On the rational monodromy-free potentials with sextic growth

DOI10.1063/1.3001604zbMath1200.34108arXiv0807.3501OpenAlexW3099144920MaRDI QIDQ3650886

John Gibbons, Alexander P. Veselov

Publication date: 7 December 2009

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0807.3501

zbMATH Keywords

Schrödinger equationeigenvalues and eigenfunctions

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Schrödinger operator, Schrödinger equation (35J10) Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms (34M35)

Related Items

Complex exceptional orthogonal polynomials and quasi-invariance ⋮ A Bochner type characterization theorem for exceptional orthogonal polynomials ⋮ Zeros of Wronskians of Hermite polynomials and Young diagrams ⋮ Liouvillian solutions for second order linear differential equations with Laurent polynomial coefficient ⋮ Inverse problem for the Sturm-Liouville equation with piecewise entire potential and piecewise constant weight on a curve ⋮ On Darboux-Treibich-Verdier potentials ⋮ Solutions of a Bessel-type differential equation using the tridiagonal representation approach ⋮ Monodromy-quasifree singular points of the Sturm-Liouville equation of standard form on the complex plane ⋮ Whittaker–Hill equation and semifinite-gap Schrödinger operators ⋮ Jointly orthogonal polynomials

Cites Work

• Differential equations in the spectral parameter
• Zeros of eigenfunctions of some anharmonic oscillators
• On a class of polynomials connected with the Korteweg-de Vries equation
• Dressing chains and the spectral theory of the Schrödinger operator
• On the two-gap elliptic potentials
• Finite-gap elliptic solutions of the KdV equation
• Picard potential and Hill's equation on a torus
• Quasi-exactly-solvable problems and sl(2) algebra
• On Stieltjes relations, Painlevé-IV hierarchy and complex monodromy
• Spectral equivalences, Bethe ansatz equations, and reality properties in 𝒫𝒯-symmetric quantum mechanics
• The energy levels of the sextic double-well potential
• Energy spectrum of the potential V=ax²+x⁴
• Rational and elliptic solutions of the korteweg-de vries equation and a related many-body problem
• NON-LINEAR EQUATIONS OF KORTEWEG-DE VRIES TYPE, FINITE-ZONE LINEAR OPERATORS, AND ABELIAN VARIETIES
• Failure of the Hill determinant method for the sextic anharmonic oscillator
• Polynomial families and Schrödinger equation: one example for nonhypergeometric type of correspondence
• On the two-gap locus for the elliptic Calogero-Moser model
• Quasi-exactly solvable systems and orthogonal polynomials
• ASSOCIATED STURM-LIOUVILLE SYSTEMS
• Monodromy-free Schrödinger operators with quadratically increasing potentials