Functional relations in Stokes multipliers - Fun with $x^6 + αx^2$ potential-

Abstract

We consider eigenvalue problems in quantum mechanics in one dimension. Hamiltonians contain a class of double well potential terms, x^6 + αx^2, for example . The space coordinate is continued to a complex plane and the connection problem of fundamental system of solutions is considered. A hidden U_q(\hat{gl}(2|1)) structure arises in "fusion relations" of Stokes multipliers. With this observation, we derive coupled nonlinear integral equations which characterize the spectral properties of both \pm αpotentials simultaneously. equations.

18 pages, minor corrections, references added