Quasi-exact solvability, resonances and trivial monodromy in ordinary differential equations

Quasi-exact solvability, resonances and trivial monodromy in ordinary differential equations

A correspondence between the sextic anharmonic oscillator and a pair of third-order ordinary differential equations is used to investigate the phenomenon of quasi-exact solvability for eigenvalue problems involving differential operators with order greater than two. In particular, links with Bender-...

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Veröffentlicht in:arXiv.org 2012-09
Hauptverfasser: Dorey, Patrick, Dunning, Clare, Tateo, Roberto
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Sprache:eng
Schlagworte:
Anharmonicity
Differential equations
Eigenvalues
Mathematical analysis
Mathematics - Mathematical Physics
Operators (mathematics)
Ordinary differential equations
Physics - High Energy Physics - Theory
Physics - Mathematical Physics
Physics - Quantum Physics
Polynomials
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description A correspondence between the sextic anharmonic oscillator and a pair of third-order ordinary differential equations is used to investigate the phenomenon of quasi-exact solvability for eigenvalue problems involving differential operators with order greater than two. In particular, links with Bender-Dunne polynomials and resonances between independent solutions are observed for certain second-order cases, and extended to the higher-order problems.
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subjects Anharmonicity
Differential equations
Eigenvalues
Mathematical analysis
Mathematics - Mathematical Physics
Operators (mathematics)
Ordinary differential equations
Physics - High Energy Physics - Theory
Physics - Mathematical Physics
Physics - Quantum Physics
Polynomials
title Quasi-exact solvability, resonances and trivial monodromy in ordinary differential equations
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