A Primary Study on Classical Particle Modeling of Electron-Wave Interference Systems

Nagata, Kouji; Nakashima, Wataru; Fujisaka, Hisato; Kamio, Takeshi; Haeiwa, Kazuhisa

doi:10.15248/proc.1.324

Cited by 1 publication

(3 citation statements)

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“…4(Td) and 7(Rd) and saw that average differences between the probability distributions of the particles and those by the wave packets were 8.4 × 10 −4 and 1.1 × 10 −3 . It was theoretically proven in [8] and confirmed with preceding numerical examples in [5,9,10] that equality (16) holds. The two comparisons shown in Figs.…”

Section: Computational Accuracysupporting

confidence: 75%

“…It guarantees that the probability distribution of the sample solutions to the NSODE coincides with that determined from the quantum wave. The equivalence between the probabilistic particles and the quantum wave was confirmed by numerical experiments [5,9,10]. Several types of electron wave splitters and filters have been proposed.…”

Section: Introductionmentioning

confidence: 79%

“…The four-stub filter is superior to the one-stub filter in blocking electron of low kinetic energy. When the four-stub filter is used in an interval [1,10] of momentumhk x , the filter possesses bandpass characteristic while the P T characteristic of the one-stub filter is moderately varying in the interval. There is no mathematical method of obtaining exact time-evolving packets that are the solutions of the Schrödinger equation (1) with the potentials shown in Fig.…”

Section: On Experimental Resultsmentioning

confidence: 99%

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Representation of electrons on symmetric electron-wave stub-filters by waves and particles

Hayakawa

Hirami

Fujisaka

2019

NOLTA

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This paper presents a method of computing sample trajectories of particle models of electrons on symmetric electron-wave stub-filters. The time-independent Schrödinger equation describing the electron-wave filters is transformed to a system of linear algebraic equations. The Fourier series expansion transforms the eigenvalues of the system to continuous and differentiable eigenfunctions. A electron wave packet is constructed from the obtained smooth eigenfunctions and a nonlinear stochastic ordinary differential equation (NSODE) which governs the behavior of the electron particle model is established by applying the stochastic quantization to the wave packet. Sample trajectories of the particles are computed by integrating the NSODE. Numerical experiments have shown that the statistical behavior of the particles is almost equal to that of the wave packets.

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