含时微扰系统中跃迁概率的衍射、干涉及共振现象

Diffaction,interference and resonance transition of probability in time-dependent perturbation quantum system

主要应用Mathematica等计算软件讨论量子力学教学中重要的量子跃迁问题.借助解析分析和计算绘图的方法,给出了量子跃迁过程中概率波所表现出的衍射和干涉现象,通过与光波的类比让学生理解概率波的波动性以及相干叠加所导致的量子共振现象.以含时微扰理论为基础,计算了恒定微扰和谐振微扰概率跃迁的叠加问题,从量子概率干涉的角度解释了概率波共振跃迁的物理机制.

This paper mainly discusses the quantum transition in the quantum mechanics education by using Mathematica software. Based on the analytical and numerical calculations,the probability diffraction and interference in the state transition process are investigated in detail. Analogy to the light wave, the corresponding wave properties of the probability wave and the resonant transition induced by the coherent superposition are clearly explained to the students. Under the perturbation theory, the resonant transitions on the constant perturbation related to probability d P iffraction and on the harmonic perturbation related to probability interference are explained by a time-dependent robability superposition mechanism.