Teaching QM has certainly made me think back on my own experience being in upper division courses. Specifically, I’ve been wondering recently what were the conditions that contributed to a handful of lectures I watched as an undergrad staying in my brain ever since. Like so much so that I clearly remember that feeling of being in that class, I can see writing on the board, the writing in my notebook, and forever have been able to recreate these particular derivations with little trouble.
Two of them are
- The method for deriving the results of gaussian integrals (from a Calc III class)
- How to derive the Green’s functions for damped SHM, and in the process applying the Residue Theorem as an integration technique (from a Classical mechanics course).
I think part of my answer for why I remember them is that I was so intrigued by both of the methods at the time, that I pondered them over and over and over, and recreated them again and again. The initial condition was certainly whatever it was that made me so intrigued at that moment, but the process of crystalizing that knowledge was not the lecture itself, but the acts of non-stop thinking about them over a long period of time.
This also reminders me in high school, I was obsessed with calculating the moment of inertia of three dimensional objects, under various geometries and mass distributions. I loved setting up the integrals and working them out, especially in spherical coordinates. I would work these out again and again again every time I was sitting in some other boring HS class. This was also something that was just “lectured” to me, but again my learning was immensely active and sustained over a long period of time.
It makes me think that a lot of the reason I did fairly well with math and physics throughout high school and college was that thinking about physics and math was not really school work, but an obsession. Re-deriving interesting things or playing with the math was like doodling, something I did constantly, all the time, anytime a piece of paper was at hand.
But this was also one of the reasons why I was not a “great” student in college. I didn’t do my HW all the time, because I’d be spending my time “doodling” what was interesting to me, rather than what the teacher wanted me to do at that time. While there was significant overlap between my doodles and the course work, this overlap was not so great as to make me a top student. [I am just remember know how much I loved solving normal modes problems].
Anyway, that’s been on my mind.