Nonlinear pseudo-supersymmetry in the framework of N-fold supersymmetry

Journal of Physics A: Mathematical and General

Volumn 39, Issue 14, 2006, Pages 3715-3723

  González López, Artemio ^a   Tanaka, Toshiaki ^b  

^a UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

^b TAMKANG UNIVERSITY   (Taiwan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33645153895     PISSN: 03054470     EISSN: 13616447     Source Type: Journal    
DOI: 10.1088/0305-4470/39/14/014     Document Type: Article

References (31)

1. Bender C M and Boettcher S 1998 Real spectra in non-Hermitian Hamiltonians having symmetry Phys. Rev. Lett. 80 5243-6 (Preprint physics/9712001)
2. Shin K C 2005 Eigenvalues of -symmetric oscillators with polynomial potentials J. Phys. A: Math. Gen. 38 6147-66 (Preprint math.SP/0407018)
3. 2- dynamo, Squire equation and -symmetric interpolation between square well and harmonic oscillator J. Math. Phys. 46 063504 (Preprint math-ph/0501069)
4. Ghosh P K 2005 Exactly solvable non-Hermitian Jaynes-Cummings-type Hamiltonian admitting entirely real spectra from supersymmetry J. Phys. A: Math. Gen. 38 7313-24 (Preprint quant-ph/0501087)
5. Trinh D T 2005 Remarks on -pseudo-norm in -symmetric quantum mechanics J. Phys. A: Math. Gen. 38 3665-78 (Preprint math-ph/0502009)
6. Bagchi B, Quesne C and Roychoudhury R 2005 Pseudo-Hermiticity and some consequences of a generalized quantum condition J. Phys. A: Math. Gen. 38 L647-52 (Preprint quant-ph/0508073)
7. Bender C M, Jones H F and Rivers R J 2005 Dual -symmetric quantum field theories Phys. Lett. B 625 333-40 (Preprint hep-th/0508105)
8. Mostafazadeh A 2002 Pseudo-Hermiticity versus PT symmetry: the necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian J. Math. Phys. 43 205-14 (Preprint math-ph/0107001)
9. Sinha A and Roy P 2005 symmetric models with nonlinear pseudo supersymmetry J. Math. Phys. 46 032102 (Preprint quant-ph/0505221)
10. Andrianov A A and Sokolov A V 2003 Nonlinear supersymmetry in quantum mechanics: algebraic properties and differential representations Nucl. Phys. B 660 25-50 (Preprint hep-th/0301062)
11. Mostafazadeh A 2002 Pseudo-Hermiticity versus PT symmetry: II. A complete characterization of non-Hermitian Hamiltonians with a real spectrum J. Math. Phys. 43 2814-6 (Preprint math-ph/0110016)
12. Mostafazadeh A 2002 Pseudo-Hermiticity versus PT symmetry: III. Equivalence of pseudo-Hermiticity and the presence of antilinear symmetries J. Math. Phys. 43 3944-51 (Preprint math-ph/0203005)
13. Mostafazadeh A 2002 Pseudo-supersymmetric quantum mechanics and isospectral pseudo-Hermitian Hamiltonians Nucl. Phys. B 640 419-34 (Preprint math-ph/0203041)
14. Mostafazadeh A 2002 On the pseudo-Hermiticity of a class of PT-symmetric Hamiltonians in one dimension Mod. Phys. Lett. A 17 1973-7 (Preprint math-ph/0204013)
15. Mostafazadeh A 2002 Pseudo-Hermiticity for a class of nondiagonalizable Hamiltonians J. Math. Phys. 43 6343-52 (Preprint math-ph/0207009)
16. Mostafazadeh A 2003 J. Math. Phys. 44 943 (erratum)
17. Mostafazadeh A 2003 Pseudo-Hermiticity and generalized PT- and CPT-symmetries J. Math. Phys. 44 974-89 (Preprint math-ph/0209018)
18. Mostafazadeh A 2004 Pseudo-unitary operators and pseudo-unitary quantum dynamics J. Math. Phys. 45 932-46 (Preprint math-ph/0302050)
19. Aoyama H, Sato M and Tanaka T 2001 -fold supersymmetry in quantum mechanics: general formalism Nucl. Phys. B 619 105-27 (Preprint quant-ph/0106037)
20. González-López A and Tanaka T 2005 A novel multi-parameter family of quantum systems with partially broken -fold supersymmetry J. Phys. A: Math. Gen. 38 5133-57 (Preprint hep-th/0405079)
21. Aoyama H, Nakayama N, Sato M and Tanaka T 2001 sl(2) construction of type A -fold supersymmetry Phys. Lett. B 519 260-8 (Preprint hep-th/0107048)
22. Tanaka T 2003 Type A -fold supersymmetry and generalized Bender-Dunne polynomials Nucl. Phys. B 662 413-46 (Preprint hep-th/0212276)
23. Turbiner A V 1988 Quasi-exactly-solvable problems and sl(2) algebra Commun. Math. Phys. 118 467-74
24. Bagrov V G and Samsonov B F 1997 Darboux transformation of the Schrödinger equation Phys. Part. Nucl. 28 374-97
25. Samsonov B F 1999 New possibilities for supersymmetry breakdown in quantum mechanics and second-order irreducible Darboux transformations Phys. Lett. A 263 274-80 (Preprint quant-ph/9904009)
26. Fernández C D J, Negro J and Nieto L M 2000 Second-order supersymmetric periodic potentials Phys. Lett. A 275 338-49
27. Fernández C D J, Mielnik B, Rosas-Ortiz O and Samsonov B F 2002 Nonlocal supersymmetric deformations of periodic potentials J. Phys. A: Math. Gen. 35 4279-91 (Preprint quant-ph/0303051)
28. Fernández C D J, Muñoz R and Ramos A 2003 Second order SUSY transformations with 'complex energies' Phys. Lett. A 308 11-6 (Preprint quant-ph/0212026)
29. Tanaka T 2006 -fold supersymmetry in quantum systems with position-dependent mass J. Phys. A: Math. Gen. 39 219-34
30. von Roos O 1983 Position-dependent effective masses in semiconductor theory Phys. Rev. B 27 7547-52
31. Mostafazadeh A 2005 Pseudo-Hermitian description of PT-symmetric systems defined on a complex contour J. Phys. A: Math. Gen. 38 3213-34 (Preprint quant-ph/0410012)