A correspondence between the sextic anharmonic oscillator and a pair of thirdorder ordinary differential equations is used to investigate the phenomenon of quasi-exact solvability for eigenvalue problems involving differential operators with order greater than 2. 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.
Quasi-exact solvability, resonances and trivial monodromy in ordinary differential equations
TATEO, Roberto
2012-01-01
Abstract
A correspondence between the sextic anharmonic oscillator and a pair of thirdorder ordinary differential equations is used to investigate the phenomenon of quasi-exact solvability for eigenvalue problems involving differential operators with order greater than 2. 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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