What Is the Bandwidth and Wave Vector Solutions for a BCC Tight Binding Model?

[abdul-pablo]

According to tight binding moment, for BCC crystalographic structures (such as Fe), energy E depends on wave vector kx, ky, kz: E(x) = const - 8t cos(kx * a/2)*cos(ky * a/2)*cos(kz * a/2), where t>0 is the model parameter. What is the bandwidth W in terms of parameter t? Can you find kx, kz, and ky at the band bottom and at the band top?

 

[ijustlost]

Well you need to find the minimum and maximum value of the band Energy - then W is the difference between them.. The easiest way is probably just by inspection.

 

[abdul-pablo]

So the maximum is Emax = const + 8t when the multiplication of cos functions gives -1 and Emin = const -8t as the multiplication of cos functions gives 1. It implies that W = 8t - (-8t) = 16t. Now I should find kx,ky and kz fow which that cos functions multiplications results in 1 and -1. I have found 4 solution for 1 on the right side of the equation (having cos on the left one) and 4 solutions for -1 on the right. Is it possible? Am I right?