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Table of Contents
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A background to how these lectures happened
My colleague, Dr. Sunethra Ramanan, and I were coordinating the course PH1020 Physics II during Jan-May 2020. This is the second course in Physics that all Engineering undergraduates take during their second semester at IIT Madras. The pandemic struck and all students were abruptly sent home towards the end of March 2020. We moved to teaching online to a class of over 900 students stuck in various parts of India with different levels of connectivity. The good news was that we went from 12 instructors simultaneously teaching the same material to a single teacher teaching all students. The bad news was that we had to figure out what was optimal. We decided to create videos with the content of the lecture and share it to all students via google classroom. I used ffmpeg to reduce the size of the videos so that students with poor connectivity could download the lectures and watch them. We followed this up with an online session where students could ask questions on the week's lectures. They were also allowed to ask questions on Google Classroom or send us email.
PH1020 used to be course devoted to Electromagnetism taught at a level just below the standard text by Griffiths. However, a recent curriculum change added roughly 8-10 lectures on quantum mechanics. I was not a fan of this addition as quantum mechanics needs a course in itself and first-year students are not quite ready to learn solving the harmonic oscillator and the hydrogen atom. These lectures are my attempt to at least convey the basic axioms of quantum mechanics to first-year undergraduates.
The Lectures
Pre-requisites: Some knowledge of linear algebra will be useful.
| Lecture Number | Content of the Lecture | Additional Info | Problem Sets/Other Links |
|---|---|---|---|
| Lecture 0 | A description of the course content. | ||
| Lecture 1 | Polarization and Complex Vectors | Slides for Lecture 1 | |
| Lecture 2 | Linear Vector Spaces | Slides for Lecture 2 | Problem Set for Lecture 2 |
| Lecture 3 | Linear maps and their matrices | Slides for Lecture 3 | |
| Lecture 4 | Inner product spaces | Slides for Lecture 4 | Problem Set for Lectures 3-4 |
| Lecture 5 | The Stern-Gerlach experiment | Slides for Lecture 5 | Stern and Gerlach: How a Bad Cigar Helped Reorient Atomic Physics |
| Lecture 6 | The postulates of quantum mechanics (Part 1 of 2) | Slides for Lecture 6 | |
| Lecture 7 | The postulates of quantum mechanics (Part 2 of 2) | Slides for Lecture 7 | Problem Set for Lecture 5-7 |
| Lecture 8 | Computing with Quantum Bits (Part 1 of 2) — Quantum Gates | Guest lecture by Dr. Prabha Mandayam | |
| Lecture 9 | Computing with Quantum Bits (Part 2 of 2) — Quantum Cryptography | Guest lecture by Dr. Prabha Mandayam | Slides for her lectures. |
Additional Material: Notes on Eigenvalues and Eigenvectors
Fun stuff
- An article from Physics World How the Stern–Gerlach experiment made physicists believe in quantum mechanics
- Doron Zeilberger calls the idea of turning a set into a linear vector space as quantum mechanics. This idea is discussed at the end of lecture 2. He makes use of this wonderful idea to prove $\binom{n}{k}\leq \binom{n}{k+1}$ if $k<n/2$ in this paper. See the last proof of this identity.
- Quantum Tic-Tac-Toe This is a quantum version of the classical tic-tac-toe that all of us have played. Several apps exists for you to play this game on both Android and iPhone. You can read about the game in this article by Alan Goff: Quantum tic-tac-toe: A teaching metaphor for superposition in quantum mechanics
- My colleague, Prof. Arul Lakshminarayan and his long-time collaborator, Prof. Karol Życzkowski and their students/postdocs showed that a quantum version of a classical problem due to Euler has a solution (The classical version doesn't have a solution.). This result was reported in the Quanta article Euler’s 243-Year-Old ‘Impossible’ Puzzle Gets a Quantum Solution (Suhail Rather is Arul's graduate student) Here is an extract from the abstract of a later paper which explains the work.
The famous combinatorial problem of Euler concerns an arrangement of officers from six different regiments in a square array. Each regiment consists of six officers each belonging to one of six ranks. The problem, originating from Saint Petersburg, requires that each row and each column of the array contains only one officer of a given rank and given regiment. Euler observed that such a configuration does not exist. In recent work, we constructed a solution to a quantum version of this problem assuming that the officers correspond to quantum states and can be entangled.
What next?
If these lectures got you interested in learning quantum mechanics, then you could do a standard course in quantum mechanics and/or quantum information theory. For those interested in quantum information theory and quantum computing, the book by Nielsen and Chuang is highly recommended.