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Acta Physica Sinica

A MACROSCOPICAL SIMULATION SOLUTION TO THE ONE-DIMENSIONAL STATIONARY STATE SCHRDINGER EQUATION

LIU JIAN-BO, CAI XI-PING, 哈尔滨工业大学应用物理系,哈尔滨150001

Published Jan 1, 2001• 1 citation
Publisher

Abstract

The experimental simulation method is introduced into the quantum mechanics.A vibrating chord system with a stationary stote equation in a form similar to that of the stationary Schr?dinger equation is designed.The system offers the theoretical and experimental methods for the simulation solution to the stationary Schr?dinger equation.The results of the macroscopical simulation presents a macroscopical analogy for the understanding of the Schr?dinger equation.

DOI
10.7498/aps.50.820

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A method is proposed for the quantum-mechanical determination of the eigenstates and eigenvalues of a particle (e.g. an electron) in a potential of general shape. For such systems the method allows one to calculate the exact solutions of the stationary Schrödinger equation. For the application of this method any well-known reference system is needed. A transition from the stationary reference system to the stationary system under investigation is performed by means of the time-dependent Schrödinger equation. The results are compared with various standard methods; alternative numerical methods will be discussed critically.
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