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TMF, 1984, Volume 61, Number 1, Pages 17–28 (Mi tmf5592)  

This article is cited in 25 scientific papers (total in 25 papers)

Supersymmetric mechanics: A new look at the equivalence of quantum systems

A. A. Andrianov, N. V. Borisov, M. V. Ioffe, M. I. Eides

Abstract: The structure of supersymmetric quantum-mechanical systems for arbitrary number of dimensions of space is investigated. The generalized factorization method is shown to have a supersymmetrie origin, and this makes it possible to establish an analytic correspondence between the spectra and wave functions of different quantum Hamiltonians.

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English version:
Theoretical and Mathematical Physics, 1984, 61:1, 965–972

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Received: 24.11.1983

Citation: A. A. Andrianov, N. V. Borisov, M. V. Ioffe, M. I. Eides, “Supersymmetric mechanics: A new look at the equivalence of quantum systems”, TMF, 61:1 (1984), 17–28; Theoret. and Math. Phys., 61:1 (1984), 965–972

Citation in format AMSBIB
\by A.~A.~Andrianov, N.~V.~Borisov, M.~V.~Ioffe, M.~I.~Eides
\paper Supersymmetric mechanics: A new look at the equivalence of quantum systems
\jour TMF
\yr 1984
\vol 61
\issue 1
\pages 17--28
\jour Theoret. and Math. Phys.
\yr 1984
\vol 61
\issue 1
\pages 965--972

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    This publication is cited in the following articles:
    1. A. A. Andrianov, N. V. Borisov, M. V. Ioffe, “Factorization method and Darboux transformation for multidimensional Hamiltonians”, Theoret. and Math. Phys., 61:2 (1984), 1078–1088  mathnet  crossref  mathscinet  isi
    2. V. P. Berezovoi, A. I. Pashnev, “Supersymmetric quantum mechanics and rearrangement of the spectra of Hamiltonians”, Theoret. and Math. Phys., 70:1 (1987), 102–107  mathnet  crossref  mathscinet  isi
    3. A. A. Andrianov, N. V. Borisov, M. V. Ioffe, “Scattering theory for supersymmetric Hamiltonian and supersymmetry of nuclear interactions”, Theoret. and Math. Phys., 72:1 (1987), 748–758  mathnet  crossref  mathscinet  isi
    4. B. S. Pavlov, “The theory of extensions and explicitly-soluble models”, Russian Math. Surveys, 42:6 (1987), 127–168  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. M. D. Vardiashvili, V. A. Matveev, L. A. Slepchenko, “Coulomb problem in supersymmetric quantum mechanics”, Theoret. and Math. Phys., 78:2 (1989), 211–216  mathnet  crossref  mathscinet  isi
    6. N. V. Borisov, K. N. Il'inskii, V. M. Uzdin, “Generalized algebras of supersymmetric quantum mechanics”, Theoret. and Math. Phys., 94:3 (1993), 294–299  mathnet  crossref  mathscinet  zmath  isi
    7. B. G. Idlis, M. M. Musakhanov, M. Sh. Usmanov, “Application of supersymmetry and factorization methods to solution of Dirac and Schrödinger equations”, Theoret. and Math. Phys., 101:1 (1994), 1191–1199  mathnet  crossref  mathscinet  zmath  isi
    8. A. A. Andrianov, M. V. Ioffe, D. N. Nishnianidze, “Polynomial supersymmetry and dynamical symmetries in quantum mechanics”, Theoret. and Math. Phys., 104:3 (1995), 1129–1140  mathnet  crossref  mathscinet  zmath  isi
    9. Andrey M. Pupasov, Boris F. Samsonov, “Exact Propagators for Soliton Potentials”, SIGMA, 1 (2005), 020, 7 pp.  mathnet  crossref  mathscinet  zmath
    10. A. A. Andrianov, A. V. Sokolov, “Factorization of nonlinear supersymmetry in one-dimensional Quantum Mechanics I: general classification of reducibility and analysis of third-order algebra”, J. Math. Sci. (N. Y.), 143:1 (2007), 2707–2722  mathnet  crossref  mathscinet  zmath  elib  elib
    11. M. D. Vereschagin, S. D. Vereschagin, A. V. Yurov, “Trekhmernoe preobrazovanie Mutara”, Matem. modelirovanie, 18:5 (2006), 111–125  mathnet  mathscinet  zmath
    12. A. V. Sokolov, “Factorization of nonlinear supersymmetry in one-dimensional quantum mechanics II: proofs of theorems on reducibility”, J. Math. Sci. (N. Y.), 151:2 (2008), 2924–2936  mathnet  crossref  mathscinet  elib
    13. M. A. González León, J. Mateos Guilarte, M. de la Torre Mayado, “Two-Dimensional Supersymmetric Quantum Mechanics: Two Fixed Centers of Force”, SIGMA, 3 (2007), 124, 24 pp.  mathnet  crossref  mathscinet  zmath
    14. Andrianov, AA, “Non-linear supersymmetry for non-Hermitian, non-diagonalizable Hamiltonians: I. General properties”, Nuclear Physics B, 773:3 (2007), 107  crossref  isi
    15. Alexander A. Andrianov, Andrey V. Sokolov, “Hidden Symmetry from Supersymmetry in One-Dimensional Quantum Mechanics”, SIGMA, 5 (2009), 064, 26 pp.  mathnet  crossref  mathscinet
    16. A. V. Sokolov, “Faktorizatsiya nelineinoi supersimmetrii v odnomernoi kvantovoi mekhanike III: tonkaya klassifikatsiya neprivodimykh spletayuschikh operatorov”, Voprosy kvantovoi teorii polya i statisticheskoi fiziki. 21, Zap. nauchn. sem. POMI, 374, POMI, SPb., 2010, 213–249  mathnet
    17. Mikhail V. Ioffe, “Supersymmetrical Separation of Variables in Two-Dimensional Quantum Mechanics”, SIGMA, 6 (2010), 075, 10 pp.  mathnet  crossref  mathscinet
    18. Alexander A. Andrianov, Andrey V. Sokolov, “Resolutions of Identity for Some Non-Hermitian Hamiltonians. I. Exceptional Point in Continuous Spectrum”, SIGMA, 7 (2011), 111, 19 pp.  mathnet  crossref  mathscinet
    19. Andrianov A.A. Ioffe M.V., “Nonlinear Supersymmetric Quantum Mechanics: Concepts and Realizations”, J. Phys. A-Math. Theor., 45:50 (2012), 503001  crossref  isi
    20. Schulze-Halberg A., “Darboux Transformations for (1+2)-Dimensional Fokker-Planck Equations with Constant Diffusion Matrix”, J. Math. Phys., 53:10 (2012), 103519  crossref  isi
    21. Gonzalez Leon M.A., Mateos Guilarte J., Senosiain M.J., de la Torre Mayado M., “On the Supersymmetric Spectra of Two Planar Integrable Quantum Systems”, Algebraic Aspects of Darboux Transformations, Quantum Integrable Systems and Supersymmetric Quantum Mechanics, Contemporary Mathematics, 563, eds. AcostaHumanez P., Finkel F., Kamran N., Olver P., Amer Mathematical Soc, 2012, 73–113  crossref  isi
    22. M. V. Ioffe, E. V. Kolevatova, D. N. Nishnianidze, “Some properties of the shape-invariant two-dimensional Scarf II model”, Theoret. and Math. Phys., 185:1 (2015), 1445–1453  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    23. Ioffe M.V. Kolevatova E.V. Nishnianidze D.N., “Solution of second order supersymmetrical intertwining relations in Minkowski plane”, J. Math. Phys., 57:8 (2016), 082102  crossref  mathscinet  zmath  isi  elib  scopus
    24. Oikonomou V.K., “Low dimensional supersymmetries in SUSY Chern–Simons systems and geometrical implications”, Int. J. Geom. Methods Mod. Phys., 13:6 (2016), 1650083  crossref  mathscinet  zmath  isi  elib  scopus
    25. Assi I.A. Bahlouli H. Hamdan A., “Exact Solvability of Two New 3D and 1D Non-Relativistic Potentials Within the Tra Framework”, Mod. Phys. Lett. A, 33:32 (2018), 1850187  crossref  mathscinet  zmath  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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