Complex SUSY Transformations and the Painlevé IV Equation

Abstract

In this paper we will explicitly work out the complex first-order SUSY transformation for the harmonic oscillator in order to obtain both real and complex new exactly-solvable potentials. Furthermore, we will show that this systems lead us to exact complex solutions of the Painlevé IV equation with complex parameters. We present some concrete examples of such solutions.

References in corpus (11)

• SUSY Quantum Mechanics with Complex Superpotentials and Real Energy Spectra
• Conditionally exactly solvable potentials: A supersymmetric construction method
• Systems with Higher-Order Shape Invariance: Spectral and Algebraic Properties
• Superintegrability with third order integrals of motion, cubic algebras and supersymmetric quantum mechanics II:Painleve transcendent potentials
• Hamiltonians separable in cartesian coordinates and third-order integrals of motion
• New hydrogen-like potentials
• Second order SUSY transformations with `complex energies'
• Non-Hermitian SUSY Hydrogen-like Hamiltonians with real spectra
• Non-hermitian Hamiltonians and Painlevé IV equation with real parameters
• Supersymmetric Quantum Mechanics and Painlevé IV Equation
• Complex solutions to Painleve IV equation through supersymmetric quantum mechanics

Cited by in corpus (7)

• Supersymmetric partners of the harmonic oscillator with an infinite potential barrier
• SUSY partners of the truncated oscillator, Painlevé transcendents and Bäcklund transformations
• Solutions to the Painlevé V equation through supersymmetric quantum mechanics
• On Integrable Ermakov-Painlevé IV Systems
• Supersymmetric Quantum Mechanics, Engineered Hierarchies of Integrable Potentials, and the Generalised Laguerre Polynomials
• Lectures on exceptional orthogonal polynomials and rational solutions to Painlevé equations
• Complete classification of rational solutions of $A_{2n}$-Painlevé systems