Asymptotically exact solutions of Harper equation

Details Asymptotically exact solutions of Harper equation Asymptotically exact solutions of Harper equation

1998-03-13

arxiv.org/abs/cond-mat/9803179v1

Phys. Rev. Lett., 81, 2112 (1998)

Physics

Condensed Matter

5 pages, 1 figure, revtex, psfig

Scientific paper

10.1103/PhysRevLett.81.2112

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.

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