Solutions lecture 7

src/7_tight_binding.md

@@ -285,13 +285,11 @@ $$ \langle \phi_n | H | \phi_{n+2}\rangle \equiv -t' ≠ 0.$$
 1. Write down the new Schrödinger equation for this system.
 
 ??? hint "hint"
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     There are now two more terms in the equation: $-t' \phi_{n-2} - t' \phi_{n+2}$.
 
 2. Solve the Schrödinger equation to find the dispersion relation $E(k)$.
 
 ??? hint "hint"
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     Use the same Ansatz as for the nearest neighbors case: $ \phi_n = \phi_0 \exp(ikna) $.
 
 3. Calculate the effective mass $m^*$.