González López, ArtemioTanaka, Toshiaki2023-06-202023-06-202004-04-22[1] A.V. Turbiner, A.G. Ushveridze, Phys. Lett. A 126 (1987) 181. [2] M.A. Shifman, Int. J. Mod. Phys. A 4 (1989) 2897. [3] A.G. Ushveridze, Quasi-Exactly Solvable Models in Quantum Mechanics, IOP, Bristol, 1994. [4] A. González-López, N. Kamran, P.J. Olver, Contemp. Math. 160 (1994) 113. [5] A.A. Andrianov, M.V. Ioffe, V.P. Spiridonov, Phys. Lett. A 174 (1993) 273. [6] E. Witten, Nucl. Phys. B 188 (1981) 513. [7] E. Witten, Nucl. Phys. B 202 (1982) 253. [8] A.A. Andrianov, M.V. Ioffe, F. Cannata, J.-P. Dedonder, Int. J. Mod. Phys. A 10 (1995) 2683. [9] A.A. Andrianov, M.V. Ioffe, D.N. Nishnianidze, Phys. Lett. A 201 (1995) 103. [10] A.A. Andrianov, M.V. Ioffe, D.N. Nishnianidze, Theor. Math. Phys. 104 (1995) 1129. [11] V.G. Bagrov, B.F. Samsonov, Theor. Math. Phys. 104 (1995) 1051. [12] B.F. Samsonov, Mod. Phys. Lett. A 11 (1996) 1563. [13] V.G. Bagrov, B.F. Samsonov, Phys. Part. Nucl. 28 (1997) 374. [14] B.F. Samsonov, Phys. Lett. A 263 (1999) 274. [15] D.J. Fernández C., Int. J. Mod. Phys. A 12 (1997) 171. [16] J.O. Rosas-Ortiz, J. Phys. A 31 (1998) 10163. [17] B. Bagchi, A. Ganguly, D. Bhaumik, A. Mitra, Mod. Phys. Lett. A 14 (1999) 27. [18] D.J. Fernández C., V. Hussin, J. Phys. A 32 (1999) 3603. [19] D.J. Fernández C., J. Negro, L.M. Nieto, Phys. Lett. A 275 (2000) 338. [20] M. Plyushchay, Int. J. Mod. Phys. A 15 (2000) 3679. [21] S. Klishevich, M. Plyushchay, Mod. Phys. Lett. A 14 (1999) 2739. [22] H. Aoyama, H. Kikuchi, I. Okouchi, M. Sato, S. Wada, Nucl. Phys. B 553 (1999) 644. [23] H. Aoyama, M. Sato, T. Tanaka, M. Yamamoto, Phys. Lett. B 498 (2001) 117. [24] S.M. Klishevich, M.S. Plyushchay, Nucl. Phys. B 606 (2001) 583. [25] S.M. Klishevich, M.S. Plyushchay, Nucl. Phys. B 616 (2001) 403. [26] P. Dorey, C. Dunning, R. Tateo, J. Phys. A 34 (2001) 5679. [27] P. Dorey, C. Dunning, R. Tateo, J. Phys. A 34 (2001) L391. [28] H. Aoyama, M. Sato, T. Tanaka, Nucl. Phys. B 619 (2001) 105. [29] H. Aoyama, M. Sato, T. Tanaka, Phys. Lett. B 503 (2001) 423. [30] H. Aoyama, N. Nakayama, M. Sato, T. Tanaka, Phys. Lett. B 519 (2001) 260. [31] T. Tanaka, Nucl. Phys. B 662 (2003) 413. [32] A.V. Turbiner, Commun. Math. Phys. 118 (1988) 467. [33] A. González-López, N. Kamran, P.J. Olver, Commun. Math. Phys. 153 (1993) 117. [34] R. Sasaki, K. Takasaki, J. Phys. A 34 (2001) 9533. [35] M. Sato, T. Tanaka, J. Math. Phys. 43 (2002) 3484. [36] F. Cannata, M.V. Ioffe, D.N. Nishnianidze, J. Phys. A 35 (2002) 1389. [37] A.A. Andrianov, A.V. Sokolov, Nucl. Phys. B 660 (2003) 25. [38] G. Post, A. Turbiner, Russ. J. Math. Phys. 3 (1995) 113. [39] T. Tanaka, Ann. Phys. 309 (2004) 239, hep- th/0306174. [40] A. González-López, T. Tanaka, in preparation.0370-269310.1016/j.physletb.2003.10.119https://hdl.handle.net/20.500.14352/51550©2004 Elsevier B.V.. This work was partially supported by the DGI under grant No. BFM2002-02646 (A.G.-L.) and by a JSPS research fellowship (T.T.). One of us (T.T.) would like to thank A.A. Andrianov and M. Sato for useful discussions, as well as all the members of the Departamento de Física Teórica II, Universidad Complutense, for their kind hospitality during his stay.We construct a new family of N -fold supersymmetric systems which is referred to as “type B”. A higher-derivative representation of the N -fold supercharge for this new family is given by a deformation of the type A N -fold supercharge. By utilizing the same method as in the sl(2) construction of type A N -fold supersymmetry, we show that this family includes two of the quasi-solvable models of Post–Turbiner typeengAtribución 3.0 Españajournal articlehttp://dx.doi.org/10.1016/j.physletb.2003.10.119http://www.sciencedirect.comopen access51-73Higher-derivative supersymmetryQuantum-mechanicsNonlinear supersymmetryDarboux transformationSchrodinger-equationBreakdownSystemsSusyFactorizationConstructionFísica-Modelos matemáticosFísica matemática