Supersymmetric partners of the harmonic oscillator with an infinite potential barrier

Abstract

Supersymmetry transformations of first and second order are used to generate Hamiltonians with known spectra departing from the harmonic oscillator with an infinite potential barrier. It is studied also the way in which the eigenfunctions of the initial Hamiltonian are transformed. The first and certain second order supersymmetric partners of the initial Hamiltonian possess third-order differential ladder operators. Since systems with this kind of operators are linked with the Painlevé IV equation, several solutions of this non-linear second-order differential equation will be simply found.

References in corpus (4)

• Nonlinear Supersymmetric Quantum Mechanics: concepts and realizations
• 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

Cited by in corpus (9)

• Trends in supersymmetric quantum mechanics
• The confluent supersymmetry algorithm for Dirac equations with pseudoscalar potentials
• Complex oscillator and Painlevé IV equation
• Coherent states for the supersymmetric partners of the truncated oscillator
• Ladder operators for the Ben Daniel-Duke Hamiltonians and their SUSY partners
• Ladder operators and coherent states for multi-step supersymmetric rational extensions of the truncated oscillator
• Higher Order Supersymmetric Truncated Oscillators
• Nonstationary deformed singular oscillator: quantum invariants and the factorization method
• Ladder operators and coherent states for the Rosen-Morse system and its rational extensions