【摘要】 时域有限差分(Finite Difference Time Domain,FDTD)法在量子力学问题中的应用越来越引起人们的关注。系统介绍了该方法的基本原理、边界处理方法和初始试探波函数的选取。在此基础上,计算模拟了三种不同的势垒如方势垒、三角形势垒和谐振势垒下系统的能量变化、概率变化,再现了量子隧道效应这一重要物理现象。进一步表明了运用FDTD法来解决量子力学问题是方便可行的,并且以系统平均能量方法处理截断边界能得到比较理想的结果。对于解决其它量子力学问题具有一定的指导意义。更多还原

【Abstract】 The application of the Finite Difference Time Domain(FDTD) method in quantum-mechanical problems becomes more and more interesting.The postulate,the boundary cut-off condition and the initial trial wave function are described.Based on the FDTD method,three different potential-barrier problems including rectangular potential-barrier,deltoid potential-barrier and syntonic potential-barrier are investigated.The energy variation and the probability variation are calculated and modeled,the important phenomenon of quantum tunnel effect reappeared.It is convenient to apply the FDTD method in quantum-mechanical problems and the results are acceptable while using the boundary cut-off based on the expectation energy of the system.And it is potentially further extended to other quantum-mechanical problems.更多还原