Patrick Dorey, Clare Dunning, Roberto Tateo

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.

http://arxiv.org/abs/1209.4736

Mathematical Physics (math-ph); High Energy Physics – Theory (hep-th); Quantum Physics (quant-ph)