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TMF, 1984, Volume 61, Number 2, Pages 183–198 (Mi tmf5684)  

This article is cited in 27 scientific papers (total in 27 papers)

Factorization method and Darboux transformation for multidimensional Hamiltonians

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


Abstract: A multidimensional generalization of the factorization and Darboux transformation which makes it possible to find connections between the spectra and eigenfunctions of quantum Hamiltonians is investigated. Multidimensional Hamiltonians whose spectra differ by one discrete level are constructed.

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English version:
Theoretical and Mathematical Physics, 1984, 61:2, 1078–1088

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Received: 16.01.1984

Citation: A. A. Andrianov, N. V. Borisov, M. V. Ioffe, “Factorization method and Darboux transformation for multidimensional Hamiltonians”, TMF, 61:2 (1984), 183–198; Theoret. and Math. Phys., 61:2 (1984), 1078–1088

Citation in format AMSBIB
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\paper Factorization method and Darboux transformation for multidimensional Hamiltonians
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\vol 61
\issue 2
\pages 183--198
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\jour Theoret. and Math. Phys.
\yr 1984
\vol 61
\issue 2
\pages 1078--1088
\crossref{https://doi.org/10.1007/BF01029109}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. A. Andrianov, N. V. Borisov, M. V. Ioffe, M. I. Eides, “Supersymmetric mechanics: A new look at the equivalence of quantum systems”, Theoret. and Math. Phys., 61:1 (1984), 965–972  mathnet  crossref  mathscinet  isi
    2. V. G. Budanov, “Methods of weyl representation of the phase space and canonical transformations. II”, Theoret. and Math. Phys., 64:1 (1985), 656–666  mathnet  crossref  mathscinet  isi
    3. O. B. Zaslavskii, V. V. Ulyanov, “Periodic effective potentials for spin systems and new exact solutions of the one-dimensional Schrödinger equation for the energy bands”, Theoret. and Math. Phys., 71:2 (1987), 520–528  mathnet  crossref  mathscinet  isi
    4. 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
    5. 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
    6. 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
    7. 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
    8. M. D. Vereschagin, S. D. Vereschagin, A. V. Yurov, “Trekhmernoe preobrazovanie Mutara”, Matem. modelirovanie, 18:5 (2006), 111–125  mathnet  mathscinet  zmath
    9. 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
    10. 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
    11. Andrianov, AA, “Non-linear supersymmetry for non-Hermitian, non-diagonalizable Hamiltonians: I. General properties”, Nuclear Physics B, 773:3 (2007), 107  crossref  isi
    12. Kouichi Takemura, “Towards Finite-Gap Integration of the Inozemtsev Model”, SIGMA, 3 (2007), 038, 17 pp.  mathnet  crossref  mathscinet  zmath
    13. Cannata, F, “Three-dimensional solutions of supersymmetrical intertwining relations and pairs of isospectral Hamiltonians”, Journal of Mathematical Physics, 50:5 (2009), 052105  crossref  isi
    14. Alexander A. Andrianov, Andrey V. Sokolov, “Hidden Symmetry from Supersymmetry in One-Dimensional Quantum Mechanics”, SIGMA, 5 (2009), 064, 26 pp.  mathnet  crossref  mathscinet
    15. Mikhail V. Ioffe, “Supersymmetrical Separation of Variables in Two-Dimensional Quantum Mechanics”, SIGMA, 6 (2010), 075, 10 pp.  mathnet  crossref  mathscinet
    16. Fernandez C D.J., “Supersymmetric Quantum Mechanics”, Advanced Summer School in Physics 2009: Frontiers in Contemporary Physics, 5th Edition, AIP Conference Proceedings, 1287, 2010, 3–36  isi
    17. Nicolás Fernández-García, Oscar Rosas-Ortiz, “Rectangular Potentials in a Semi-Harmonic Background: Spectrum, Resonances and Dwell Time”, SIGMA, 7 (2011), 044, 17 pp.  mathnet  crossref  mathscinet
    18. M. Gianfreda, G. Landolfi, “Wave packets and statistics concerned with SUSY-QM partners of Paul trap Hamiltonians”, Theoret. and Math. Phys., 168:1 (2011), 924–938  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    19. 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
    20. 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, ed. AcostaHumanez P. Finkel F. Kamran N. Olver P., Amer Mathematical Soc, 2012, 73–113  crossref  isi
    21. Andrianov A.A. Ioffe M.V., “Nonlinear Supersymmetric Quantum Mechanics: Concepts and Realizations”, J. Phys. A-Math. Theor., 45:50 (2012), 503001  crossref  isi
    22. 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
    23. A. A. Andrianov, V. A. Andrianov, O. O. Novikov, “CP violation in the models of fermion localization on a domain wall (brane)”, Theoret. and Math. Phys., 175:3 (2013), 735–743  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    24. 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
    25. A. A. Andrianov, A. V. Sokolov, “Extended supersymmetry and hidden symmetries in one-dimensional matrix quantum mechanics”, Theoret. and Math. Phys., 186:1 (2016), 2–20  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    26. 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
    27. Hovhannisyan G., Ruff O., Zhang Z., “Higher Dimensional Darboux Transformations”, J. Math. Anal. Appl., 464:1 (2018), 776–805  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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