Coherent states for the supersymmetric partners of the truncated oscillator

TL;DR

This paper constructs and analyzes coherent states for supersymmetric partners of the truncated oscillator, addressing their unique eigenfunction structure and exploring their properties such as continuity, resolution of identity, and entanglement.

Contribution

It introduces a new definition of coherent states for these systems using linearized ladder operators, enabling comprehensive analysis of their properties.

Findings

Coherent states exhibit continuity in the complex parameter.

Resolution of the identity is achieved for these states.

States demonstrate interesting time evolution and entanglement properties.

Abstract

We build the coherent states for a family of solvable singular Schr\"odinger 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.