Painlevé IV Coherent States

Abstract

A simple way to find solutions of the Painlevé IV equation is by identifying Hamiltonian systems with third-order differential ladder operators. Some of these systems can be obtained by applying supersymmetric quantum mechanics (SUSY QM) to the harmonic oscillator. In this work, we will construct families of coherent states for such subset of SUSY partner Hamiltonians which are connected with the Painlevé IV equation. First, these coherent states are built up as eigenstates of the annihilation operator, then as displaced versions of the extremal states, both involving the third-order ladder operators, and finally as extremal states which are also displaced but now using the so called linearized ladder operators. To each SUSY partner Hamiltonian corresponds two families of coherent states: one inside the infinite subspace associated with the isospectral part of the spectrum and another one in the finite subspace generated by the states created through the SUSY technique.

26 pages, 4 figures

References in corpus (2)

• Non-hermitian Hamiltonians and Painlevé IV equation with real parameters
• Supersymmetric quantum mechanics and Painleve equations

Cited by in corpus (5)

• Trends in supersymmetric quantum mechanics
• Connection between quantum systems involving the fourth Painleve transcendent and $k$-step rational extensions of the harmonic oscillator related to Hermite EOP
• Coherent states for the supersymmetric partners of the truncated oscillator
• On Integrable Ermakov-Painlevé IV Systems
• Multiphoton coherent states for bilayer graphene