**Spin:**A discrete and finite system where the observables of interest are spin components \(S_n\) and energy. We use this simple system to introduce the quantum postulates and discussion of measurement.- Spin-1/2
- Spin-1
- Spin-3/2
- Spin-s

**Intro to Bound States:**With these systems, we introduce the position operator, the position representation of quantum states, and review all the quantum postulates.To connect with the previous unit on Spin, we emphasize:

- measurement and finding the particle in a region
- the position basis and the position operator
- representing a quantum state with various representations
- time evolution

**Infinite Square Well:**(i.e., Particle in Box) A 1-D potential where energy (discrete but unbounded) and position (continuous but bounded) are of interest.**Particle Confined to a Ring**A 1-D potential where both orbital angular momentum and position are of interest. Has periodic boundary conditions and degeneracy in \(L^2\) and the energy.**Particle Confined to a Sphere**(i.e., a quantum rigid rotor) A 2-D potential with periodic boundary conditions. Introduces the spherical harmonics. Separation of variables is needed to solve the energy eigenvalue equation.**Hydrogen Atom**A central force potential with 3 spatial dimensions. Adds solutions to the radial equation.

**Raising & Lowering Operators****Angular Momentum****Harmonic Oscillator**Review bound states for a 1-D system but solve for energy eigenstates using raising and lower operators.

**Free Particle:**Normalization and the linear momentum basis.**Intro to Scattering States:****Delta Function Barrier/Well****Finite Well/Barrier****Periodic Wells**Introduces LCAO approximation (linear combination of atomic orbitals)