Vibrations in Solids: Harmonic Oscillators and Phonons

This lecture covers the vibrations in solids, including classical and quantum harmonic oscillators, phonons, and the Einstein model of heat capacity. It starts by discussing the energy for small displacements in a solid and how to diagonalize the Hamiltonian to analyze normal modes. The concept of phonons as quasiparticles with energy levels is introduced, along with the quantum oscillator's properties such as energy levels, free energy, mean energy, and heat capacity. The lecture also explores the heat capacity of an Einstein solid, comparing the classical and quantum behaviors. Finally, it delves into how vibrations in a real solid can be studied using inelastic neutron scattering and various spectroscopies.