Nonlinear supersymmetry for spectral design in quantum mechanics

Journal of Physics A: Mathematical and General

Volumn 37, Issue 43, 2004, Pages 10297-10321

  Andrianov, A A ^a   Cannata, F ^b  

^a ST PETERSBURG STATE UNIVERSITY   (Russian Federation)

^b INFN SEZIONE DI BOLOGNA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 8744293633     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/37/43/019     Document Type: Conference Paper

References (166)

1. Nicolai H 1976 J. Phys. A: Math. Gen. 9 1497
2. Witten E 1981 Nucl. Phys. B 188 513 Witten E 1982 Nucl. Phys. B 202 253
3. Witten E 1981 Nucl. Phys. B 188 513 Witten E 1982 Nucl. Phys. B 202 253
4. Salomonson P and van Holten J W 1982 Nucl. Phys. B 196 509
5. De Crombrugghe M and Rittenberg V 1983 Ann. Phys., NY 151 99
6. Akulov V P and Pashnev A I 1985 Theor. Math. Phys. 65 1027
7. Cooper F and Freedman B 1983 Ann. Phys., NY 146 262
8. Andrianov A A, Borisov N V and Ioffe M V 1984 JETP Lett. 39 93 Andrianov A A, Borisov N V and Ioffe M V 1984 Phys. Lett. A 105 19 Andrianov A A, Borisov N V and Ioffe M V 1984 Theor. Math. Phys. 61 1078
9. Andrianov A A, Borisov N V and Ioffe M V 1984 JETP Lett. 39 93 Andrianov A A, Borisov N V and Ioffe M V 1984 Phys. Lett. A 105 19 Andrianov A A, Borisov N V and Ioffe M V 1984 Theor. Math. Phys. 61 1078
10. Andrianov A A, Borisov N V and Ioffe M V 1984 JETP Lett. 39 93 Andrianov A A, Borisov N V and Ioffe M V 1984 Phys. Lett. A 105 19 Andrianov A A, Borisov N V and Ioffe M V 1984 Theor. Math. Phys. 61 1078
11. Mielnik B 1984 J. Math. Phys. 25 3387
12. Nieto M M 1984 Phys. Lett. B 145 208
13. Fernández D J C 1984 Lett. Math. Phys. 8 337 (Preprint physics/0006119)
14. Darboux G 1882 C. R. Acad. Sci., Paris 94 1456 (Preprint physics/9908003)
15. Crum M M 1955 Q. J. Math., Oxford 6 121 (Preprint physics/9908019)
16. Delsart J and Lions J L 1957 Comment. Math. Helv. 32 113
17. Krein M G 1957 Dold. Akad. Nauk Tadzhik. SSSR 113 970
18. Faddeev L D 1959 Usp. Mat. Nauk 14 57 Faddeev L D 1963 J. Math. Phys. 4 72 (Engl. Transl.)
19. Faddeev L D 1959 Usp. Mat. Nauk 14 57 Faddeev L D 1963 J. Math. Phys. 4 72 (Engl. Transl.)
20. Matveev V B and Salle M 1991 Darboux Transformations and Solitons (Berlin: Springer)
21. Schrödinger E 1941 Proc. R. Irish Acad. A 47 53 (Preprint physics/9910003)
22. Infeld L and Hull T E 1951 Rev. Mod. Phys. 23 21
23. Andrianov A A, Borisov N V, Eides M I and Ioffe M V 1984 Theor. Math. Phys. 61 965 Andrianov A A, Borisov N V, Eides M I and Ioffe M V 1985 Phys. Lett. A 109 143
24. Andrianov A A, Borisov N V, Eides M I and Ioffe M V 1984 Theor. Math. Phys. 61 965 Andrianov A A, Borisov N V, Eides M I and Ioffe M V 1985 Phys. Lett. A 109 143
25. Sukumar C V 1985 J. Phys. A: Math. Gen. 18 L57 Sukumar C V 1985 J. Phys. A: Math. Gen. 18 2917
26. Sukumar C V 1985 J. Phys. A: Math. Gen. 18 L57 Sukumar C V 1985 J. Phys. A: Math. Gen. 18 2917
27. Balantekin A B 1985 Ann. Phys., NY 164 277
28. Pursey D L 1986 Phys. Rev. D 33 2267
29. Berezovoi V N and Pashnev A I 1987 Theor. Math. Phys. 70 102
30. Alves N A and Drigo Filho E 1988 J. Phys. A: Math. Gen. 21 3215
31. Drigo Filho E and Ricotta R M 1989 Mod. Phys. Lett. A 4 2283
32. Keung W Y, Sukhatme U P, Wang Q and Imbo T 1989 J. Phys. A: Math. Gen. 22 987
33. Anderson A and Camporesi R 1990 Commun. Math. Phys. 130 61
34. Cervero J M 1991 Phys. Lett. A 153 1
35. Shabat A B 1992 Inverse Problems 8 303
36. Andreev V, Kharchev S and Shmakova M 1993 Phys. Lett. A 181 142
37. Veselov A P and Shabat A B 1993 Funct. Anal. Appl. 27 81
38. Adler V E 1994 Theor. Math. Phys. 101 1381
39. Stahlhofen A 1995 Phys. Rev. A 51 934
40. Fernández D J C, Hussin V and Mielnik B 1998 Phys. Lett. A 244 309
41. Akulov V P and Duplij S 1998 Nilpotent marsh and SUSY QM Preprint hep-th/9809089
42. Milanovic V and Ikonic Z 1999 J. Phys. A: Math. Gen. 32 7001
43. Rosu H 1999 Nuovo Cimenta B 114 723
44. Mielnik B, Nieto L M and Rosas-Ortiz O 2000 Phys. Lett. A 269 70
45. Kirchberg A, Lange J D, Pisani P A G and Wipf A 2003 Ann. Phys., NY 303 359
46. Sukumar C V 1985 J. Phys. A: Math. Gen. 18 2937
47. Kwong W and Rosner J L 1986 Prog. Theor. Phys. Suppl. 86 366
48. Andrianov A A, Borisov N V and Ioffe M V 1986 Phys. Lett. B 181 141 Andrianov A A, Borisov N V and Ioffe M V 1986 Theor. Math. Phys. 72 748
49. Andrianov A A, Borisov N V and Ioffe M V 1986 Phys. Lett. B 181 141 Andrianov A A, Borisov N V and Ioffe M V 1986 Theor. Math. Phys. 72 748
50. Baye D 1987 Phys. Rev. Lett. 58 2738
51. Cooper F, Ginocchio J N and Wipf A 1988 Phys. Lett. A 129 145
52. Amado R D, Cannata F and Dedonder J-P 1988 Phys. Rev. Lett. 61 2901 Amado R D, Cannata F and Dedonder J-P 1988 Phys. Rev. A 38 3797 Amado R D, Cannata F and Dedonder J-P 1990 Int. J. Mod. Phys. A 5 3401
53. Amado R D, Cannata F and Dedonder J-P 1988 Phys. Rev. Lett. 61 2901 Amado R D, Cannata F and Dedonder J-P 1988 Phys. Rev. A 38 3797 Amado R D, Cannata F and Dedonder J-P 1990 Int. J. Mod. Phys. A 5 3401
54. Amado R D, Cannata F and Dedonder J-P 1988 Phys. Rev. Lett. 61 2901 Amado R D, Cannata F and Dedonder J-P 1988 Phys. Rev. A 38 3797 Amado R D, Cannata F and Dedonder J-P 1990 Int. J. Mod. Phys. A 5 3401
55. Khare A and Sukhatme U 1989 J. Phys. A: Math. Gen. 22 2847
56. Pappademos J, Sukhatme U and Pagnamenta A 1993 Phys. Rev. A 48 3525
57. Sparenberg J M and Baye D 1995 J. Phys. A: Math. Gen. 28 5079
58. Levai G, Baye D and Sparenberg J M 1997 J. Phys. A: Math. Gen. 30 8257
59. Samsonov B F and Stancu F 2002 Phys. Rev. C 66 034001
60. Sukumar C V 1986 J. Phys. A: Math. Gen. 19 2297
61. Kumar C N 1987 J. Phys. A: Math. Gen. 20 5397
62. Andrianov A A, Ioffe M V and Spiridonov V P 1993 Phys. Lett. A 174 273
63. Andrianov A A, Cannata F, Dedonder J-P and Ioffe M V 1995 Int. J. Mod. Phys. A 10 2683 (Preprint hep-th/9404061)
64. Andrianov A A, Ioffe M V and Nishnianidze D N 1995 Phys. Lett. A 201 103 (Preprint hep-th/9404120)
65. Bagrov V G and Samsonov B F 1995 Theor. Math. Phys. 104 1051
66. Andrianov A A, Ioffe M V and Nishnianidze D N 1995 Theor. Math. Phys. 104 1129
67. Spiridonov V 1996 Phys. Rev. A 52 1909
68. Andrianov A A, Cannata F and Ioffe M V 1996 Mod. Phys. Lett. A 11 1417
69. Fernández D J C 1997 Int. J. Mod. Phys. A 12 171 (Preprint quant-ph/9609009)
70. Samsonov B F 1996 Mod. Phys. Lett. A 11 1563 Samsonov B F 1999 Phys. Lett. A 263 274
71. Samsonov B F 1996 Mod. Phys. Lett. A 11 1563 Samsonov B F 1999 Phys. Lett. A 263 274
72. Robnik M 1997 J. Phys. A: Math. Gen. 30 1287
73. Junker J and Roy P 1998 Phys. At. Nucl. 61 1736
74. Bagchi B and Ganguly A 1998 Int. J. Mod. Phys. A 13 3721
75. Rosas-Ortiz J O 1998 J. Phys. A: Math. Gen. 31 L507 Rosas-Ortiz J O 1998 J. Phys. A: Math. Gen. 31 10163
76. Rosas-Ortiz J O 1998 J. Phys. A: Math. Gen. 31 L507 Rosas-Ortiz J O 1998 J. Phys. A: Math. Gen. 31 10163
77. Márquez I F, Negro J and Nieto L M 1998 J. Phys. A: Math. Gen. 31 4115
78. Fernández D J C and Hussin V 1999 J. Phys. A: Math. Gen. 32 3603
79. Aoyama H, Kikuchi H, Okouchi I, Sato M and Wada S 1999 Nucl. Phys. B 553 644
80. Bagchi B, Ganguly A, Bhaumik D and Mitra A 1999 Mod. Phys. Lett. A 14 27
81. Khare A and Sukhatme U 1999 J. Math. Phys. 40 5473
82. Fernández D J C, Negro J and Nieto L M 2000 Phys. Lett. A 275 338
83. Cariñena J F and Ramos A 2000 Mod. Phys. Lett. A 15 1079
84. Aoyama A, Sato M and Tanaka T 2001 Phys. Lett. B 503 423
85. Aoyama A, Sato M and Tanaka T 2001 Nucl. Phys. B 619 105 Cariñena J F, Fernández D J C and Ramos A 2001 Ann. Phys., NY 292 42
86. Aoyama A, Sato M and Tanaka T 2001 Nucl. Phys. B 619 105 Cariñena J F, Fernández D J C and Ramos A 2001 Ann. Phys., NY 292 42
87. Sasaki R and Takasaki K 2001 J. Phys. A: Math. Gen. 34 9533 Sasaki R and Takasaki K 2001 J. Phys. A: Math. Gen. 34 10335 (erratum)
88. Sasaki R and Takasaki K 2001 J. Phys. A: Math. Gen. 34 9533 Sasaki R and Takasaki K 2001 J. Phys. A: Math. Gen. 34 10335 (erratum)
89. Fernández D J C and Rosu H 2001 Phys. Scr. 64 177
90. Dorey P, Dunning C and Tateo R 2001 J. Phys. A: Math. Gen. 34 5679
91. Aoyama H, Nakayama N, Sato M and Tanaka T 2001 Phys. Lett. B 519 260 Aoyama H, Nakayama N, Sato M and Tanaka T 2001 Phys. Lett. B 521 400
92. Aoyama H, Nakayama N, Sato M and Tanaka T 2001 Phys. Lett. B 519 260 Aoyama H, Nakayama N, Sato M and Tanaka T 2001 Phys. Lett. B 521 400
93. Sato M and Tanaka T 2002 J. Math. Phys. 43 3484
94. Klishevich S M and Plyushchay M S 2001 Nucl. Phys. B 606 583 Klishevich S M and Plyushchay M S 2002 Nucl. Phys. B 628 217 Klishevich S M and Plyushchay M S 2002 Nucl. Phys. B 640 481
95. Klishevich S M and Plyushchay M S 2001 Nucl. Phys. B 606 583 Klishevich S M and Plyushchay M S 2002 Nucl. Phys. B 628 217 Klishevich S M and Plyushchay M S 2002 Nucl. Phys. B 640 481
96. Klishevich S M and Plyushchay M S 2001 Nucl. Phys. B 606 583 Klishevich S M and Plyushchay M S 2002 Nucl. Phys. B 628 217 Klishevich S M and Plyushchay M S 2002 Nucl. Phys. B 640 481
97. Tanaka T 2003 Phys. Lett. B 567 100
98. Debergh N, Van den Bossche B and Samsonov B F 2002 Int. J. Mod. Phys. A 17 1577
99. Fernández D J C, Mielnik B, Rosas-Ortiz O and Samsonov B F 2002 Phys. Lett. A 294 168
100. Fernández D J C, Muñoz R and Ramos A 2003 Phys. Lett. A 308 11
101. Andrianov A A and Sokolov A V 2003 Nucl. Phys. B 660 25
102. Anabalon A and Plyushchay M S 2003 Phys. Lett. B 572 202
103. Fernández D J C and Salinas-Hernández E 2003 J. Phys. A: Math. Gen. 36 2537
104. Leiva C and Plyushchay M S 2003 J. High Energy Phys. JHEP10(2003)069
105. Plyushchay M 2004 Nonlinear supersymmetry: from classical to quantum mechanics Preprint hep-th/0402025
106. Ioffe M V and Nishnianidze D N 2004 Phys. Lett. A 327 425
107. Gendenshtein L E and Krive I V 1985 Sov. Phys.-Usp. 28 645
108. Kostelecky V A and Campbell D K 1983 Physica D 15 1
109. Haymaker R W and Rau A R P 1986 Am. J. Phys. 54 928
110. Lahiri A, Roy P K and Bagchi B 1990 Int. J. Mod. Phys. A 5 1383
111. Cooper F, Khare A and Sukhatme U 1995 Phys. Rep. 251 267
112. Junker G 1996 Supersymmetric Methods in Quantum and Statistical Physics (Berlin: Springer)
113. Bagrov V G and Samsonov B F 1997 Phys. Part. Nucl. 28 374
114. Zakharev B N and Chabanov V M 1997 Inverse Problems 13 R47
115. Rosu H C 1998 Short survey of Darboux transformations Preprint quant-ph/9809056
116. Zakharev B N and Chabanov V M 1999 Phys. Part. Nucl. 30 111
117. Bagchi B 2001 Supersymmetry in Quantum and Classical Mechanics (Singapore: World Scientific)
118. De Lima Rodrigues R 2002 The quantum mechanics SUSY algebra: an introductory review Preprint hep-th/0205017
119. Spiridonov V P 2003 The factorization method, self-similar potentials and quantum algebras Preprint hep-th/0302046
120. Rubakov V A and Spiridonov V P 1988 Mod. Phys. Lett. A 3 1337
121. Durand S and Vinet S 1989 Mod. Phys. Lett. A 4 2519
122. Backers J and Debergh N 1990 Nucl. Phys. B 340 767
123. Andrianov A A and Ioffe M V 1991 Phys. Lett. B 255 543
124. Andrianov A A, Ioffe M V, Spiridonov V P and Vinet L 1991 Phys. Lett. B 272 297
125. Plyushchay M 2000 Int. J. Mod. Phys. A 15 3679
126. Smilga A V 2003 Weak supersymmetry Preprint hep-th/0311023
127. Ivanov E V, Krivonos S O and Pashnev AI 1991 Class. Quantum Grav. 8 19
128. Gantmacher F R 1998 The Theory of Matrices (Providence, RI: AMS Chelsea)
129. Naimark M A 1967 Linear Differential Operators (New York: Ungar)
130. Turbiner A V 1988 Commun. Math. Phys. 118 467
131. Shifman M A 1989 Int. J. Mod. Phys. A 4 3305
132. Andrianov A A, Cannata F, Ioffe M and Nishnianidze D 2000 Phys. Lett. A 266 341 (Preprint quant-ph/9902057)
133. Flügge S 1971 Practical Quantum Mechanics (Berlin: Springer) Zakhariev B N and Suzko A A 1990 Direct and Inverse Methods (Berlin: Springer)
134. Flügge S 1971 Practical Quantum Mechanics (Berlin: Springer) Zakhariev B N and Suzko A A 1990 Direct and Inverse Methods (Berlin: Springer)
135. Fushchych W I and Nikitin A G 1997 J. Math. Phys. 38 5944
136. Bagrov V G and Samsonov B F 1996 Phys. Lett. A 210 60
137. Sergheyev A 1998 On time-dependent symmetries of Schrödinger equation Preprint math.AP/9802124
138. Finkel F, González-López A, Kamran N and Rodríguez M A 1999 J. Math. Phys. 40 3268
139. Cannata F, Ioffe M, Junker G and Nishnianidze D 1999 J. Phys. A: Math. Gen. 32 3583
140. Beckers J, Debergh N and Gotti C 1998 Helv. Phys. Acta 71 214
141. Boyer C P 1974 Helv. Phys. Acta 47 589
142. Okubo S 2003 Global symmetries of time-dependent Schrodinger equations Preprint math-ph/0303017
143. Bluman G and Shtelen V 1996 J. Phys. A: Math. Gen. 29 4473
144. Miller W Jr 1977 Symmetry and Separation of Variables (London: Addison-Wesley) chapter 2.1
145. Galindo A and Pascual P 1990 Quantum Mechanics I (Berlin: Springer) chapter 17
146. Fernández D J C and Russin V 2001 Polynomial Heisenberg algebras and higher order supersymmetry Preprint quant-ph/0011004
147. Englefield M J 1988 J. Stat. Phys. 52 369
148. Cannata F and Ioffe M V 1992 Phys. Lett. B 278 399 Cannata F and Ioffe M V 1993 J. Phys. A: Math. Gen. 26 L89
149. Cannata F and Ioffe M V 1992 Phys. Lett. B 278 399 Cannata F and Ioffe M V 1993 J. Phys. A: Math. Gen. 26 L89
150. Andrianov A A, Cannata F, Ioffe M V and Nishnianidze D N 1997 J. Phys. A: Math. Gen. 30 5037
151. Das T K and Chakrabarti B 1999 J. Phys. A: Math. Gen. 32 2387
152. De Lima Rodrigues R and Vaidya A N 2003 SUSY QM via 2×2 matrix superpotential Preprint hep-th/0308189
153. Andrianov A A, Cannata F, Ioffe M V and Nishnianidze D N 1996 Higher order SUSY in quantum mechanics and integrability of two-dimensional Hamiltonians Preprint solv-int/9605007 Andrianov A A, Ioffe M V and Nishnianidze D N 1999 J. Phys. A: Math. Gen. 32 4641 Cannata F, Ioffe M V and Nishnianidze D N 2002 J. Phys. A: Math. Gen. 35 1389 Cannata F, Ioffe M V and Nishnianidze D N 2003 Phys. Lett. A 310 344 Ioffe M V 2004 SUSY-approach for investigation of two-dimensional quantum mechanical systems J. Phys. A: Math. Gen. 37 10363-74
154. Andrianov A A, Cannata F, Ioffe M V and Nishnianidze D N 1996 Higher order SUSY in quantum mechanics and integrability of two-dimensional Hamiltonians Preprint solv-int/9605007 Andrianov A A, Ioffe M V and Nishnianidze D N 1999 J. Phys. A: Math. Gen. 32 4641 Cannata F, Ioffe M V and Nishnianidze D N 2002 J. Phys. A: Math. Gen. 35 1389 Cannata F, Ioffe M V and Nishnianidze D N 2003 Phys. Lett. A 310 344 Ioffe M V 2004 SUSY-approach for investigation of two-dimensional quantum mechanical systems J. Phys. A: Math. Gen. 37 10363-74
155. Andrianov A A, Cannata F, Ioffe M V and Nishnianidze D N 1996 Higher order SUSY in quantum mechanics and integrability of two-dimensional Hamiltonians Preprint solv-int/9605007 Andrianov A A, Ioffe M V and Nishnianidze D N 1999 J. Phys. A: Math. Gen. 32 4641 Cannata F, Ioffe M V and Nishnianidze D N 2002 J. Phys. A: Math. Gen. 35 1389 Cannata F, Ioffe M V and Nishnianidze D N 2003 Phys. Lett. A 310 344 Ioffe M V 2004 SUSY-approach for investigation of two-dimensional quantum mechanical systems J. Phys. A: Math. Gen. 37 10363-74
156. Andrianov A A, Cannata F, Ioffe M V and Nishnianidze D N 1996 Higher order SUSY in quantum mechanics and integrability of two-dimensional Hamiltonians Preprint solv-int/9605007 Andrianov A A, Ioffe M V and Nishnianidze D N 1999 J. Phys. A: Math. Gen. 32 4641 Cannata F, Ioffe M V and Nishnianidze D N 2002 J. Phys. A: Math. Gen. 35 1389 Cannata F, Ioffe M V and Nishnianidze D N 2003 Phys. Lett. A 310 344 Ioffe M V 2004 SUSY-approach for investigation of two-dimensional quantum mechanical systems J. Phys. A: Math. Gen. 37 10363-74
157. Andrianov A A, Cannata F, Ioffe M V and Nishnianidze D N 1996 Higher order SUSY in quantum mechanics and integrability of two-dimensional Hamiltonians Preprint solv-int/9605007 Andrianov A A, Ioffe M V and Nishnianidze D N 1999 J. Phys. A: Math. Gen. 32 4641 Cannata F, Ioffe M V and Nishnianidze D N 2002 J. Phys. A: Math. Gen. 35 1389 Cannata F, Ioffe M V and Nishnianidze D N 2003 Phys. Lett. A 310 344 Ioffe M V 2004 SUSY-approach for investigation of two-dimensional quantum mechanical systems J. Phys. A: Math. Gen. 37 10363-74
158. Cannata F, Junker G and Trost J 1998 Phys. Lett. A 246 219
159. Andrianov A A, Cannata F, Dedonder J-P and Ioffe M V 1999 Int. J. Mod. Phys. A 14 2675
160. Ramírez A and Mielnik B 2003 Rev. Mex. Fis. 49 S2 130
161. Rosas-Ortiz O and Muñoz R 2003 J. Phys. A: Math. Gen. 36 8497
162. Bender C, Brod J, Refig A and Reuter M 2004 The C operator in PT-symmetric quantum theories Preprint quant-ph/0402026 (and references therein)
163. Mostafazadeh A 2002 Nucl. Phys. B 640 419 Mostafazadeh A 2002 J. Math. Phys. 43 6343 Mostafazadeh A 2003 J. Math. Phys. 44 943 (erratum)
164. Mostafazadeh A 2002 Nucl. Phys. B 640 419 Mostafazadeh A 2002 J. Math. Phys. 43 6343 Mostafazadeh A 2003 J. Math. Phys. 44 943 (erratum)
165. Mostafazadeh A 2002 Nucl. Phys. B 640 419 Mostafazadeh A 2002 J. Math. Phys. 43 6343 Mostafazadeh A 2003 J. Math. Phys. 44 943 (erratum)
166. Znojil M, Cannata F, Bagchi B and Roychoudhury R 2000 Phys. Lett. B 483 284