Algorithm to solve the time-dependent Schrödinger equation for a charged particle in an inhomogeneous magnetic field: Application to the Aharonov–Bohm effect
- 1 January 1994
- journal article
- research article
- Published by AIP Publishing in Computers in Physics
- Vol. 8 (5) , 600
- https://doi.org/10.1063/1.168483
Abstract
This paper introduces an unconditionally stable, accurate, and efficient algorithm to solve the time‐dependent Schrödinger equation for a particle moving in an inhomogeneous magnetic field. The algorithm is used to simulate a fundamental thought experiment of quantum mechanics: the magnetic Aharonov–Bohm effect. The calculations demonstrate that the Aharonov–Bohm prediction of the phase shift holds with great precision, even when the dimensions of the interferometer are comparable to the de Broglie wavelength of the particle.Keywords
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