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## Homework Statement

The energy-band dispersion for a 3D crystal is given by

$$E(\mathbf k) = E_0 - Acos(k_xa) - Bcos(k_yb) - Ccos(k_zc)$$

What is the value of the effective mass tensor at ## \mathbf k = 0 ##?

## Homework Equations

The effective mass tensor is given by

$$ \left( \frac{1}{m^*} \right)_{ij} = \frac{1}{\hbar ^2} \frac {\partial^2 E(\mathbf k)} {\partial k_i \partial k_j}$$

where ## i,j = x, y, z. ##

## The Attempt at a Solution

I guess I'm supposed to carry out the second order derivative of the expression for the energy in order to find the effective mass, but I don't know how to actually evaluate it. Can someone tell me how to do it please!