Advanced Quantum Mechanics Schwabl · Problem 12.3

Quantization of Relativistic Fields

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

Problem

Show that transforming the Hamiltonian (12.1.1) into normal coordinates according to (12.1.5a,b) yields the Hamiltonian (12.1.11) with the vibration frequency ωk2=Ω2(2sin⁡ka2)2+Ω02 .\omega_k^2 = \Omega^2\left(2\sin\frac{ka}{2}\right)^2 + \Omega_0^2\,.

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