# Derivation of Effective Mass from a Parabola

1. Oct 23, 2011

### Morberticus

There is some fundamental about effective mass that I am misunderstanding about effective masses.

I understand the relation

$E\left(k\right) = E_0 + \frac{1}{2m^*}k^2$

But I'm not sure when it's appropriate to fit this to a parabola.

I would have thought the fitting is only done when you have an independent-particle model, and know the energies associated with each k "orbital".

The data I have is a parabola of energies built by systematically adding electrons and calculating the corresponding Hartree-Fock energy.

For example, the minimum of my data is the HF energy of n electrons. The next point is the HF energy of n+1 electrons. The next point is the energy of n+2 electrons. So these points, strictly speaking, aren't energies of k values. I was told I can still fit this data to a parabola and derive an effective mass. The data fits a parabola shape very well, but I am assuming I can't simply use the above equation, as my energies are N-electron energies and no "k number" energies. Or can I?