Calculate the energies for the band structure in the first Brillouin zone of a s

Question

Calculate the energies for the band structure in the first Brillouin zone of a simple cubic lattice. The BZ boundary is for the simple cubic lattice in the [100] direction positioned at ?/a, where a is the lattice constant in real space. The vector G is the reciprocal lattice vector. Please draw the bands in an E(k) diagram. We assume a free electron system in the empty lattice approximation: E=h^2/2m [k+G]^2 Please calculate the 5 lowest energy bands. You can select your from the following equivalent directions in this lattice [note: this is not a complete set: : (000), (100),(-100), (010), (0-10), (001), (00-1), (110), (101) Please calculate at least 2 of the bands "by hand" without the aid of software, and show your work.

Explanation / Answer

very useful for you..............http://lamp.tu-graz.ac.at/~hadley/ss1/bzones/sc.php

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