# Graphene coherent states

## TL;DR

This paper constructs and analyzes coherent states for a Dirac electron in graphene under a magnetic field, exploring their physical properties and quantum characteristics.

## Contribution

It introduces a method to derive coherent states for graphene electrons in magnetic fields, including analysis of their physical and quantum properties.

## Key findings

- Coherent states are explicitly constructed as eigenstates of the annihilation operator.
- Heisenberg uncertainty product and probability density are analyzed.
- Mean energy values of the states are calculated.

## Abstract

In this paper, we will construct the coherent states for a Dirac electron in graphene placed in a constant homogeneous magnetic field which is orthogonal to the graphene surface. First of all, we will identify the appropriate annihilation and creation operators. Then, we will derive the coherent states as eigenstates of the annihilation operator, with complex eigenvalues. Several physical quantities, as the Heisenberg uncertainty product, probability density and mean energy value, will be as well explored.