# Quantum and classical dynamics comparison: A way for selecting the vector potential across diverse frames

## TL;DR

This paper compares quantum and classical electron behavior in laser fields to determine the correct vector potential in different frames.

## Contribution

A new method is introduced for selecting the vector potential in the laboratory frame based on quantum-classical alignment.

## Key findings

- Quantum paths align with classical trajectories in the lab frame for a specific vector potential.
- Alternative gauges show agreement with classical trajectories in their respective moving frames.
- The method works both within and beyond the dipole approximation.

## Abstract

This study explores the quantum dynamics of a free electron subjected to an intense laser field, considering various gauges within and beyond the dipole approximation. The quantum path, as dictated by the Ehrenfest theorem, is systematically computed. Notably, it is revealed that the quantum path aligns with the classical trajectory in the laboratory frame exclusively for a specific vector potential. Additionally, the quantum paths derived from alternative gauges exhibit notable agreement with the classical trajectories within their respective moving frames. This novel approach introduces a method for selecting the appropriate vector potential in the laboratory frame.

•The quantum dynamics of a free electron in an intense laser field is investigated.•The quantum proposed path is computed within dipole approximation and beyond it.•We provide a method for selecting the vector potential across diverse frames.

The quantum dynamics of a free electron in an intense laser field is investigated.

The quantum proposed path is computed within dipole approximation and beyond it.

We provide a method for selecting the vector potential across diverse frames.