On the Stability of Coherent States for Pais-Uhlenbeck Oscillator

TL;DR

This paper constructs and analyzes coherent states for the Pais-Uhlenbeck Oscillator, including a novel method for negative energy levels, revealing their properties and potential for positive energies.

Contribution

It introduces a new approach to formulating coherent states for higher derivative oscillators with negative energies, maintaining key quantum properties.

Findings

Coherent states exhibit constant dispersions and modified uncertainty relations.

Negative energy coherent states can have positive energies under certain conditions.

The method applies to higher derivative quantum systems with stability considerations.

Abstract

We have constructed coherent states for the higher derivative Pais-Uhlenbeck Oscillator. 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 Pais-Uhlenbeck Oscillator have constant dispersions and a modified Heisenberg Uncertainty Relation. Moreover, under reasonable assumptions on parameters these coherent states can have positive energies.