A. A. Oblomkov, “Monodromy-free Schrödinger operators with quadratically increasing potentials”, TMF, 121:3 (1999), 374–386; Theoret. and Math. Phys., 121:3 (1999), 1574

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Teoreticheskaya i Matematicheskaya Fizika, 1999, Volume 121, Number 3, Pages 374–386
DOI: https://doi.org/10.4213/tmf817 (Mi tmf817)

This article is cited in 47 scientific papers (total in 47 papers)

Monodromy-free Schrödinger operators with quadratically increasing potentials

A. A. Oblomkov

M. V. Lomonosov Moscow State University

Full-text PDF (260 kB) Citations (47)

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DOI: https://doi.org/10.4213/tmf817

Abstract: We consider one-dimensional monodromy-free Schrödinger operators with quadratically increasing rational potentials. It is shown that all these operators can be obtained from the operator

- \partial^{2} + x^{2}

$-\partial^2+x^2$ by finitely many rational Darboux transformations. An explicit expression is found for the corresponding potentials in terms of Hermite polynomials.

Received: 23.03.1999

English version:
Theoretical and Mathematical Physics, 1999, Volume 121, Issue 3, Pages 1574–1584
DOI: https://doi.org/10.1007/BF02557204

Bibliographic databases:

Language: Russian

Citation: A. A. Oblomkov, “Monodromy-free Schrödinger operators with quadratically increasing potentials”, TMF, 121:3 (1999), 374–386; Theoret. and Math. Phys., 121:3 (1999), 1574–1584

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tmf817

https://doi.org/10.4213/tmf817

https://www.mathnet.ru/eng/tmf/v121/i3/p374

This publication is cited in the following 47 articles:

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Hussin V., Marquette I., Zelaya K., “Third-Order Ladder Operators, Generalized Okamoto and Exceptional Orthogonal Polynomials”, J. Phys. A-Math. Theor., 55:4 (2022), 045205
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A. A. Golubkov, “Monodromy-Quasifree Singular Points of the Sturm–Liouville Equation of Standard Form on the Complex Plane”, Diff Equat, 58:8 (2022), 1021
Sarbarish Chakravarty, Michael Zowada, “Classification of KPI lumps”, J. Phys. A: Math. Theor., 55:21 (2022), 215701
Codruţ Grosu, Corina Grosu, “The Expansion of Wronskian Hermite Polynomials in the Hermite Basis”, SIGMA, 17 (2021), 003, 14 pp.
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A. A. Golubkov, “Inverse problem for the Sturm–Liouville equation with piecewise entire potential and piecewise constant weight on a curve”, Sib. elektron. matem. izv., 18:2 (2021), 951–974
Kudryashov N.A., “Generalized Hermite Polynomials For the Burgers Hierarchy and Point Vortices”, Chaos Solitons Fractals, 151 (2021), 111256
Grosu C. Grosu C., “The Irreducibility of Some Wronskian Hermite Polynomials”, Indag. Math.-New Ser., 32:2 (2021), 456–497
Gomez-Ullate D. Grandati Y. Milson R., “Complete Classification of Rational Solutions of a(2N)-Painleve Systems”, Adv. Math., 385 (2021), 1077707
Chalifour V. Grundland A.M., “General Solution of the Exceptional Hermite Differential Equation and Its Minimal Surface Representation”, Ann. Henri Poincare, 21:10 (2020), 3341–3384
Kasman A., Milson R., “The Adelic Grassmannian and Exceptional Hermite Polynomials”, Math. Phys. Anal. Geom., 23:4 (2020), 40
Clarkson P.A. Gomez-Ullate D. Grandati Y. Milson R., “Cyclic Maya Diagrams and Rational Solutions of Higher Order Painleve Systems”, Stud. Appl. Math., 144:3 (2020), 357–385
Bonneux N. Dunning C. Stevens M., “Coefficients of Wronskian Hermite Polynomials”, Stud. Appl. Math., 144:3 (2020), 245–288

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

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