Phys. Rev. Lett. 81, 2112–2115 (1998)Asymptotically Exact Wave Functions of the Harper EquationReceived 13 March 1998; published in the issue dated 7 September 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
|
|
About | Terms and Conditions | Subscriptions | Search | Help
Use of the American Physical Society websites and journals implies that the user has read and agrees to our Terms and Conditions and any applicable Subscription Agreement. Physical Review®, Physical Review Letters®, Reviews of Modern Physics®, and Physical Review Special Topics® are trademarks of the American Physical Society.