Quantum mechanical evolution operator in the presence of a scalar linear potential: discussion on the evolved state

TL;DR

This paper explores the quantum evolution of a wave-function under a scalar linear potential, focusing on phase analysis, proposing an experiment to measure quantum phases, and re-analyzing the Stern-Gerlach experiment to demonstrate spin manipulation.

Contribution

It provides a detailed analysis of quantum phases in linear potentials, introduces an experimental proposal to measure quantum phases, and applies the evolution equations to spin manipulation techniques.

Findings

Identification of quantum-origin phases in wave-function evolution

Proposal of an experimental setup to measure quantum phases

Re-analysis of Stern-Gerlach experiment for spin control

Abstract

We discuss the form of the wave-function of a state subjected to a scalar linear potential, paying special attention to quantum tunneling. We analyze the phases acquired by the evolved state and show that some of them have a pure quantum mechanical origin. In order to measure one of these phases, we propose a simple experimental scenario. We finally apply the evolution equations to re-analyze the Stern\&Gerlach experiment and to show how to manipulate spin by employing constant electric fields.