Simulation of Time-Independent Aharanov-Bohm Effect Using Matlab

We simulated time-varying Aharanov-Bohm effect (ABE) under time-independent magnetic field using Matlab, taking into account the influence of time-varying magnetic field on charged particles moving in a two-dimensional plane. According to our models, we discovered the time evolution of wave function and interference patterns. We also developed two mathematical models to analyze this phenomenon, of which the first mode focuses on the time evolution of the wave function, governed by the time-dependent Schrödinger equation incorporating electromagnetic potentials, while the second one is responsible for simulating the resulting interference patterns by modifying the intensity of wave packet based on the frequency-dependent phase shift caused by the sinusoidal magnetic field in the solenoid. Our results align with theoretical expectations and provide new insights into the frequency-dependent nature of the time-varying ABE.