The Wave Equation for Many Electrons

George Paget Thomson

Xiang-Yao Wu, Xiao-Jing Liu, Baijun Zhang +1 more

As well known, an electron will produce radiative reaction force when the electron emits electromagnetism radiation. The electron radiative effect had not been considered in Schrödinger wave equation. In this paper, we give the nonlinear quantum wave equations for the radiative electron and some dissipative systems.

Clinton J. Davisson

Shota Hayakawa, Nobuyuki Hirami, Hisato Fujisaka

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.

G.F.S.

LASZLO SOLYMAR, Donald Walsh, R.R.A. Syms

Abstract Introduces the Schrödinger wave equation as the key equation governing the behaviour of electrons, and presents simple solutions (known as wave functions) as electron waves, and packets of electron waves, which can represent localised, particle-like electrons. Considers the behaviour of electron waves on meeting a potential barrier and trapped in potential wells with finite and infinite walls, and introduces the idea of energy levels. Discusses the accepted interpretation of the electron wave function, namely that its modulus square leads to the probability of finding an electron in a given region of space. Considers further the uncertainty relationship and associated philosophical implications.