 Solution

ID: past-exam-of-the-condensed-matter-physics-major-option-course-of-the-university-of-oxford/2019/4/c/ii/solution

Complete the square:

E (ϵ) = \frac{β}{2} (ϵ - \frac{α}{β})^{2} - \frac{α ^{2}}{2 β} .

The minimum is stable because

d^{2} E / d ϵ^{2} = β > 0

. Hence

ϵ_{0} = \frac{α}{β}, E_{JT} = E (0) - E (ϵ_{0}) = \frac{α ^{2}}{2 β} .

Here the Jahn-Teller stabilization energy is the positive magnitude of the energy reduction.

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