Coherent states approach to Penning trap

TL;DR

This paper derives and analyzes coherent states for a Penning trap using matrix techniques, showing they minimize the Heisenberg uncertainty and comparing different state constructions.

Contribution

It introduces a matrix method to directly identify ladder operators and construct Penning trap coherent states, comparing them with displacement operator states.

Findings

Penning trap coherent states are eigenstates of annihilation operators

These states minimize the Heisenberg uncertainty relation

Wave functions and expectation values are explicitly calculated

Abstract

By using a matrix technique, which allows to identify directly the ladder operators, the Penning trap coherent states are derived as eigenstates of the appropriate annihilation operators. These states are compared with the ones obtained through the displacement operator. The associated wave functions and mean values for some relevant operators in these states are also evaluated. It turns out that the Penning trap coherent states minimize the Heisenberg uncertainty relation.