一维费米赝势理论及其应用
Theory and application of Fermi pseudo-potential in one dimension
摘要：
本文对一维薛定谔方程发展了一点相互作用理论。与三维情况类似，所产生的相互作用被称为费米赝势。这个一维问题的主要特征来自这样一个事实，即当一个点被移除时，实数线变得不连通。在一个点上的一般相互作用被发现是三项之和，著名的δ函数势和两个费米赝势，一个奇数下的空间反射和其他偶数。奇数的一个给出了delta '（x）势的正确解释，而偶数的一个是意想不到的，更有趣。在这些费米赝势的许多应用中，最简单的一个被描述。它由δ函数势和偶赝势叠加而成，适用于双通道散射。这个最简单的应用导致了量子存储器的模型，这是任何量子计算机的重要组成部分。
英文摘要：
The theory of interaction at one point is developed for the one-dimensional Schrodinger equation. In analog with the three-dimensional case, the resulting interaction is referred to as the Fermi pseudo-potential. The dominant feature of this one-dimensional problem comes from the fact that the real line becomes disconnected when one point is removed. The general interaction at one point is found to be the sum of three terms, the well-known delta-function potential and two Fermi pseudo-potentials, one odd under space reflection and the other even. The odd one gives the proper interpretation for the delta'(x) potential, while the even one is unexpected and more interesting. Among the many applications of these Fermi pseudo-potentials, the simplest one is described. It consists of a superposition of the delta-function potential and the even pseudo-potential applied to two-channel scattering. This simplest application leads to a model of the quantum memory, an essential component of any quantum computer.
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