Spin-aware movement of electrons and time-of-flight momentum spectroscopy

TL;DR

This paper explores the spin-aware movement of electrons within the de Broglie-Bohm framework, analyzing bound and unbound states, and linking theoretical insights to time-of-flight momentum spectroscopy methods.

Contribution

It provides a detailed analysis of spin-1/2 particle dynamics in Bohmian mechanics, connecting theoretical models with experimental momentum measurement techniques.

Findings

Bohmian trajectories for spin-1/2 particles are characterized in bound and unbound states.

The Fourier transform of wave functions relates to particle velocity distributions.

Insights into the interpretation of time-of-flight momentum spectroscopy are provided.

Abstract

In the framework of the de Broglie-Bohm pilot-wave theory, or Bohmian mechanics, we examine two pedagogical problems that illustrate the bound and unbound motion of spin-1/2 particles: First, a single spin-1/2 particle trapped in the ground state of a spherical box is studied in both the relativistic and nonrelativistic versions of the theory; second, the free time evolution of this particle once the confinement is released is examined, demonstrating how the Fourier transform of the prepared wave function yields the statistics of the particle's far-field (asymptotic) velocity, thereby providing a deeper understanding of time-of-flight momentum spectroscopy techniques.