= Solution
The <drift velocity> is the small ensemble-average velocity acquired by <charge carriers> in an applied <electric field>. It is distinct from their much larger random thermal or <Fermi velocity>. For conduction <Electrons> of charge $-e$, the isotropic <Drude model> gives
$$
\boxed{\mathbf v_d=-\frac{e\tau}{m^*}\mathbf E=-\mu_e\mathbf E,}
$$
where $\tau$ is the <momentum relaxation time>.
The positive <electron mobility> $\mu_e=|\mathbf v_d|/|\mathbf E|$ measures the ease of this drift in <linear response>. In the same approximation,
$$
\boxed{\mu_e=\frac{e\tau}{m^*},\qquad\sigma=ne\mu_e.}
$$
Its units are $\mathrm{m^2\,V^{-1}\,s^{-1}}$; in an anisotropic crystal the mobility is a <tensor>.
The <band effective mass> describes the acceleration implied by the curvature of the <dispersion relation>. The <group velocity> is $\mathbf v=\hbar^{-1}\nabla_{\mathbf k}E$, while $\hbar\dot{\mathbf k}=-e\mathbf E$. Thus
$$
\boxed{(m^{*-1})_{ij}=\frac1{\hbar^2}\frac{\partial^2E}{\partial k_i\partial k_j}.}
$$
For an isotropic parabolic minimum this reduces to $E=E_c+\hbar^2k^2/(2m^*)$ and $m^*\dot{\mathbf v}=-e\mathbf E$. It incorporates the periodic crystal potential and need not equal the bare <electron mass>. Negative electronic curvature near a band maximum is conveniently described by positive-mass <electron holes>.
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