On the Schrödinger equation with steplike potentials
On the Schrödinger equation with steplike potentials
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关于具有阶梯势的薛定谔方程
DOI：
10.1063/1.533032
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发表时间：
1999
影响因子：
2.5
通讯作者：
T. Aktosun
中科院分区：
文献类型：
--
作者：
T. Aktosun
考虑了势在右半线上在一定意义下渐近于一个正常数时的一维薛定谔方程。散射系数的零能量极限是在比其他地方使用的更弱的假设下得到的，并且从左边开始的散射系数的连续性被建立。势的散射系数用正半线和负半线上的势块的相应系数来表示。整个势的束缚态的数目与两个部分的束缚态的数目有关。最后，给出了半直线上势场反射系数的小能量渐近性的一个改进结果。
The one-dimensional Schrodinger equation is considered when the potential is asymptotic to a positive constant on the right half line in a certain sense. The zero-energy limits of the scattering coefficients are obtained under weaker assumptions than used elsewhere, and the continuity of the scattering coefficients from the left are established. The scattering coefficients for the potential are expressed in terms of the corresponding coefficients for the pieces of the potential on the positive and negative half lines. The number of bound states for the whole potential is related to the number of bound states for the two pieces. Finally, an improved result is given on the small-energy asymptotics of reflection coefficients for potentials supported on a half line.