J4 ›› 2011, Vol. 28 ›› Issue (5): 534-539.

• 量子物理 • 上一篇    下一篇

非均匀势场中物质波的反射和透射

肖平平, 邓满兰   

  1. 宜春学院物理科学与工程技术学院, 江西 宜春 336000
  • 收稿日期:2010-11-11 修回日期:2010-12-09 出版日期:2011-09-28 发布日期:2011-08-18
  • 通讯作者: 曹庄琪(1945-),上海人,上海交通大学,教授,主要从事导波光电子器件的研究。 E-mail:zqcao@sjtu.edu.cn
  • 作者简介:肖平平(1972-),江西省宜春人,副教授,博士生,主要从事光纤通信、导波光学、集成光学及其应用领域的研究。
  • 基金资助:

    江西省教育厅(JXJG-08-14-12)资助课题

Reflection and transmission of material wave through an arbitrary potential barrier

XIAO Pingping,DENG Manlan   

  1. School of Physics Science and Engineering Technology, Yichun University,  Yichun 336000, China
  • Received:2010-11-11 Revised:2010-12-09 Published:2011-09-28 Online:2011-08-18

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。最终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。

关键词: 量子光学, 反射几率, 分析转移矩阵方法, 导波光学

Abstract:

Based on the similarity between time-independent Schrödinger equation and Helmholtz equation, the analytical transfer matrix method was utilized to analyze macroscopic quantum tunneling effect, and the potential filed and engine valve were corresponded to the refractive index and propagation constant, respectively. Without solving the Schrödinger equation and any approximation, the exact analytic expressions of the 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.

Key words: quantum optics, reflection probabilities, analytical transfer matrix method, guide-wave optics

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