Coherent states for the supersymmetric partners of the truncated oscillator

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.