Coherent states for quadratic Hamiltonians

TL;DR

This paper constructs and analyzes coherent states for quadratic Hamiltonians in the trap regime, introducing a matrix technique to identify operators and comparing different methods to derive these states, with applications to Penning traps.

Contribution

It presents a novel matrix technique for directly identifying creation and annihilation operators for quadratic Hamiltonians and compares methods for constructing coherent states.

Findings

Coherent states are explicitly constructed for quadratic Hamiltonians.

A matrix method simplifies the identification of creation and annihilation operators.

Application to the asymmetric Penning trap demonstrates the approach's effectiveness.

Abstract

The coherent states for a set of quadratic Hamiltonians in the trap regime are constructed. A matrix technique which allows to identify directly the creation and annihilation operators will be presented. Then, the coherent states as simultaneous eigenstates of the annihilation operators will be derived, and they are going to be compared with those attained through the displacement operator method. The corresponding wave function will be found, and a general procedure for obtaining several expected values involving the canonical operators in these states will be described. The results will be illustrated through the asymmetric Penning trap.