时域有限差分法在势垒贯穿问题中的应用  

The application of the Finite Difference Time Domain method in the problem of potential barrier

作　　者：谷桂初[1] 周庆[1] 

机构地区：[1]云南大学物理系,云南昆明650091

出　　处：《云南师范大学学报（自然科学版）》2007年第5期43-48,共6页Journal of Yunnan Normal University:Natural Sciences Edition

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。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 - barber 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.

关 键 词：时域有限差分法 势垒贯穿 量子隧道效应 

分 类 号：O411.3[理学—理论物理] O413.1[理学—物理]