An infinite family of superintegrable systems from higher order ladder operators and supersymmetry

Abstract

We will discuss how we can obtain new quantum superintegrable Hamiltonians allowing the separation of variables in Cartesian coordinates with higher order integrals of motion from ladder operators. We will discuss also how higher order supersymmetric quantum mechanics can be used to obtain systems with higher order ladder operators and their polynomial Heisenberg algebra. We will present a new family of superintegrable systems involving the fifth Painleve transcendent which possess fourth order ladder operators constructed from second order supersymmetric quantum mechanics. We present the polynomial algebra of this family of superintegrable systems.

8 pages, presented at ICGTMP 28, accepted for j.conf.series

References in corpus (11)

• Hamiltonians separable in cartesian coordinates and third-order integrals of motion
• Anisotropic harmonic oscillator, non-commutative Landau problem and exotic Newton-Hooke symmetry
• Aharonov-Bohm effect on AdS_2 and nonlinear supersymmetry of reflectionless Poschl-Teller system
• Superintegrability with third order integrals of motion, cubic algebras and supersymmetric quantum mechanics I:Rational function potentials
• Reduction of superintegrable systems: the anisotropic harmonic oscillator
• Superintegrability of the Caged Anisotropic Oscillator
• Finite-gap systems, tri-supersymmetry and self-isospectrality
• Superintegrable Systems with a Third Order Integrals of Motion
• Hidden nonlinear supersymmetry of finite-gap Lame equation
• New Two-Dimensional Integrable Quantum Models from SUSY Intertwining
• Intertwining symmetry algebras of quantum superintegrable systems on the hyperboloid

Cited by in corpus (6)

• Polynomial algebras of superintegrable systems separating in Cartesian coordinates from higher order ladder operators
• Superintegrable systems with spin and second-order (pseudo)tensor integrals of motion
• Massless geodesics in $Ad{S}_5\times Y(p,q)$ as a superintegrable system
• A family of fourth-order superintegable systems with rational potentials related to Painlevé VI
• Construction of polynomial algebras from intermediate Casimir invariants of Lie algebras
• Singular Isotonic Oscillator, Supersymmetry and Superintegrability