IB Physics A Quantum Mechanics Supervisions

The IB Physics A Quantum Mechanics course is aimed at second year undergraduate students who have already taken an introductory course to quantum mechanics. This page contains material to consolidate and expand on what is covered in lectures, and to be discussed during supervisions.

Wave mechanics

Infinite square well. Finding the eigenvalues and eigenstates of an inifinite square well potential is one of the very first problems every student of quantum mechanics encounters. Using what you learnt last term in the Oscillations, waves and optics course, can you qualitatively discuss what the eigenstates look like when written as momentum wave functions?
Associated Jupyter notebook.

Time evolution: Schrödinger equation

What happens after a measurement? Consider two physical observables, the Hamiltonian Ĥ and another observable Â. Describe the differences in the time evolution of the quantum state obtained after measuring the physical property associated with either observable.


Angular momentum

Compatible observables and angular momentum. The square of the angular momentum operator J2 commutes with the angular momentum components J1 and J3. This means that J2 and J1 share a common set of eigenstates, and that J2 and J3 also share a common set of eigenstates. However, J1 and J3 do not commute, so they do not share a common set of eigenstates. How is this possible?


What next?

Identical particles. If you want to expand on some of the topics covered during the course, and prepare for the third year, a good option is to follow the videos on identical particles. Whether you do Physics, Chemistry, or Materials in Part II, the quantum mechanics of systems with many identical electrons will take centre stage, so learning how to describe systems of identical particles will get you ready for next year.