ASYMPTOTICALLY EXACT WAVE FUNCTIONS OF THE HARPER EQUATION
ASYMPTOTICALLY EXACT WAVE FUNCTIONS OF THE HARPER EQUATION
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哈珀方程的渐近精确波函数
DOI：
10.1103/physrevlett.81.2112
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发表时间：
1998
影响因子：
8.6
通讯作者：
P. Wiegmann
中科院分区：
文献类型：
--
作者：
A. Abanov;J. Talstra;P. Wiegmann
我们给出了一个不相称的Harper方程的渐近精确解——一个粒子在余弦势晶格上的一维薛定谔方程。波函数可以写成弦多项式的无穷积。这些多项式的根是贝特方程的解。它们是根据弦假设分类的。弦假设给出了根的渐近精确值，揭示了哈珀方程谱的层次结构。
We present asymptotically exact solutions of an incommensurate Harper equation---one-dimensional Schroedinger equation of one particle on a lattice in a cosine potential. The wave functions can be written as an infinite product of string polynomials. The roots of these polynomials are solutions of Bethe equations. They are classified according to the string hypothesis. The string hypothesis gives asymptotically exact values of roots and reveals the hierarchical structure of the spectrum of the Harper equation.