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Finite-Barrier Double-Slit Scattering in Standard Quantum Mechanics: Numerical Separation of Through-Thickness and Finite-Wall Responses

Ali Alhawarat M, Pasquale Camelia

Published Sep 27, 2026• 0 citations
Publisher

Abstract

This work studies a finite-potential, finite-thickness electron double slit entirely within the time-dependent Schrödinger equation. Three main findings survive numerical and adversarial checks. First, a sharp real-space partition between material and aperture contributions is not unique: small shifts of the partition can alter the assigned bulk contribution and reverse its sign. Second, thickness scans separate a through-thickness term, independently calibrated in a no-slit geometry, from a finite-wall residual that remains when direct barrier transmission becomes very small. Third, varying the wall height through a finite 8 eV control drives the finite-minus-control residual through zero and reverses its sign. The wall-height dependence transports across thickness with one fitted geometry constant, while the physical carrier of that dependence remains unresolved. No result requires an additional quantum path, a Born-rule violation, or dynamics beyond standard quantum mechanics.

DOI
10.5281/zenodo.22999453

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Finite-barrier electron double slit in standard quantum mechanics: frozen numerical record, detector-position supplement, and wall-height scaling

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arXiv:quant-ph/0109111•Journal of Physics A Mathematical and General•May 18, 2002•14 citations
This work studies a finite-potential, finite-thickness electron double slit entirely within the time-dependent Schrödinger equation. Three main findings survive numerical and adversarial checks. First, a sharp real-space partition between material and aperture contributions is not unique: small shifts of the partition can alter the assigned bulk contribution and reverse its sign. Second, thickness scans separate a through-thickness term, independently calibrated in a no-slit geometry, from a finite-wall residual that remains when direct barrier transmission becomes very small. Third, varying the wall height through a finite 8 eV control drives the finite-minus-control residual through zero and reverses its sign. The wall-height dependence transports across thickness with one fitted geometry constant, while the physical carrier of that dependence remains unresolved. No result requires an additional quantum path, a Born-rule violation, or dynamics beyond standard quantum mechanics.
A frozen numerical record of a two-dimensional electron double slit in which the idealized impenetrable wall is replaced by a barrier of finite height and finite thickness, and the response is measured against a finite low-transmission control rather than against an infinite wall. Three artifacts. The primary record contains a preregistration of five cases, an independent split-operator solver, the closure evidence and a gate ledger; it was cryptographically committed before a blind exchange with an independent worker who had frozen his own calculation. A detector-position supplement varies only the plane at which the current is recorded, 1–14 nm, and identifies which planes are physically usable rather than forcing them. A wall-height record varies only the barrier height, 2.35–24 eV on both sides of the control, and both thicknesses. What the records establish: the finite-minus-control response separates into a through-thickness term, calibrated independently by the no-slit geometry, and a face and edge term that survives when the thickness kills tunnelling; a hard spatial partition into "material" and "aperture" contributions is not well defined, since shifting the mask by one or two grid cells reverses the sign of the attributed bulk contribution; the residual vanishes only when the two walls are identical and reverses sign when the test wall is the harder one, so it is the difference between two standard responses and not a property of one wall; and its form is one scalar function of the wall height times one geometry constant. What they do not establish, and prove they cannot establish in this geometry: which property of the wall carries that function, since a null regressor with no derivation behind it fits equally well and the measurement that would separate the two is smaller than the numerical systematics. No additional quantum path, no Born-rule violation and no physics beyond the time-dependent Schrödinger equation is claimed or supported. Withdrawn constructions, corrections and errata are retained in the records rather than removed. Each archive carries a manifest, a verifier that re-derives its summary from the raw output and rebuilds its report byte-identically, and a set of mutations that must each be caught — six, five and seven negative controls respectively. The two supplements reproduce values of the primary record's gate ledger bit for bit. Every claim carries its register: exact result, computed here, conditional, constitutive, open, or prediction.
We performed time-evolved numerical simulation of a two-dimensional electron wave packet through a double slit by solving the time-dependent Schrödinger equation using the finite difference method to simulate the electron interference phenomenon of a single electron. The propagating directions of interference peaks show that the starting point of electron interference is the center between the two slit exits. The number of interference peaks and their angles are found to be independent of potential barrier thickness. These results are compared with the results of our previous calculation of electron diffraction through a single slit.
This record contains the archived materials for Simulation B of the finite-barrier electron double-slit study conducted entirely within standard nonrelativistic quantum mechanics.The deposit includes four distinct records: the post-exchange protocol reconstruction, the frozen Simulation B outcome package dated 24 September 2026, the final numerical closure record, and a separately labelled post-exchange reconstruction of the setup-specific ~0.13 numerical scale using only values preserved in the frozen outcome record.The historical raw solver archive for Simulation B was not preserved. Accordingly, the protocol reconstruction and the ~0.13 reconstruction are explicitly identified as post-exchange records and are not presented as original preregistration artifacts or as reproductions of the historical solver.The frozen outcome package remains unchanged and serves as the primary provenance commitment for Simulation B.Simulation B provides an independent qualitative consistency record for the study, but it is not treated as a point-by-point numerical replication of Simulation A because the geometries, controls, detector coordinates, and normalization differ.The associated joint numerical record for Simulation A, including the frozen technical package, detector-position supplement, and wall-height scaling supplement, is available at:DOI: 10.17605/OSF.IO/V65H3Associated manuscript:Finite-Barrier Double-Slit Scattering in Standard Quantum Mechanics: Numerical Separation of Through-Thickness and Finite-Wall ResponsesAuthors: Ali Alhawarat and Pasquale Camelia.
The mainstream quantum mechanics uses “probability wave superposition and single-electron self-interference” to explain electron single-slit and double-slit diffraction. This theory deviates from the essential nature of real particle interactions and has fundamental logical flaws. The electron is a negatively charged real particle with a definite physical size and high-frequency transverse oscillation; a single real particle has no physical basis for self-interference. Abandoning the abstract probability wave hypothesis, this paper establishes a complete real-interaction model including electrostatic repulsion deflection, surface electron exchange, collision scattering, microscopic refraction, and barrier diffraction, based on the three-dimensional random transverse oscillation and charge repulsion of electrons. The model uniformly explains the real formation mechanism of electron single-slit diffraction and double-slit interference fringes. This paper proves that in single-electron sequential emission, each electron passes through only one slit; all bright and dark fringes are the statistical result of multiple microscopic interactions between electrons and slit walls or the central barrier. The disappearance of fringes under observation is caused by external disturbance to the inherent oscillation and wall-interaction equilibrium, not by wave function collapse. This paper further clarifies that whether an electron can pass through a slit is determined by its transverse oscillation amplitude, not by wavelength. Amplitude directly corresponds to slit width and is the core controlling variable of diffraction. Meanwhile, if no slit is placed, electrons flying directly to the screen produce no diffraction or interference fringes, proving that electrons themselves have no self-interference ability. Fringes are generated by slit structures, not by intrinsic wave interference of electrons. This study corrects the century-long misunderstanding of electron diffraction and establishes a new microscopic diffraction mechanism consistent with classical real-particle physics.
At the turn of the twentieth century, the establishment of quantum theory propelled rapid advancements, particularly in the understanding of quantum tunnelling—a fundamental phenomenon in quantum mechanics crucial for various physical processes. The quantum phenomenon of particle passes through potential barriers is of great importance. In classical physics, when the energy of a particle is less than the height of a double barrier structure, it is impossible for it to pass through. However, quantum mechanics allows a particle to penetrate the barrier and emerge on the other side. This paper explores the quantum tunnelling effect, focusing on the single potential barrier model in one dimension and subsequently extending to the double potential barrier model. The Schrödinger equation provides the foundational framework for elucidating the motion of microscopic particles, emphasizing wave-particle duality inherent in quantum mechanics. The analysis of the single potential barrier model involves solving the Schrödinger equation in different regions, determining wave functions and coefficients through boundary conditions. The transmission coefficient is derived, representing the probability of a particle passing through a barrier. In the case of a “thick” barrier, an approximate form for transmission coefficient is provided, demonstrating the exponential decrease in transmission probability with increasing barrier thickness.