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Qeios

Evanescent Electron Wave Spin

Ju Gao, Fang Shen

Published Sep 29, 2023• 0 citations
Publisher

Abstract

We demonstrate that an evanescent wave spin exists outside a finite quantum well by solving the Dirac equation in a finite cylindrical quantum well. The analytical analysis validates the wavefunction inside an infinite quantum well but recovers a non-zero evanescent wave outside the well. We propose that it is possible to probe or eavesdrop on quantum spin information through the evanescent wave spin without destroying the entire spin state. We argue that a spin-based quantum process or device is deterministic rather than probabilistic.

DOI
10.32388/ewv928

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We demonstrate that an evanescent wave spin exists outside a finite quantum well by solving the Dirac equation in a finite cylindrical quantum well. The analytical analysis validates the wavefunction inside an infinite quantum well but recovers a non-zero evanescent wave outside the well. We propose that it is possible to probe or eavesdrop on quantum spin information through the evanescent wave spin without destroying the entire spin state. We argue that a spin-based quantum process or device is deterministic rather than probabilistic.
Our study shows that an evanescent electron wave exists outside both finite and infinite quantum wells, by solving exact solutions of the Dirac equation in a cylindrical quantum well and maintaining wavefunction continuity at the boundary. Furthermore, we have derived analytical expressions of the current density to demonstrate that the evanescent wave spins concurrently with the wave inside the quantum well. Our findings suggest that it is possible to probe or eavesdrop on quantum spin information through the evanescent wave spin without destroying the entire spin state. The wave spin picture interprets spin as a global and deterministic property of the electron wave that includes both the evanescent and confined wavefunctions. This suggests that a quantum process or device based on the manipulation and probing of the electron wave spin is deterministic in nature rather than probabilistic.
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.
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 quantum 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.
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.
Our study reveals electron spin in a cavity as a stable circulating current density, characterized by a torus topology. This current density circulates concentrically beyond the cavity boundary, illustrating the concept of evanescent wave spin. While the interaction with a uniform magnetic field aligns with established spin-field observations, our analysis of regional contributions deviates from particle-based spin predictions. The integration of charge and spin properties into a single Lorentz covariant entity suggests that the electron wave constitutes the fundamental and deterministic reality of the electron.
It is not possible to use the Schrödinger equation to describe the motion of a particle with relativistic effects since it is not invariant relative to the Lorentz transformation. However, the attempt to generalize quantum mechanics in the relativistic domain on the basis of the one particle theory is somehow difficult. So we find the appropriate equations on the basis of the relativistic invariance. To obtain the non-relativistic equations, we take the limit as the speed of light tends to infinity. This obviously recovers the Schrödinger equation. Under this heading, we extend the non-relativistic Schrödinger equation in the description of particles with speeds comparable with that of light. This extension should be consistent with the Lorentz transformation [ 12 ]. The characteristic feature of the relativistic wave equations is the spin which provides a useful gauge in the applicability of particular equations that describe particular kinds of particles. We have two types of relativistic equations, i.e., the equation with spin-zero due to Schrödinger and spin-half due to Dirac that describes the electron.