8  Phonons I

NoteLearning Objectives

• Explain why each harmonic normal mode of a crystal becomes a quantum harmonic oscillator.
• Define phonons as bosonic quanta of lattice vibration and interpret the meaning of zero-point motion.
• Derive the Bose–Einstein occupation factor and the mean energy of a phonon mode.
• Construct the phonon density of states from mode counting in \(\mathbf q\)-space and interpret the Debye approximation.
• Write the lattice internal energy as an integral over the phonon DOS and prepare the route to heat capacity.