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Problem: Nearly Free Electrons in Two Dimensions

   Assume we have a two-dimensional nearly free-electron system on a square lattice of lattice spacing a. The Fourier transform of the weak lattice potential is tex2html_wrap_inline5973 .

    We want to investigate the band structure around the tex2html_wrap_inline5975 point in the reciprocal lattice. The unperturbed spectrum has a fourfold degeneracy at this point. Only the tex2html_wrap_inline5977 and the tex2html_wrap_inline5979 components of tex2html_wrap_inline5981 are important. Find the gap if tex2html_wrap_inline5983 and tex2html_wrap_inline5985 . Also, find the gap if tex2html_wrap_inline5987 and tex2html_wrap_inline5989 .

 

This document can be accessed on the World Wide Web at "http//:solidstate.physics.sunysb.edu/book/prob/ ".

Laszlo Mihaly
Thu Oct 31 13:23:11 EST 1996

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