ON THE STABILITY OF COHERENT STATES FOR PAIS–UHLENBECK OSCILLATOR

Abstract

We have constructed coherent states for the higher derivative Pais–Uhlenbeck Oscillator (PUO). In the process, we have suggested a novel way to construct coherent states for the oscillator having only negative energy levels. These coherent states have negative energies in general but their coordinate and momentum expectation values and dispersions behave in an identical manner as that of normal (positive energy) oscillator. The coherent states for the PUO have constant dispersions and a modified Heisenberg Uncertainty Relation. Moreover, under reasonable assumptions on parameters these coherent states can have positive energies.