# Solid state physics-effective mass problem.

1. Jan 29, 2012

### humanist rho

1. The problem statement, all variables and given/known data

Tha band structure of a simple cubic lattice is given by,

$E = E_{0}-A(\cos k_{x}a+\cos k_{y}a+\cos k_{z}a)$

where a is the lattice constant and A is a positive constant.

Find the effective mass for the electron at the values of k corresponding to the top and bottom of the band.

2. Relevant equations

$m^{\ast }=\frac{\hbar ^{2}}{\left( \frac{d^{2}E}{dk^{2}}\right) }$

3. The attempt at a solution

The components kx,ky,kz and the condition 'top and bottom of the band' are confusing me.
Is these top and bottom correspond to brollouin zone edges?
How can i put these components of k in above equation?

Thanks.

2. Jan 30, 2012

### humanist rho

Hi friends, need help here.