# Charges carried by wave packets that are superimposed on plane waves

## TL;DR

This paper investigates the extra charge carried by wave packets superimposed on plane waves, providing an analytic Fourier transform method to calculate it, with applications to laser-induced local excitations.

## Contribution

It introduces an analytic Fourier transform approach to determine the extra charge in wave packets, enhancing understanding of local excitations in quantum systems.

## Key findings

- The method accurately calculates extra charge for Gaussian wave packets.
- Comparison with numerical results validates the analytic approach.
- Application to laser pulses demonstrates practical relevance.

## Abstract

We consider the superposition of plane waves and localized wave packets. This kind of wave function can result from a local excitation of a particle described by a plane wave. For charged particles, the wave packet means a current, the time integral of which results in an extra charge, additionally to the one carried by the plane wave. When the duration of the wave packet is too short for its details to be resolved experimentally, it is the extra charge that can be determined and analyzed for information regarding the nature of the interaction that created the wave packet. Assuming that the wave function is known initially, we show an analytic method for the calculation of the extra charge by the aid of Fourier transform. Our approach is verified by comparing to both the well-known case of a Gaussian wave packet and numerically obtained results. As an important physical example, finally we consider the case of local excitation by laser pulses.