Electron Wave Spin in a Quantum Well

TL;DR

This paper investigates the wave nature of electron spin within a quantum well by solving the Dirac equation, revealing stable circulating currents and the influence of confinement on spin, while also analyzing wavepacket stability.

Contribution

It provides an exact 4-spinor solution to the Dirac equation in a quantum well, demonstrating stable current patterns and geometry-dependent spin modifications.

Findings

Stable circulating current density with donut shape inside the well

Spin value affected by the well's confining geometry

Free electron wavepacket is unstable and decoheres quickly

Abstract

The particle-wave duality of the electron poses a principle question of whether the spin is a property of the particle or the wave. In this paper, the wave nature of the spin is studied for an electron inside a two-dimensional quantum well. By solving the exact $4-$spinor eigen solution to the Dirac equation, we show that a stable circulating total current density exists inside the well with a donut shaped topography. A spin value is modified by the confining geometry of the well. Our analysis also shows that a free electron Gaussian wavepacket is unstable and experiences quick decoherence.