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Displacements of atoms or ions about equilibrium positions. In the harmonic approximation the coupled motion decomposes into normal modes with acoustic and, for multi-atom bases, possible optical branches.
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This is an authored directed relation from the source endpoint to the target endpoint.
Lattice vibrations describe time-dependent displacements about the crystal’s equilibrium structure; harmonic normal modes are an approximation to the full anharmonic dynamics.
The target represents a state, property, observable, or state-dependent description associated with the source system or theory.
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This is an authored directed relation from the source endpoint to the target endpoint.
Quantizing the harmonic lattice normal modes yields phonon creation and annihilation operators. Anharmonic interactions give phonons finite lifetimes and mode coupling.
A classical system or field theory is used to construct a quantum theory through a stated quantization procedure. Quantization need not be unique and is not guaranteed to preserve every classical structure.
wp-physics-phonontong-solid-state-physicsmit-theory-of-solids