= Solution
Differentiating the <tight binding> dispersion produced by the <Hückel method> gives
$$
\frac{dE_k}{dk}=-2\beta a\sin(ka),\qquad
\frac{d^2E_k}{dk^2}=-2\beta a^2\cos(ka).
$$
Hence
$$
\boxed{\frac1{m_e^*(k)}=-\frac{2\beta a^2}{\hbar^2}\cos(ka),\qquad
m_e^*(k)=-\frac{\hbar^2}{2\beta a^2\cos(ka)}.}
$$
Unlike a free particle, the <band effective mass> depends on <wavevector> and can change sign. At an inflection point $\cos(ka)=0$, the inverse <mass> vanishes and the curvature-based <mass> diverges; a quadratic approximation then ceases to describe the dispersion locally. For the usual $\beta<0$ convention, the bottom at $k=0$ has positive <mass> and the top at $k=\pi/a$ has negative <electron mass>. The constant $\alpha$ has no effect on curvature.
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