Quantum-mechanical effects in a linear time-dependent potential

TL;DR

This paper analyzes the quantum dynamics of a particle in a half-space with a linear potential under various sudden changes, providing solutions to the Schrödinger equation and discussing quantum statistical implications.

Contribution

It presents exact solutions to the time-dependent Schrödinger equation for a particle in a half-space with a linear potential under different sudden boundary and potential changes, a novel analysis in this context.

Findings

Exact solutions for different sudden changes in boundary conditions and potential.

Insights into quantum statistical behavior in these scenarios.

Discussion of implications for quantum dynamics and control.

Abstract

The solution of the time-dependent Schr\"odinger equation is discussed for a particle confined in half-space $x>0$ with a linear potential $V(x)=Kx$ in the following situations: (a) sudden removal of the wall and switching on the linear potential $V(x)=Kx$ at $x \leq 0$, (b) sudden removal of the wall and the potential and (c) sudden removal of the potential. A brief discussion of the quantum statistic is presented.