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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-Dunne polynomials and resonances between independent solutions are observed for certain second-order cases, and extended to the higher-order problems.

preprint2012arXivOpen access
Patrick DoreyClare DunningRoberto Tateo
math-phmath.MPhep-thquant-ph
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Patrick DoreyClare DunningRoberto Tateo

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