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Journal of Shenyang Normal University

Computer Simulation of Dynamic Stochastic Process of Potential Barrier Penetration

Luo Li-jin

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

This paper demonstrates the dynamic and stochastic process of the potential barrier penetration of microcosmic particle,based on Monte Carlo method and the transmission coefficient of microcosmic particle potential barrier penetration,by using the programming and visualization of Matlab.

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In this paper,transmission coefficient that the micro particle penetrate two potential barriers successively is calculated by solving the stationary schrodinger equation.Our numerical results show that the micro particle could penetrate potential barriers no matter energy of particle is taller or smaller than the height of potential barriers.But the transmission coefficient varies in several different circumstances.Particularly,it may arise resonance transmission in conditions.In a word,the transmission coefficient could changes with the height and width of two potential barriers,and have nothing to do with the distance between two potential barriers.
Elementary numerical methods are used to evaluate solutions to Schrödinger’s equation for a variety of one-dimensional potential barriers and to determine the transmission coefficients of free particles. These techniques are used to study the oscillatory variations in transmission coefficients for both continuous and discontinuous potentials. The amplitude of the variations is found to be strongly increased by discontinuities in the potential function but small variations exist even for a smooth, continuous potential function. The techniques described are suitable for intermediate-level undergraduate physics students.