Yesterday I finished the final lecture in the Theoretical Minimum Quantum Mechanics course. I very much enjoyed the final two lectures as we finally began discussing the one-dimensional particle case. It was fascinating to see the interplay between the position space and momentum space, which was simply a manifestation of the Fourier Transform. I’m also gaining a good ability to calculate using the logic of QM, namely that of infinite-dimensional vector spaces. This isn’t surprising, since this was a big part of my undergraduate mathematics degree, but it was rather exciting to see it applied to less abstract situations.
While I’ve now finished the lectures, I still have to finish the accompanying text. I’m actually now onto the material covered in the final two lectures so am not too far behind the video content. The book does include some discussion on the quantum harmonic oscillator, as I alluded to in previous posts, so this will hopefully prepare me somewhat for tackling -very basic- introductory Quantum Field Theory texts.
Again, as I’ve alluded to in previous posts I’m now going to move onto the Special Relativity and Electrodynamics course, which goes into significant detail on Classical Field Theory via the Lagrangian/Hamiltonian approach. Prior to tackling this, however, I might brush up on Lagrangian Mechanics for continuous systems (at least for one dimension). The usual example given here is the derivation of the wave equation via the one-dimensional constrained vibrating string. There’s a good discussion of it in A Student’s Guide to Lagrangians and Hamiltonians.
Concurrently to the Theoretical Minimum lectures I am going to try working my way through Landau & Lifshitz Vol II (The Classical Theory of Fields). I’ve had some suggestions as to which sections are worthwhile to pursue. In addition I’ve been recommended the Feynmann Lectures on Physics as a more intuitive guide when L&L becomes a bit terse! Although the latter is somewhat pricey, so it may have to wait.