The analytical transfer matrix method for quantum reflection

doi:10.1088/1674-1056/19/4/040307

中国物理B ›› 2010, Vol. 19 ›› Issue (4): 40307-040307.doi: 10.1088/1674-1056/19/4/040307

The analytical transfer matrix method for quantum reflection

曹庄琪¹, 许田², 方靖淮²

(1)Institute of Optics and Photonics, Shanghai Jiao Tong University, Shanghai 200240, China; (2)Physics Department, Nantong University, Nantong 226001, China

收稿日期:2008-06-12 修回日期:2009-07-04 出版日期:2010-04-15 发布日期:2010-04-15
基金资助:
Project supported by Science Foundation of Nantong University (Grant Nos.~03080122 and 09ZY001).

The analytical transfer matrix method for quantum reflection

Xu Tian(许田)^a)^†, Cao Zhuang-Qi(曹庄琪)^b), and Fang Jing-Huai(方靖淮)^a)

^a Physics Department, Nantong University, Nantong 226001, China; ^b Institute of Optics and Photonics, Shanghai Jiao Tong University, Shanghai 200240, China

Received:2008-06-12 Revised:2009-07-04 Online:2010-04-15 Published:2010-04-15
Supported by:
Project supported by Science Foundation of Nantong University (Grant Nos.~03080122 and 09ZY001).

摘要/Abstract

摘要： In this paper, the analytical transfer matrix method (ATMM) is applied to study the properties of quantum reflection in three systems: a sech$^{2}$ barrier, a ramp potential and an inverse harmonic oscillator. Our results agree with those obtained by Landau and Lifshitz [Landau L D and Lifshitz E M 1977 \wx{Quantum Mechanics (Non-relativistic Theory)}{} (New York: Pergamon)], which proves that ATMM is a simple and effective method for quantum reflection.

Abstract: In this paper, the analytical transfer matrix method (ATMM) is applied to study the properties of quantum reflection in three systems: a sech$^{2}$ barrier, a ramp potential and an inverse harmonic oscillator. Our results agree with those obtained by Landau and Lifshitz [Landau L D and Lifshitz E M 1977 Quantum Mechanics (Non-relativistic Theory) (New York: Pergamon)], which proves that ATMM is a simple and effective method for quantum reflection.

Key words: analytical transfer matrix method, quantum reflection, reflection coefficient, transmission coefficient, reflection time

中图分类号: (Solutions of wave equations: bound states)

03.65.Ge

03.65.Fd (Algebraic methods) 02.10.Yn (Matrix theory)

许田, 曹庄琪, 方靖淮. The analytical transfer matrix method for quantum reflection[J]. 中国物理B, 2010, 19(4): 40307-040307.

Xu Tian(许田), Cao Zhuang-Qi(曹庄琪), and Fang Jing-Huai(方靖淮). The analytical transfer matrix method for quantum reflection[J]. Chin. Phys. B, 2010, 19(4): 40307-040307.

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The analytical transfer matrix method for quantum reflection

The analytical transfer matrix method for quantum reflection

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