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

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.