Reflectionless eigenstates of the sech2 potential

被引:112
作者
Lekner, John
机构
[1] School of Chemical and Physical Sciences, Victoria University of Wellington, Wellington
关键词
D O I
10.1119/1.2787015
中图分类号
G40 [教育学];
学科分类号
040101 ; 120403 ;
摘要
The one-dimensional potential well V(x)=-(h(2)v(v+1)/2ma(2)) sech(2) (x/a) does not reflect waves of any energy when v is a positive integer. We show that in this reflectionless case the,solutions of Schrodinger's equation can be expressed in terms of elementary functions. Wave packets can be constructed from these energy eigenstates, and the propagation of such wave packets through the potential region can be studied analytically. We find that the group velocity of a particular packet can substantially exceed the group velocity of a free-space Gaussian packet. The bound states of the potential can also be expressed in terms of elementary, functions when v is an integer. The special properties of the integer v potentials are associated with critical binding. (C) 2007 American Association of Physics Teachers.
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页码:1151 / 1157
页数:7
相关论文
共 14 条
[1]  
[Anonymous], SUPERSYMMETRY QUANTU
[3]   The penetration of a potential barrier by electrons [J].
Eckart, C .
PHYSICAL REVIEW, 1930, 35 (11) :1303-1309
[4]   Reflection of waves in an inhomogeneous absorbing medium [J].
Epstein, PS .
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1930, 16 :627-637
[5]  
Flugge S., 1974, Practical Quantum Mechanics
[6]  
GAUTSCHI W, 1964, NBS APPL MATH SERIES, V55, pCH7
[7]   REFLECTIONLESS TRANSMISSION THROUGH DIELECTRICS AND SCATTERING POTENTIALS [J].
KAY, I ;
MOSES, HE .
JOURNAL OF APPLIED PHYSICS, 1956, 27 (12) :1503-1508
[8]  
Kennard E H., 1927, Z. Phys, V44, P326, DOI [DOI 10.1007/BF01391200, 10.1007/bf01391200]
[9]   Scattering of a Gaussian wave packet by a reflectionless potential [J].
Kiriushcheva, N ;
Kuzmin, S .
AMERICAN JOURNAL OF PHYSICS, 1998, 66 (10) :867-872
[10]  
Landau L., 1965, QUANTUM MECH