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

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.