In the last post I described how I was beginning to learn Quantum Mechanics again. To that end, I watched the first two lectures of the Theoretical Minimum Quantum Mechanics course.

Since then I’ve managed to watch the next four and I would say I’m starting to gain a reasonable intuition for quantum systems. It’s particularly fascinating that the topic of states, which in Classical Mechanics barely requires 10-20 minutes of explanation, requires almost half the lecture course to describe in Quantum Mechanics!

Susskind has concentrated primarily on the single qubit system for the majority of the lectures so far, but has now started to discuss correlated singlets and the mathematics of entanglement. We’ve also had a good look at the time-dependent SchrÃ¶dinger equation and (briefly) the time-independent SchrÃ¶dinger equation (although I suspect we will look at the latter substantially later).

In previous Quantum Mechanics courses that I have studied, the path taken (excuse the pun) towards understanding of the key topics such as the uncertainty principle, entanglement, angular momentum and such was very “experimentally” oriented. That is, some key phenomena was described and then some theory was quickly “rushed in” to provide a model for the effect.

This course is fundamentally different since it teaches QM in a theoretical manner. The mathematical formalism (Hilbert spaces and observables, eigenstates etc) was outlined almost from the beginning. The implications of the mathematical formalism were fully explored for the simplest possible system. In my opinion this is a much better way to go since it helps break down the assumptions about behaviours that hold over from the classical world.

I also decided to take a brief trip to the famous Blackwell bookshop in Oxford yesterday and picked up both of the current Theoretical Minimum books – Classical Mechanics and Quantum Mechanics, as well as Binney and Skinner’s The Physics of Quantum Mechanics and (rather ambitiously) Quantum Field Theory for the Gifted Amateur by Lancaster and Blundell. I decided to skim the latter on the train home.

The book has really helped explain the whole idea of QFT for me, which I had not previously had a good grasp on, as well as the concept of Creation/Annihilation operators and the quantum harmonic oscillator. Having peeked ahead in the Theoretical Minimum text on QM, I see that these topics are both covered in the final section of the book.

I’ve now got four lectures remaining for the Theoretical Minimum QM course and afterwards I hope to find a book (or three) where I can practice QM questions, just as I’ve done with the books on Lagrangian/Hamiltonian Mechanics. I find I only truly gain insight *by doing*. As one of my mathematics Professors at the University of Warwick was fond of saying “Mathematics is NOT a spectator sport.”