 Solution

ID: past-exam-of-the-quantum-condensed-matter-course-of-the-university-of-cambridge/2021/section-b/4/f/solution

W (a) = 24 E_{1} e^{- a / a_{1}}

. With

a

reduced from

a_{1}

0.99 a_{1}

\frac{Δ W}{W} = \frac{W ( 0.99 a _{1} )}{W ( a _{1} )} - 1 = e^{0.01} - 1 ≃ 0.01005.

Thus the energy band widens by approximately 1.005 percent, or 1 percent to first order. Compression increases the orbital coupling.

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