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Qeios

Evanescent Electron Wave Spin

Ju Gao, Fang Shen

Published Oct 27, 2023• 1 citation
Publisher

Abstract

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.

DOI
10.32388/ewv928.2

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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.
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.
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.
This work proposes a wave-entity perspective of the electron spin qubit, treating the electron as a continuous physical wave rather than a point-like particle. In this theoretical framework, each spin qubit corresponds to a distinct current density configuration, offering a resolution to the paradox of a particle appearing to spin both up and down simultaneously. We further predict the existence of a persistent, azimuthally asymmetric magnetic field associated with the wave-spin qubit, an effect not anticipated by the conventional particle-spin model. Notably, the qubit’s relative phase governs the orientation of both the current and the magnetic field, suggesting a mechanism for direct, local interactions between qubits. This phase-dependent coupling could form the basis for inherently parallel quantum computing architectures, in contrast to the sequential operations of gate-based logic. While this framework is grounded in theoretical analysis, it yields testable predictions—particularly regarding the magnetic field structure—that invite experimental verification. By treating the electron wave as the fundamental physical entity, rather than a probabilistic abstraction, we explore the possibility of a quantum model that is deterministic, local, causal, and fully consistent with special relativity.