Take the 2-minute tour ×  How do we calculate the effective mass
of an electron in an Aluminium lattice? Is there any simple
analytical way to work it out?  share|improve this question I
think the answer is "no", almost without qualification... – 
genneth Mar 17 '11 at 23:18 @genneth please correct me if I'm
wrong, but isn't the inverse effective mass given by an
expression of the form $m^{-1} = \partial^2 E(k)/\partial k_a
\partial k_b $, where $E(k)$ is the dispersion relation, $k_a,
k_b$ are directions in momentum space, and for simplicity we
assume that $m^{-1}_{ab} := m^{-1}$? So given the energy
spectrum of Aluminum one can calculate the effective mass for
any excitation of momentum $k$ in its brillouin zone? –  user346
Mar 18 '11 at 0:33 The last sentence is meant as a statement,
not a question. –  user346 Mar 18 '11 at 1:05 That gives the
band mass, but actual electron masses (the things one measures
via heat capacity, for example) also get renormalisations from
the Coulomb interaction. The 2nd bit is