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In this Lecture we consider the phonon spectrumPhononphonon spectrumSpectrumphonon spectrum in crystals with the pairwise interactions. We analyze the long wavelength part of the phonon spectrumPhononphonon spectrumSpectrumphonon spectrum and show the emergence of the longitudinal and transverse soundSoundtransverse sound modes in this case. We discuss an interplay of the sound modes with static compressibility and shear modulusShearshear modulus of the crystal and show the formation of sound in metalsSoundsound in metal. In the end of the Lecture, we derive the phonon HamiltonianHamiltonianphonon Hamiltonian in the second quantizationQuantizationsecond quantization techniqueSecond quantizationsecond quantization technique thus quantizing the phonon spectrumPhononphonon spectrumSpectrumphonon spectrum.

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Lecture 8. Phonon Spectrum in Crystals with Pairwise Interaction: Quantization of the Lattice Vibrations

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  • 发表日期：

    2026年

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  • Maxim Kagan

摘要

In this Lecture we consider the phonon spectrumPhononphonon spectrumSpectrumphonon spectrum in crystals with the pairwise interactions. We analyze the long wavelength part of the phonon spectrumPhononphonon spectrumSpectrumphonon spectrum and show the emergence of the longitudinal and transverse soundSoundtransverse sound modes in this case. We discuss an interplay of the sound modes with static compressibility and shear modulusShearshear modulus of the crystal and show the formation of sound in metalsSoundsound in metal. In the end of the Lecture, we derive the phonon HamiltonianHamiltonianphonon Hamiltonian in the second quantizationQuantizationsecond quantization techniqueSecond quantizationsecond quantization technique thus quantizing the phonon spectrumPhononphonon spectrumSpectrumphonon spectrum.