Coherent states for the supersymmetric partners of the truncated oscillator

Abstract

We build the coherent states for a family of solvable singular Schrödinger Hamiltonians obtained through supersymmetric quantum mechanics from the truncated oscillator. The main feature of such systems is the fact that their eigenfunctions are not completely connected by their natural ladder operators. We find a definition that behaves appropriately in the complete Hilbert space of the system, through linearised ladder operators. In doing so, we study basic properties of such states like continuity in the complex parameter, resolution of the identity, probability density, time evolution and possibility of entanglement.

References in corpus (3)

• Group theoretical approach to the intertwined Hamiltonians
• Completeness and Nonclassicality of Coherent States for Generalized Oscillator Algebras
• Higher Order Supersymmetric Truncated Oscillators

Cited by in corpus (5)

• Trends in supersymmetric quantum mechanics
• Ladder operators and coherent states for multi-step supersymmetric rational extensions of the truncated oscillator
• Nonstationary deformed singular oscillator: quantum invariants and the factorization method
• Ladder operators and coherent states for the Rosen-Morse system and its rational extensions
• Coherent states of the two-dimensional non-separable supersymmetric Morse potential