A. A. Andrianov, M. V. Ioffe, D. N. Nishnianidze, “Polynomial supersymmetry and dynamical symmetries in quantum mechanics”, TMF, 104:3 (1995), 463–478; Theoret. and Math. Phys., 104:3 (1995), 1129

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Teoreticheskaya i Matematicheskaya Fizika, 1995, Volume 104, Number 3, Pages 463–478 (Mi tmf1351)

This article is cited in 64 scientific papers (total in 64 papers)

Polynomial supersymmetry and dynamical symmetries in quantum mechanics

A. A. Andrianov, M. V. Ioffe, D. N. Nishnianidze

Saint-Petersburg State University

Full-text PDF (1586 kB) Citations (64)

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Abstract: A polynomial generalization of supersymmetry in quantum mechanics is proposed in one and two dimensions. The classification of polynomial suyperalgebras is developed in one dimension. In two dimensions the comprehensive analysis is made for supercharges of second order in derivatives and it is shown that the binomial superalgebra always entails the hidden dynamical symmetry induced by a central charge.

Received: 05.12.1994

English version:
Theoretical and Mathematical Physics, 1995, Volume 104, Issue 3, Pages 1129–1140
DOI: https://doi.org/10.1007/BF02068745

Bibliographic databases:

Language: Russian

Citation: A. A. Andrianov, M. V. Ioffe, D. N. Nishnianidze, “Polynomial supersymmetry and dynamical symmetries in quantum mechanics”, TMF, 104:3 (1995), 463–478; Theoret. and Math. Phys., 104:3 (1995), 1129–1140

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tmf1351

https://www.mathnet.ru/eng/tmf/v104/i3/p463

This publication is cited in the following 64 articles:

Bijan Bagchi, Rahul Ghosh, “Dirac Hamiltonian in a supersymmetric framework”, Journal of Mathematical Physics, 62:7 (2021)
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
Ioffe M.V., Kolevatova E.V., Nishnianidze D.N., “SUSY method for the three-dimensional Schr?dinger equation with effective mass”, Phys. Lett. A, 380:41 (2016), 3349–3354
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
Chia-Chun Chou, Ching-Teh Li, “Asymptotic Functional Form Preservation Method with Supersymmetric Quantum Mechanics for Anharmonic Oscillators”, Aust. J. Chem., 69:9 (2016), 950
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
F. Cannata, M.V. Ioffe, E.V. Kolevatova, D.N. Nishnianidze, “New implicitly solvable potential produced by second order shape invariance”, Annals of Physics, 356 (2015), 438
Bijan Bagchi, Abhijit Banerjee, Partha Mandal, “A generalized Swanson Hamiltonian in a second-derivative pseudo-supersymmetric framework”, Int. J. Mod. Phys. A, 30:09 (2015), 1550037
Marquette I. Quesne Ch., “Combined State-Adding and State-Deleting Approaches To Type III Multi-Step Rationally Extended Potentials: Applications To Ladder Operators and Superintegrability”, J. Math. Phys., 55:11 (2014), 112103
M.S. Bardavelidze, M.V. Ioffe, D.N. Nishnianidze, “General solution of the two-dimensional intertwining relations for supercharges with hyperbolic (Lorentz) metrics”, Physics Letters A, 377:3-4 (2013), 195
Chia-Chun Chou, Donald J. Kouri, “Multidimensional Supersymmetric Quantum Mechanics: Spurious States for the Tensor Sector Two Hamiltonian”, J. Phys. Chem. A, 117:16 (2013), 3442
Chia-Chun Chou, Donald J. Kouri, “Multidimensional Supersymmetric Quantum Mechanics: A Scalar Hamiltonian Approach to Excited States by the Imaginary Time Propagation Method”, J. Phys. Chem. A, 117:16 (2013), 3449
Andrianov A.A. Ioffe M.V., “Nonlinear Supersymmetric Quantum Mechanics: Concepts and Realizations”, J. Phys. A-Math. Theor., 45:50 (2012), 503001
Chia-Chun Chou, Thomas Markovich, Donald J. Kouri, “Adiabatic switching approach to multidimensional supersymmetric quantum mechanics for several excited states”, Molecular Physics, 110:23 (2012), 2977
M. V. Ioffe, E. V. Krupitskaya, D. N. Nishnianidze, “Supersymmetrical separation of variables for Scarf II model: Partial solvability”, EPL, 98:1 (2012), 10013
M.V. Ioffe, E.V. Krupitskaya, D.N. Nishnianidze, “Analytical solution of two-dimensional Scarf II model by means of SUSY methods”, Annals of Physics, 327:3 (2012), 764
Christiane Quesne, “Revisiting the Symmetries of the Quantum Smorodinsky–Winternitz System in $D$ Dimensions”, SIGMA, 7 (2011), 035, 21 pp.
Tomoaki Nagasawa, Satoshi Ohya, Kazuki Sakamoto, Makoto Sakamoto, “Emergent Supersymmetry in Warped Backgrounds”, SIGMA, 7 (2011), 065, 13 pp.
F. Cannata, M. V. Ioffe, D. N. Nishnianidze, “New two-dimensional quantum models with shape invariance”, Journal of Mathematical Physics, 52:2 (2011)
Mikhail V. Ioffe, “Supersymmetrical Separation of Variables in Two-Dimensional Quantum Mechanics”, SIGMA, 6 (2010), 075, 10 pp.

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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