TIME EVOLUTION OF A PARTICLE IN A ONE-DIMENSIONAL INFINITE SQUARE WELL POTENTIAL WITH MOVING BOUNDARY

As a useful tool to manipulate the feature of quantum systems, periodic drive has attracted widespread attention. Various exotic phases and rich dynamics have been found in the periodically driven quantum systems, such as adiabatic evolution and time crystals. Displaying these strange properties in a simple physical system can not only deepen the understanding of quantum mechanics, but also cultivate students' interest in scientific research. Here, we are interested in a specific case that the well-geometry changing is caused by boundary contraction or expansion. The simplest one-dimensional square well with periodically moving boundary is examined. We explore the influence of the frequency and the intensity of the drive on the time evolution of the system. By numerical simulations, we calculate the evolution of the ground state occupation taking two cases under different boundary parameters and moving paths in both adiabatic and non adiabatic cases. By solving the expected value and deviation value of the energy of the system, the influence of the vibration frequency and intensity of the boundary on the probability of the particles at different energy levels is given. The results show that the expansion and contraction of the potential well with the same velocity have different effects on the time evolution of the particles in the well; Different well wall periodic motion modes have different effects on the time evolution of particles. The results obtained by the numerical method are also explained in this paper.