Solution
= Solution
{c}
Complete the square:
$$
E(\epsilon)=\frac\beta2\left(\epsilon-\frac\alpha\beta\right)^2-\frac{\alpha^2}{2\beta}.
$$
The minimum is stable because $d^2E/d\epsilon^2=\beta>0$. Hence
$$
\boxed{\epsilon_0=\frac\alpha\beta,\qquad E_{\mathrm{JT}}=E(0)-E(\epsilon_0)=\frac{\alpha^2}{2\beta}.}
$$
Here the <Jahn-Teller stabilization energy> is the positive magnitude of the energy reduction.