×

zbMATH — the first resource for mathematics

The finite difference algorithm for higher order supersymmetry. (English) Zbl 1115.81350
Summary: The higher order supersymmetric partners of the Schrödinger’s Hamiltonians can be explicitly constructed by iterating a simple finite difference equation corresponding to the Bäcklund transformation. The method can completely replace the Crum determinants. Its limiting, differential case offers some new operational advantages.

MSC:
81Q60 Supersymmetry and quantum mechanics
81U15 Exactly and quasi-solvable systems arising in quantum theory
81-08 Computational methods for problems pertaining to quantum theory
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] B.N. Zakhariev, V.M. Chabanov, Inverse Problems 13, R 47 (1997). · Zbl 0896.35116
[2] E. Schrödinger, Proc. R. Irish, Acad. A 46 (1940) 183.
[3] P.A.M. Dirac, The Principles of Quantum Mechanics, Oxford University Press, 1947. · Zbl 0030.04801
[4] Infeld, L; Hull, T.E, Rev. mod. phys., 23, 21, (1951)
[5] Mielnik, B, J. math. phys., 25, 3387, (1984)
[6] Fernández, D.J.C, Lett. math. phys., 8, 337, (1984)
[7] Nieto, M.M, Phys. lett. B, 145, 208, (1984)
[8] Darboux, G; Acad, C.R, Sci. Paris, 94, 1456, (1882)
[9] Andrianov, A.A; Borisov, N.V; Ioffe, M.V, Theor. math. phys., 61, 1078, (1985)
[10] Crum, M.M, Quart. J. math., 6, 121, (1955)
[11] Krein, M.G, Dokl. acad. nauk. SSSR, 113, 970, (1957)
[12] Adler, M; Moser, J, Commun. math. phys., 61, 1, (1978)
[13] Boya, L.J, Eur. J. phys., 9, 139, (1988)
[14] Alves, N.A; Drigo Filho, E, J. phys. A, 21, 3215, (1988)
[15] Fernández, D.J.C; Negro, J; del Olmo, M.A, Ann. phys., 252, 386, (1996)
[16] D.J.C. Fernández, Master Thesis, Phys. Department, CINVESTAV-IPN (1984).
[17] Sukumar, C.V, J. phys. A, 19, 2297, (1986)
[18] Veselov, A.P; Shabat, A.B, Funct. anal. appl., 27, 1, (1993)
[19] Andrianov, A.A; Ioffe, M.V; Cannata, F; Dedonder, J.-P, Int. J. mod. phys. A, 10, 2683, (1995)
[20] Eleonsky, V.M; Korolev, V.G, J. phys. A, 28, 4973, (1995)
[21] Eleonsky, V.M; Korolev, V.G, J. phys. A, 29, 241, (1996), L
[22] Eleonsky, V.M; Korolev, V.G, Phys. rev. A, 55, 2580, (1997)
[23] Samsonov, B.F, J. phys. A, 28, 6989, (1995)
[24] Samsonov, B.F, Mod. phys. lett. A, 11, 1563, (1996)
[25] Bagrov, V.G; Samsonov, B.F, Theor. math. phys., 104, 356, (1995)
[26] Bagrov, V.G; Samsonov, B.F, J. phys. A, 29, 1011, (1996)
[27] Bagrov, V.G; Samsonov, B.F, Phys. part. nucl., 28, 374, (1997)
[28] Fernández C, D.J, Int. J. mod. phys. A, 12, 171, (1997)
[29] Fernández, D.J.C; Hussin, V; Mielnik, B, Phys. lett. A, 244, 1, (1998)
[30] Fernández, D.J.C; Hussin, V, J. phys. A: math. gen., 32, 3603, (1999)
[31] Fernández, D.J.C; Glasser, M.L; Nieto, L.M, Phys. lett. A, 240, 15, (1998)
[32] Rosas-Ortiz, J.O, J. phys. A, 31, 507, (1998), L
[33] Rosas-Ortiz, J.O, J. phys. A, 31, 10163, (1998)
[34] C. Rogers, W.F. Shadwick, Bäcklund Transformations and Their Applicatios, Academic Press, New York, 1984.
[35] B.N. Zakhariev, A. A Suzko, Direct and Inverse Problems, Springer, Berlin, 1990. · Zbl 0636.35002
[36] V.B. Matveev, M.A. Salle, Darboux Transformations and Solitons, Springer, Berlin, 1991. · Zbl 0744.35045
[37] Stahlhofen, A, Phys. rev. A, 51, 934, (1995)
[38] Adler, V.E, Funct. anal. appl., 27, 79, (1993)
[39] Adler, V.E, Physica D, 73, 335, (1994)
[40] Wahlquist, H.D; Estabrook, F.B, Phys. rev. lett., 31, 1386, (1973)
[41] G.L. Lamb, Elements of Soliton Theory, Wiley, New York, 1984. · Zbl 0445.35001
[42] Cooper, F; Khare, A; Sukhatme, U, Phys. rep., 251, 267, (1995)
[43] Leble, S.B, Computers math. appl., 35, 73, (1998)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.