In April 2019, I decided to tackle a short, but challenging, project to learn the basics of quantum mechanics.
I had always had a fascination for physics. I devoured copies of books like Brian Greene’s The Elegant Universe [1] or Stephen Hawking’s A Brief History of Time [2]. They described the rules of the world as being so strange and perplexing, that they would seem science fiction if they weren’t scientific fact.
Unfortunately, I believe that without understanding the math, it’s difficult to appreciate what these theories are saying. Analogies to everyday life break down, so instead you need to think about things in a new way. Taking on an MIT class in the subject seemed like a good starting point because MIT classes are hard and won’t shy away from really teaching the same math physicists use to think about reality.
The second reason for tackling the class was that I wanted to try livestreaming an entire project from start to finish. In the past, I had tried various ways of documenting my projects. Doing the entire project, live on camera, seemed like a good approach since it could make the entire process transparent without adding on too much extra work.
Watch Any Part of the Complete Project
The complete project can be viewed through this playlist here [3] (feel free to jump around).
Additionally, I posted a few weekly updates while the project was going on, to give a higher-level summary of what I was doing and why:
- Project Announcement [4]
- Week One Update [5]
- Week Two Update [6]
- Week Three Update [7]
- Project Complete! [8]
- What is Quantum Mechanics (An Incomplete and Amateur Summary) [9]
Obviously, watching through over a hundred hours of footage of me studying may not be the easiest thing in the world to follow, therefore, I’ve prepared a few different timestamps of the project, for different categories, in case you’re interested in seeing me apply different learning techniques, or discussing my thinking on learning hard subjects.
Some Highlights
- 1. 0:00:18 [10]. Introduction to my project, why I’m doing it and what I plan to do.
- 1. 2:28:44 [11]. Plan of action for tackling initial lectures and problem sets.
- 5. 0:01:25 [12]. My thinking about why I want to tackle the course in two ‘chunks’.
- 16. 0:00:54 [13]. Day 7, plan and review.
- 21. 0:00:23 [14]. Day 10 plan and review.
- 34. 0:13:41 [15]. Visualizing how to think of studying.
- 35. 0:00:24 [16]. Day 14 plan and review.
- 50. 0:00:02 [17]. Midterms and Final Exam (no solutions)
- 51. 0:17:22 [18]. Final Exam (solutions — video froze halfway through, but it resumes after the exam finished when I reset the feed)
- 51. 2:52:27 [19]. Grading Final Exam and Project Final Discussion.
The Feynman Technique
- 10. 3:30:38 [20]. Understanding Waves, Phase and Group Velocity.
- 11. 2:55:04 [21]. Understanding the “Brute Force” Method for Solving the HO. (Active Recall Part)
- 12. 0:05:23 [22]. “Brute Force” Method with textbook.
- 13. 0:03:36 [23]. “Brute Force” Method, second pass on lecture.
- 28. 0:06:21 [24]. Understanding Spherical Coordinates for Integration
- 37. 1:50:37 [25]. Understanding Integration by Parts.
- 38. 1:12:25 [26]. Understanding g0 and dimensionless strength of a scattering potential.
- 38. 1:26:26 [27]. Understanding crystal momentum.
Practice and Problem Solving
- 2. 2:50:30. [28] Active recall on what was just discussed in a lecture.
- 6. 0:14:30 [29]. First start on problem sets.
- 21. 1:59:13 [30]. Second batch of problem sets.
- 34. 0:30:10 [31]. Reviewing all problem sets and lectures for weak points.
- 34. 2:17:18 [32]. Taking my weak points and creating a “to-learn” list.
- 42. 0:00:20 [33]. Working on a second pass of some problems.
The Outcome and Final Thoughts
Overall the project was a success, but not spectacularly so. I didn’t have an exam from the actual session I studied from, so I had to use another. This class taught slightly different material, so 10% of the exam involved questions for material I hadn’t studied. That complications aside, I scored roughly 60-65% on the final exam.
I hadn’t done much of the prerequisite math since the MIT Challenge almost eight years ago. This meant that I spent quite a bit of time getting brushed up on some finer points of advanced calculus and physics. Additionally, I skipped one of the prerequisite classes before taking this one.
I don’t regret tackling this project directly, rather than spending time getting caught up first. However, it does mean that the amount of work to learn the class was probably higher than it would have been if I had been doing this class in sequence, without skipping any prerequisites or with large delays between previous classes and this one.
That said, while I don’t think my outcome from a month of concentrated practice was anything record-breaking, it might still be useful since having to tackle classes where you’re rusty on the prerequisite material and feel a little overwhelmed is a pretty common scenario.
Resources and Materials
I used the following materials for this class:
- 8.04 – Quantum Physics I [34]
- Assorted lectures and material from 18.01 [35], 18.02 [36], 8.03 [37] as well as Stellar Public sessions for 8.04 [38].
- Introduction to Quantum Mechanics [39] textbook. Additionally some sections relied on Ohanian’s Physics [40].
- Pens, pencils, notebooks and a lot of eraser!