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SIGMA, 2011, том 7, 025, 14 страниц (Mi sigma583)  

Эта публикация цитируется в 31 научных статьях (всего в 31 статьях)

Supersymmetric Quantum Mechanics and Painlevé IV Equation

David Bermúdez, David J. Fernández C.

Departamento de Física, Cinvestav, AP 14-740, 07000 México DF, Mexico

Аннотация: As it has been proven, the determination of general one-dimensional Schrödinger Hamiltonians having third-order differential ladder operators requires to solve the Painlevé IV equation. In this work, it will be shown that some specific subsets of the higher-order supersymmetric partners of the harmonic oscillator possess third-order differential ladder operators. This allows us to introduce a simple technique for generating solutions of the Painlevé IV equation. Finally, we classify these solutions into three relevant hierarchies.

Ключевые слова: supersymmetric quantum mechanics; Painlevé equations

DOI: https://doi.org/10.3842/SIGMA.2011.025

Полный текст: PDF файл (581 kB)
Полный текст: http://emis.mi.ras.ru/journals/SIGMA/2011/025/
Список литературы: PDF файл   HTML файл

Реферативные базы данных:

ArXiv: 1012.0290
Тип публикации: Статья
MSC: 81Q60; 35G20
Поступила: 30 ноября 2010 г.; в окончательном варианте 4 марта 2011 г.; опубликована 8 марта 2011 г.
Язык публикации: английский

Образец цитирования: David Bermúdez, David J. Fernández C., “Supersymmetric Quantum Mechanics and Painlevé IV Equation”, SIGMA, 7 (2011), 025, 14 pp.

Цитирование в формате AMSBIB
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\paper Supersymmetric Quantum Mechanics and Painlev\'e IV Equation
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    Эта публикация цитируется в следующих статьяx:
    1. Fernandez C D.J., Salinas-Hernandez E., “Hyperconfluent third-order supersymmetric quantum mechanics”, Journal of Physics A-Mathematical and Theoretical, 44:36 (2011), 365302  crossref  mathscinet  zmath  adsnasa  isi  scopus
    2. Bermudez D., Fernandez C D.J., “Non-Hermitian Hamiltonians and the Painlevé IV equation with real parameters”, Phys Lett A, 375:33 (2011), 2974–2978  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    3. David J. Fernández, “Harmonic oscillator SUSY partners and evolution loops”, SIGMA, 8 (2012), 041, 12 pp.  mathnet  crossref  mathscinet
    4. Ian Marquette, “Singular isotonic oscillator, supersymmetry and superintegrability”, SIGMA, 8 (2012), 063, 14 pp.  mathnet  crossref  mathscinet
    5. David Bermúdez, “Complex SUSY transformations and the Painlevé IV equation”, SIGMA, 8 (2012), 069, 10 pp.  mathnet  crossref  mathscinet
    6. Andrianov A.A. Ioffe M.V., “Nonlinear Supersymmetric Quantum Mechanics: Concepts and Realizations”, J. Phys. A-Math. Theor., 45:50 (2012), 503001  crossref  mathscinet  zmath  isi  elib  scopus
    7. Bermudez D., Fernandez C D.J., “Complex Solutions to the Painlevé IV Equation Through Supersymmetric Quantum Mechanics”, Advanced Summer School in Physics 2011 (Eav 2011), AIP Conference Proceedings, 1420, eds. CondeGallardo A., AyonBeato E., GodinaNava J., HernandezContreras M., VelascoSevilla L., Amer Inst Physics, 2012, 47–51  crossref  adsnasa  isi  scopus
    8. Marquette I., Quesne C., “Two-Step Rational Extensions of the Harmonic Oscillator: Exceptional Orthogonal Polynomials and Ladder Operators”, J. Phys. A-Math. Theor., 46:15 (2013), 155201  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    9. Marquette I., Quesne Ch., “New Ladder Operators for a Rational Extension of the Harmonic Oscillator and Superintegrability of Some Two-Dimensional Systems”, J. Math. Phys., 54:10 (2013), 102102  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    10. Iyela D.B., Govaerts J., Hounkonnou M.N., “Supersymmetric Quantum Mechanics: Engineered Hierarchies of Integrable Potentials and Related Orthogonal Polynomials”, J. Math. Phys., 54:9 (2013), 093502  crossref  mathscinet  zmath  adsnasa  isi  scopus
    11. Fernandez D.J., Morales-Salgado V.S., “Supersymmetric Partners of the Harmonic Oscillator with an Infinite Potential Barrier”, J. Phys. A-Math. Theor., 47:3 (2014), 035304  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    12. Reeger J.A., Fornberg B., “Painlevé IV: a Numerical Study of the Fundamental Domain and Beyond”, Physica D, 280 (2014), 1–13  crossref  mathscinet  zmath  adsnasa  isi  scopus
    13. Bermudez D., Contreras-Astorga A., Fernandez D.J.C., “Painlevé Iv Coherent States”, Ann. Phys., 350 (2014), 615–634  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    14. Bermudez D., Contreras-Astorga A., Fernandez C D.J., “Linearized Coherent States For Hamiltonian Systems With Two Equidistant Ladder Spectra”, 8Th International Symposium on Quantum Theory and Symmetries (Qts8), Journal of Physics Conference Series, 512, IOP Publishing Ltd, 2014, 012018  crossref  isi  scopus
    15. Bermudez D., Fernandez C D.J., “Hamiltonians With Two-Ladder Spectra and Solutions to the Painlevé IV Equation”, 8th International Symposium on Quantum Theory and Symmetries, Journal of Physics Conference Series, 512, IOP Publishing Ltd, 2014, 012017  crossref  isi  scopus
    16. Fernandez C D.J., Morales-Salgado V.S., “Supersymmetric Partners of the Truncated Harmonic Oscillator”, 8th International Symposium on Quantum Theory and Symmetries, Journal of Physics Conference Series, 512, IOP Publishing Ltd, 2014, 012024  crossref  isi  scopus
    17. Bermudez D., Fernandez C D.J., “Supersymmetric Quantum Mechanics and Painlevé Equations”, Latin-American School of Physics Marcos Moshinsky Elaf: Nonlinear Dynamics in Hamiltonian Systems, AIP Conference Proceedings, 1575, eds. Bijker R., Castanos O., Jauregui R., Lemus R., RosasOrtiz O., Amer Inst Physics, 2014, 50–88  crossref  isi  scopus
    18. Fernandez C. David J., Gonzalez J.C., “Complex Oscillator and Painlevé Iv Equation”, Ann. Phys., 359 (2015), 213–229  crossref  mathscinet  zmath  isi  scopus
    19. Bermudez D., Fernandez C D.J., “a Connection Between Supersymmetric Quantum Mechanics and Painlevé V Equation”, International Conference on Quantum Control, Exact Or Perturbative, Linear Or Nonlinear To Celebrate 50 Years of the Scientific Career of Professor Bogdan Mielnik, Journal of Physics Conference Series, 624, eds. Breton N., Fernandez D., Kielanowski P., IOP Publishing Ltd, 2015, 012012  crossref  isi  scopus
    20. Fernandez C D.J., Morales-Salgado V.S., “Truncated Harmonic Oscillator and Painlevé IV and V Equations”, International Conference on Quantum Control, Exact Or Perturbative, Linear Or Nonlinear To Celebrate 50 Years of the Scientific Career of Professor Bogdan Mielnik, Journal of Physics Conference Series, 624, eds. Breton N., Fernandez D., Kielanowski P., IOP Publishing Ltd, 2015, 012017  crossref  isi  scopus
    21. Fernandez C D.J., Gonzalez J.C., “Susy Partners of the Complex Oscillator and Painlevé IV Equation”, International Conference on Quantum Control, Exact Or Perturbative, Linear Or Nonlinear To Celebrate 50 Years of the Scientific Career of Professor Bogdan Mielnik, Journal of Physics Conference Series, 624, eds. Breton N., Fernandez D., Kielanowski P., IOP Publishing Ltd, 2015, 012015  crossref  isi  scopus
    22. Bermudez D., Contreras-Astorga A., Fernandez C D.J., “Painlevé Iv Hamiltonian Systems and Coherent States”, Xxxth International Colloquium on Group Theoretical Methods in Physics (Icgtmp) (Group30), Journal of Physics Conference Series, 597, IOP Publishing Ltd, 2015, 012017  crossref  isi  scopus
    23. Fernandez C D.J., Morales-Salgado V.S., “Factorization Method For the Truncated Harmonic Oscillator”, Xxxth International Colloquium on Group Theoretical Methods in Physics (Icgtmp) (Group30), Journal of Physics Conference Series, 597, IOP Publishing Ltd, 2015, 012035  crossref  isi  scopus
    24. Bermudez D. Fernandez C D.J. Negro J., “Solutions to the Painlevé V equation through supersymmetric quantum mechanics”, J. Phys. A-Math. Theor., 49:33 (2016), 335203  crossref  mathscinet  zmath  isi  elib  scopus
    25. Fernandez C D.J. Morales-Salgado V.S., “SUSY partners of the truncated oscillator, Painlevé transcendents and Bäcklund transformations”, J. Phys. A-Math. Theor., 49:19 (2016), 195202  crossref  mathscinet  zmath  isi  elib  scopus
    26. Marquette I., Quesne Ch., “Connection between quantum systems involving the fourth Painlevé transcendent and $k$-step rational extensions of the harmonic oscillator related to Hermite exceptional orthogonal polynomial”, J. Math. Phys., 57:5 (2016), 052101  crossref  mathscinet  zmath  isi  elib  scopus
    27. Estrada-Delgado, M. I.; Fernandez, C. D. J., “Painlevé IV Solutions from Hamiltonians with Equidistant Gapped Spectrum”, Journal of Physics: Conference Series, 698:1 (2016), 012027  crossref  scopus
    28. Fernandez D.J.C., “Painlevé Equations and Supersymmetric Quantum Mechanics”, Geometric Methods in Physics, Trends in Mathematics, ed. Kielanowski P. Ali S. Bieliavsky P. Odzijewicz A. Schlichenmaier M. Voronov T., Springer Int Publishing Ag, 2016, 213–231  crossref  mathscinet  zmath  isi
    29. Rogers C. Bassom A.P. Clarkson P.A., “On Integrable Ermakov-Painlevé Iv Systems”, J. Math. Anal. Appl., 462:2 (2018), 1225–1241  crossref  mathscinet  zmath  isi  scopus
    30. Victor Yu. Novokshenov, “Generalized Hermite Polynomials and Monodromy-Free Schrödinger Operators”, SIGMA, 14 (2018), 106, 13 pp.  mathnet  crossref
    31. Fernandez C D.J., Hussin V., Said Morales-Salgado V., “Coherent States For the Supersymmetric Partners of the Truncated Oscillator”, Eur. Phys. J. Plus, 134:1 (2019), 18  crossref  mathscinet  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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