SUSY partners of the truncated oscillator, Painlevé transcendents and Bäcklund transformations

Abstract

In this work the supersymmetric technique is applied to the truncated oscillator to generate Hamiltonians ruled by second and third-order polynomial Heisenberg algebras, which are connected to the Painlevé IV and Painlevé V equations respectively. The aforementioned connection is exploited to produce particular solutions to both non-linear differential equations and the Bäcklund transformations relating them.

This article is a natural continuation of arXiv:1310.5628

References in corpus (5)

• Rational extensions of the quantum harmonic oscillator and exceptional Hermite polynomials
• Group theoretical approach to the intertwined Hamiltonians
• Non-hermitian Hamiltonians and Painlevé IV equation with real parameters
• Complex SUSY Transformations and the Painlevé IV Equation
• Solutions to the Painlevé V equation through supersymmetric quantum mechanics

Cited by in corpus (7)

• Trends in supersymmetric quantum mechanics
• Fourth order superintegrable systems separating in Polar Coordinates. I. Exotic Potentials
• Coherent states for the supersymmetric partners of the truncated oscillator
• Ladder operators and coherent states for multi-step supersymmetric rational extensions of the truncated oscillator
• Higher Order Supersymmetric Truncated Oscillators
• A family of fourth-order superintegable systems with rational potentials related to Painlevé VI
• Multiphoton coherent states for bilayer graphene