Gaussian wave packet solution of the Schrodinger equation in the presence of a time-dependent linear potential

TL;DR

This paper presents a method to solve the Schrödinger equation with a time-dependent linear potential using a Hermitian invariant operator, demonstrating that Gaussian wave packets are its eigenfunctions.

Contribution

It introduces a Hermitian linear invariant operator approach within the Lewis-Riesenfeld framework for this class of quantum problems.

Findings

Gaussian wave packets are eigenfunctions of the invariant operator

The method provides a general solution framework for time-dependent linear potentials

Hermitian invariants simplify solving the Schrödinger equation in this context

Abstract

We argue that the way to get the general solution of a Schrodinger equation in the presence of a time-dependent linear potential based on the Lewis-Riesenfeld framework is to use a Hermitian linear invariant operator. We demonstrate that the linear invariant proposed in p and q is an Hermitian operator which has the Gaussian wave packet as its eigenfunction.