Computer simulation-based evolution and measurement of quantum mechanical wave functions

The purpose of this article is to deeply study the evolution process and measurement behavior of wave function in quantum mechanics by computer simulation. Based on Schrodinger equation and quantum measurement postulate, a set of numerical simulation framework is constructed, and typical models such as one-dimensional infinite potential well, simple harmonic oscillator, double-slit interference and two-level system are simulated by Crank-Nicolson method. Probability sampling mechanism is introduced in the simulation process to reproduce the wave function collapse caused by measurement, and the key results in the evolution process are shown. It includes the change of maximum probability density at different time steps (0.78 → 0.63 → 0.78), the exchange of kinetic energy and potential energy under the condition of energy conservation, the distribution characteristics of measurement positions in the double-slit interference experiment and the statistical frequency of the measurement results of the two-level system (0.503:0.497). The research shows that the designed simulation method can effectively reproduce the dynamic evolution law of quantum system and the statistical characteristics of measurement, and provide a visual auxiliary tool for understanding quantum phenomena.