- Solutions to Schrodinger’s equation
- Time evolution of observables
- Spin in a magnetic field
- Time evolution of a pair of electrons

In this final lecture we first derive the general solution to Schrodingerâ€™s equation, and so show how the evolution of states depend on the Hamiltonian associated with the system.

We then move on to the time evolution of observables. Observables are not usually *direct* functions of time, but they do evolve due to the fact that states they are measuring evolve. The notion of the **commutator** of an observable with the Hamiltonian is then introduced and we see how it can be used to generate conservation laws.

We then consider two examples in detail. Firstly we work out the evolution of spin of a single electron in a magnetic field, and secondly we consider a pair of electrons subject only to each other's magnetic fields.