Answer Happy

Consider the tight binding approximation for energy band calculation. Assume that there is only one atom in the unit cell. We consider a single s atomic orbital, o(r). (a) Write down a LCAO (linear combination of atomic orbitals) wavefunction, Yk(r). Show that the wavefunction actually fulfills Bloch's theorem. (b) Derive the energy eigenvalue for the LCAO wavefunction. Take into account only nearest neighbors. (c) Derive the tight-binding energy band for a cubic bce lattice with lattice constant a. (d) Derive e(k) for a simple cubic lattice. Express the dispersion relations for 1-X axis, X-M axis and I-R axis and plot them. (e) (Bonus question) Discuss how the energy band structure changes when a s atomic orbital is replaced by a p atomic orbital. Include a rough sketch of the expected energy bands.