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Phys. Rev. Lett. 81, 2112 - 2115 (1998)

Asymptotically Exact Wave Functions of the Harper Equation

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A. G. Abanov and J. C. Talstra
James Franck Institute of the University of Chicago, 5640 S. Ellis Avenue, Chicago, Illinois 60637

P. B. Wiegmann
James Franck and Enrico Fermi Institutes of the University of Chicago, 5640 S. Ellis Avenue, Chicago, Illinois 60637
and Landau Institute for Theoretical Physics, Kosygina Str. 2, 117940 Moscow, Russia

Received 13 March 1998

We present asymptotically exact wave functions of an incommensurate Harper equation—one-dimensional Schrödinger 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.


©1998 The American Physical Society

URL: http://link.aps.org/doi/10.1103/PhysRevLett.81.2112
DOI: 10.1103/PhysRevLett.81.2112
PACS: 05.45.+b, 71.23.Ft, 71.30.+h

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