ASYMPTOTICALLY EXACT WAVE-FUNCTIONS OF THE HARPER EQUATION

We present asymptotically exact wave functions of an incommensurate Ha rper equation-one-dimensional Schrodinger 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 polynomi als are solutions of Bethe equations. They are classified according to the string hypothesis. The string hypothesis gives asymptotically exa ct values of roots and reveals the hierarchical structure of the spect rum of the Harper equation.