The analytical transfer matrix method for quantum reflection

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

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.

Keywords: analytical transfer matrix method quantum reflection reflection coefficient transmission coefficient reflection time

Received: 12 June 2008
Revised: 04 July 2009
Accepted manuscript online:

PACS:	03.65.Ge	(Solutions of wave equations: bound states)
	03.65.Fd	(Algebraic methods)
	02.10.Yn	(Matrix theory)

Fund: Project supported by Science Foundation of Nantong University (Grant Nos.~03080122 and 09ZY001).

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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 2010 Chin. Phys. B 19 040307

[1]	Kasevich M and Chu S 1992 Phys. Rev. Lett. 69 1741
[2]	Lawall J, Bardou F, Saubamea B, Shimizu K, Leduc M, Aspect A and Cohen-Tannoudji C 1994 Phys. Rev. Lett. 73 1915
[3]	Reichel J, Bardou F, Ben-Dahan M, Peik E, Rand S, Solomon C and Cohen-Tannoudji C 1995 Phys. Rev. Lett. 75 4575
[4]	Dahan M B, Peik E, Reichel J, Castin Y and Salomon C 1996 Phys. Rev. Lett. 76 4508
[5]	Jurisch A and Friedrich H 2004 Phys. Rev. A 70 032711
[6]	Friedrich H, Jacoby G and Meister C G 2002 Phys. Rev. A 65 032902
[7]	Cao Z Q, Liu Q, Shen Q S, Dou X M and Chen Y L 2001 Phys. Rev. A 63 054103
[8]	Xu T, Cao Z Q and Shen Q S 2005 Chin. Phys. Lett. 22 2746
[9]	Xu T, Cao Z Q, Shen Q S and Zhu G L 2006 Chin. Phys. 15 1172
[10]	Xu T, Cao Z Q and Fang J H 2008 Chin. Phys. B17 4379
[11]	He Y, Cao Z Q and Shen Q S 2004 Chin. Phys. Lett. 21 2089
[12]	Ou Y C, Cao Z Q and Shen Q S 2004 J. Chem. Phys. 121 8175

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