= Band effective mass
{title2=$m^*$}
= Effective mass
{synonym}
In one dimension the <band effective mass> is defined by $1/m^*(k)=E''(k)/\hbar^2$. Together with $v=E'(k)/\hbar$ and $\hbar\dot k=F$, this gives $\dot v=F/m^*$. Negative band curvature produces negative <effective mass> for the electron <wave packet>; near a filled-band maximum the equivalent missing-electron description uses positively responding holes. In several dimensions the inverse mass is the Hessian $\partial_i\partial_jE/\hbar^2$.
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