Coherent states and related quantizations for unbounded motions

TL;DR

This paper develops new coherent states for unbounded quantum motions using two methods: adapting quadratic Hamiltonian techniques to linear potentials and extending action-angle states for continuous spectra, enhancing energy quantization.

Contribution

It introduces two novel procedures for constructing coherent states applicable to unbounded motions and continuous spectra, broadening the scope of quantum state representations.

Findings

Constructed coherent states for linear potentials.

Generalized to arbitrary potentials.

Provided a framework for consistent energy quantization.

Abstract

We build coherent states (CS) for unbounded motions along two different procedures. In the first one we adapt the Malkin-Manko construction for quadratic Hamiltonians to the motion of a particle in a linear potential. A generalization to arbitrary potentials is discussed. The second one extends to continuous spectrum previous constructions of action-angle coherent states in view of a consistent energy quantization.