Evanescent Electron Wave Spin

TL;DR

This paper demonstrates that evanescent electron waves exist outside quantum wells and share spin properties with confined waves, implying that electrons cannot be perfectly confined and quantum information can leak through boundaries.

Contribution

It provides analytical solutions for evanescent electron waves outside quantum wells using the Dirac equation, highlighting the non-confinement and spin characteristics of these waves.

Findings

Evanescent electron waves exist outside quantum wells.

Evanescent waves share spin properties with confined waves.

Electrons cannot be perfectly confined, allowing quantum information leakage.

Abstract

This study demonstrates the existence of an evanescent electron wave outside both finite and infinite quantum wells by solving the Dirac equation and ensuring the continuity of the spinor wavefunction at the boundaries. We show that this evanescent wave shares the spin characteristics of the wave confined within the well, as indicated by analytical expressions for the current density across all regions. Our findings suggest that the electron cannot be confined to a mathematical singularity and that quantum information, or quantum entropy, can leak through any confinement. These results emphasize that the electron wave, fully characterized by Lorentz-invariant charge and current densities, should be considered the true and sole entity of the electron.