Examples of nonrelativistic quantum particle dynamics

After spending some time with abstract discussions of dofferent Hilbert spaces, and simple two-state systems, we will now dig into an important class of quantum problems, that of a nonrelativistic particle moving in various potentials.

After introducing the free particle we will first discuss bound state problems. The square well (which should be review) will provide an introduction to solving discrete eigenvalue problems, and the importance of boundary conditions for this. The simple harmonic oscillator will serve as an introduction to a number of important concepts; dimensional analysis and scaling; effective/low-energy approximations; and operator methods. Finally (given time) we will embark on some simple discussion of scattering-type problems.