2001); R. N. Deb, A. Khare, and B. Dutta Roy, Phys. Lett. A 307, 215 (2003).
15. C. M. Bender and S. Boettcher, J. Phys. A 0305-4470 10.1088/0305-4470/31/ 14/001 31, L273 (1998); C. M. Bender, S. Boettcher, and P. N. Meisinger, J. Math. Phys. 0022-2488 40, 2210 (1999); F. M. Fernandez, R. Guardiola, J. Ros, and M. Znojil, J. Phys. A 0305-4470 10.1088/0305-4470/32/17/303 32, 3105 (1999); M. Znojil, J. Phys. A 0305-4470 10.1088/0305-4470/32/24/318 32, 4563 (1999); M. Znojil, Phys. Lett. A 0375-9601 10.1016/S0375-9601(99)00805-1 264, 108 (1999); F. Cannata, G. Junker, and J. Trost, Phys. Lett. A 0375-9601 10.1016/S0375-9601(98)00517-9 246, 219 (1998); B. Bagchi and R. Roy-Choudhury, J. Phys. A 0305-4470 10.1088/0305-4470/33/1/101 33, L1 (2000); P. Dorey, C. Dunning, and R. Tateo, J. Phys. A 0305-4470 10.1088/0305-4470/34/28/102 34, L391 (2001); P. Dorey, C. Dunning, and R. Tateo, J. Phys. A 0305-4470 10.1088/0305-4470/34/28/305 34, 5679 (2001); A. Khare and B. P. Mandal, Phys. Lett. A 0375-9601 10.1016/S0375-9601(00)00409-6 272, 53 (2000); G. Levai and M. Znojil, J. Phys. A 0305-4470 10.1088/0305-4470/33/40/313 33, 7165 (2000); B. Bagchi and C. Quesne, Phys. Lett. A 0375-9601 10.1016/S0375-9601(02)00689-8 300, 18 (2002); A. Mostafazadeh, J. Math. Phys. 0022-2488 10.1063/1.1418246 43, 205 (2003); A. Mostafazadeh, J. Math. Phys. 0022-2488 10.1063/1.1461427 43, 2814 (2003); A. Mostafazadeh, J. Math. Phys. 0022-2488 10.1063/1.1489072 43, 3944 (2003); Z. Ahmad, Phys. Lett. A 0375-9601 10.1016/S0375-9601(01)00622-3 290, 19 (2001); R. N. Deb, A. Khare, and B. Dutta Roy, Phys. Lett. A 307, 215 (2003).
16. C. M. Bender and S. Boettcher, J. Phys. A 0305-4470 10.1088/0305-4470/31/ 14/001 31, L273 (1998); C. M. Bender, S. Boettcher, and P. N. Meisinger, J. Math. Phys. 0022-2488 40, 2210 (1999); F. M. Fernandez, R. Guardiola, J. Ros, and M. Znojil, J. Phys. A 0305-4470 10.1088/0305-4470/32/17/303 32, 3105 (1999); M. Znojil, J. Phys. A 0305-4470 10.1088/0305-4470/32/24/318 32, 4563 (1999); M. Znojil, Phys. Lett. A 0375-9601 10.1016/S0375-9601(99)00805-1 264, 108 (1999); F. Cannata, G. Junker, and J. Trost, Phys. Lett. A 0375-9601 10.1016/S0375-9601(98)00517-9 246, 219 (1998); B. Bagchi and R. Roy-Choudhury, J. Phys. A 0305-4470 10.1088/0305-4470/33/1/101 33, L1 (2000); P. Dorey, C. Dunning, and R. Tateo, J. Phys. A 0305-4470 10.1088/0305-4470/34/28/102 34, L391 (2001); P. Dorey, C. Dunning, and R. Tateo, J. Phys. A 0305-4470 10.1088/0305-4470/34/28/305 34, 5679 (2001); A. Khare and B. P. Mandal, Phys. Lett. A 0375-9601 10.1016/S0375-9601(00)00409-6 272, 53 (2000); G. Levai and M. Znojil, J. Phys. A 0305-4470 10.1088/0305-4470/33/40/313 33, 7165 (2000); B. Bagchi and C. Quesne, Phys. Lett. A 0375-9601 10.1016/S0375-9601(02)00689-8 300, 18 (2002); A. Mostafazadeh, J. Math. Phys. 0022-2488 10.1063/1.1418246 43, 205 (2003); A. Mostafazadeh, J. Math. Phys. 0022-2488 10.1063/1.1461427 43, 2814 (2003); A. Mostafazadeh, J. Math. Phys. 0022-2488 10.1063/1.1489072 43, 3944 (2003); Z. Ahmad, Phys. Lett. A 0375-9601 10.1016/S0375-9601(01)00622-3 290, 19 (2001); R. N. Deb, A. Khare, and B. Dutta Roy, Phys. Lett. A 307, 215 (2003).
17. C. M. Bender and S. Boettcher, J. Phys. A 0305-4470 10.1088/0305-4470/31/ 14/001 31, L273 (1998); C. M. Bender, S. Boettcher, and P. N. Meisinger, J. Math. Phys. 0022-2488 40, 2210 (1999); F. M. Fernandez, R. Guardiola, J. Ros, and M. Znojil, J. Phys. A 0305-4470 10.1088/0305-4470/32/17/303 32, 3105 (1999); M. Znojil, J. Phys. A 0305-4470 10.1088/0305-4470/32/24/318 32, 4563 (1999); M. Znojil, Phys. Lett. A 0375-9601 10.1016/S0375-9601(99)00805-1 264, 108 (1999); F. Cannata, G. Junker, and J. Trost, Phys. Lett. A 0375-9601 10.1016/S0375-9601(98)00517-9 246, 219 (1998); B. Bagchi and R. Roy-Choudhury, J. Phys. A 0305-4470 10.1088/0305-4470/33/1/101 33, L1 (2000); P. Dorey, C. Dunning, and R. Tateo, J. Phys. A 0305-4470 10.1088/0305-4470/34/28/102 34, L391 (2001); P. Dorey, C. Dunning, and R. Tateo, J. Phys. A 0305-4470 10.1088/0305-4470/34/28/305 34, 5679 (2001); A. Khare and B. P. Mandal, Phys. Lett. A 0375-9601 10.1016/S0375-9601(00)00409-6 272, 53 (2000); G. Levai and M. Znojil, J. Phys. A 0305-4470 10.1088/0305-4470/33/40/313 33, 7165 (2000); B. Bagchi and C. Quesne, Phys. Lett. A 0375-9601 10.1016/S0375-9601(02)00689-8 300, 18 (2002); A. Mostafazadeh, J. Math. Phys. 0022-2488 10.1063/1.1418246 43, 205 (2003); A. Mostafazadeh, J. Math. Phys. 0022-2488 10.1063/1.1461427 43, 2814 (2003); A. Mostafazadeh, J. Math. Phys. 0022-2488 10.1063/1.1489072 43, 3944 (2003); Z. Ahmad, Phys. Lett. A 0375-9601 10.1016/S0375-9601(01)00622-3 290, 19 (2001); R. N. Deb, A. Khare, and B. Dutta Roy, Phys. Lett. A 307, 215 (2003).
18. C. M. Bender and S. Boettcher, J. Phys. A 0305-4470 10.1088/0305-4470/31/ 14/001 31, L273 (1998); C. M. Bender, S. Boettcher, and P. N. Meisinger, J. Math. Phys. 0022-2488 40, 2210 (1999); F. M. Fernandez, R. Guardiola, J. Ros, and M. Znojil, J. Phys. A 0305-4470 10.1088/0305-4470/32/17/303 32, 3105 (1999); M. Znojil, J. Phys. A 0305-4470 10.1088/0305-4470/32/24/318 32, 4563 (1999); M. Znojil, Phys. Lett. A 0375-9601 10.1016/S0375-9601(99)00805-1 264, 108 (1999); F. Cannata, G. Junker, and J. Trost, Phys. Lett. A 0375-9601 10.1016/S0375-9601(98)00517-9 246, 219 (1998); B. Bagchi and R. Roy-Choudhury, J. Phys. A 0305-4470 10.1088/0305-4470/33/1/101 33, L1 (2000); P. Dorey, C. Dunning, and R. Tateo, J. Phys. A 0305-4470 10.1088/0305-4470/34/28/102 34, L391 (2001); P. Dorey, C. Dunning, and R. Tateo, J. Phys. A 0305-4470 10.1088/0305-4470/34/28/305 34, 5679 (2001); A. Khare and B. P. Mandal, Phys. Lett. A 0375-9601 10.1016/S0375-9601(00)00409-6 272, 53 (2000); G. Levai and M. Znojil, J. Phys. A 0305-4470 10.1088/0305-4470/33/40/313 33, 7165 (2000); B. Bagchi and C. Quesne, Phys. Lett. A 0375-9601 10.1016/S0375-9601(02)00689-8 300, 18 (2002); A. Mostafazadeh, J. Math. Phys. 0022-2488 10.1063/1.1418246 43, 205 (2003); A. Mostafazadeh, J. Math. Phys. 0022-2488 10.1063/1.1461427 43, 2814 (2003); A. Mostafazadeh, J. Math. Phys. 0022-2488 10.1063/1.1489072 43, 3944 (2003); Z. Ahmad, Phys. Lett. A 0375-9601 10.1016/S0375-9601(01)00622-3 290, 19 (2001); R. N. Deb, A. Khare, and B. Dutta Roy, Phys. Lett. A 307, 215 (2003).
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