1. Last hour: Raising & Lowering Operators
Express Hamiltonian through ladder operators
Define number operator
EFs of are also EFs of
are EFs of with EVs v±1 and EFs of with EVs Ev ± ħ0

2. Learning Goals for Chapter 10 – The QM harmonic oscillator
After this chapter, the related homework problems, and reading the relevant parts of the textbook, you should be able to:
give examples for where the model of a harmonic oscillator can be applied;
recognize physical situations that can be modeled using the harmonic oscillator vs. the Morse oscillator;
explain the form of the harmonic oscillator Hamiltonian;
qualitatively describe the eigenfunctions of the harmonic oscillator;
calculate the energy levels of a harmonic oscillator and of a Morse oscillator for a given physical situation;
describe the level structure of a Morse oscillator and the concept of anharmonicity;
use raising and lowering operators.

3. Learning Goals for Chapter 11 – The Postulates of QM
After this chapter, the related homework problems, and reading the relevant parts of the textbook, you should be able to:
apply the postulates of QM to predict the outcome of a single measurement on a single quantum system.
apply the postulates of QM to predict the outcome of a large number of identical measurements on identically prepared quantum systems.
apply the postulates of QM to construct the time dependence of a wave function.
construct an operator for any observable.