Advanced Quantum Mechanics Schwabl · Problem 12.1

Quantization of Relativistic Fields

Physics — Quantum Mechanics · linear-chain-coupled-oscillators

Problem

Prove the completeness relation

\frac{1}{N}\sum_k \mathrm{e}^{-\mathrm{i}kan}\mathrm{e}^{\mathrm{i}kan'} = \delta_{nn'}\,,

where the summation variable

k

is restricted to the first Brillouin zone.