摘要
利用与时间无关的薛定谔方程和亥姆霍兹方程的形式相似性,把势场分布和能量本征值分别与光波导中的折射率分布和传播常数相对应,将分析光波导的分析转移矩阵用于分析微观粒子贯穿势垒的量子隧道效应。在不求解薛定谔方程且不引入任何近似的情况下得到了微观粒子穿越任意势垒的反射系数和反射几率的精确解析式。分析表明所得公式精确,物理意义非常清楚,通用性强。在研究量子隧道效应、量子反射、量子粒子和隧道共振等方面具有一定的应用价值。
Based on the similarity between time-independent SchrSdinger equation and Helmholtz equation, the analytical transfer matrix method was utilized to analyze macroscopic quantum tunneling effect and the potential filed and eigenvalue were corresponded to the refractive index and propagation constant respectively. Without solving the SchrSdinger equation and any approximation, the exact analytic expressions of reflection coefficient and reflection probability of the particle were obtained. Initial results show the equations obtained here are exact and have clear physical meanings. It is expected to be applied in the researches of many basic quantum phenomena, such as quantum tunneling effect, quantum reflection quantum particles and tunneling resonance
出处
《量子电子学报》
CAS
CSCD
北大核心
2011年第5期534-539,共6页
Chinese Journal of Quantum Electronics
基金
江西省教育厅(JXJG-08-14-12)资助课题
关键词
量子光学
反射几率
分析转移矩阵方法
导波光学
quantum optics
reflection probabilities
analytical transfer matrix method
guide-wave optics
