Before beginning this topic, students should:
Know how to represent the displacement of a chain of monatomic molecules using an envelope function.
Have some experience in quantum mechanics, including using the energy eigenvalue equation and Schrodinger's equation.
Understand how to represent quantum states using bra-ket notation or function notation.
Be able to comfortably transition between bra-ket notation and function notation.
Have experience with the properties of observables.
Know how to find the eigenvectors and eigenvalues for a matrix.