### Lecture 6: Debye Approximation and Free Electron Model

The Debye approximation is a way of calculating phonon properties. Here's the approximation: 1. Pretend the phonon dispersion is linear.

2. Set a high frequency cutoff ωD = Debye frequency that gets the total number of modes in the system correct.

That's it -- now you're guaranteed to get both the low temperature and high temperature limits of the heat capacity correct.

We also start the free electron model. Free means the electrons do not interact with each other's Coulomb potentials, or the Coulomb potential of the crystalline lattice. Rather, they have only kinetic energy, and only "interact" through the Pauli Exclusion Principle. Remarkably, this gives a good starting point for describing the behavior of real metals.

Lecture Audio

2. Set a high frequency cutoff ωD = Debye frequency that gets the total number of modes in the system correct.

That's it -- now you're guaranteed to get both the low temperature and high temperature limits of the heat capacity correct.

We also start the free electron model. Free means the electrons do not interact with each other's Coulomb potentials, or the Coulomb potential of the crystalline lattice. Rather, they have only kinetic energy, and only "interact" through the Pauli Exclusion Principle. Remarkably, this gives a good starting point for describing the behavior of real metals.

Lecture Audio

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