Functional relations in Stokes multipliers - Fun with $x^6+\alpha x^2$ 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

References in corpus (4)

• On the relation between Stokes multipliers and the T-Q systems of conformal field theory
• Differential equations and integrable models: the SU(3) case
• Functional Relations in Stokes Multipliers and Solvable Models related to U_q(A^{(1)}_n)
• Exact resolution method for general 1D polynomial Schrödinger equation

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• Pseudo-differential equations, and the Bethe Ansatz for the classical Lie algebras
• Quantum Inozemtsev model, quasi-exact solvability and N-fold supersymmetry
• Nonlinear supersymmetry on the plane in magnetic field and quasi-exactly solvable systems
• Beyond the WKB approximation in PT-symmetric quantum mechanics
• Geometric aspects of the ODE/IM correspondence
• A reality proof in PT-symmetric quantum mechanics
• Finite lattice Bethe ansatz systems and the Heun equation
• PT symmetry breaking and exceptional points for a class of inhomogeneous complex potentials
• Ordinary Differential Equations and Integrable Models
• Bethe state norms for the Heisenberg spin chain in the scaling limit
• On the origin of the correspondence between classical and quantum integrable theories
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• Massive ODE/IM Correspondence and Non-linear Integral Equations for $A_r^{(1)}$-type modified Affine Toda Field Equations
• Aspects of the ODE/IM correspondence
• Bukhvostov-Lipatov model and quantum-classical duality
• Vacuum energy of the Bukhvostov-Lipatov model
• Folding QQ-relations and transfer matrix eigenvalues: towards a unified approach to Bethe ansatz for super spin chains
• From exact-WKB towards singular quantum perturbation theory
• Complex WKB Analysis of a PT Symmetric Eigenvalue Problem
• Quasi-exact solvability, resonances and trivial monodromy in ordinary differential equations
• A(2|1) spectral equivalences and nonlocal integrals of motion
• The ODE/IM correspondence and PT-symmetric quantum mechanics