Lecture notes ^

There is no required textbook for this course. The official course lecture notes, written by the lecturer, will contain everything you need to know. References to textbooks for additional study beyond the course material may be given as needed.

Update: After teaching this course, I continued to update and expand these notes. The new and improved notes can be downloaded here.

Schedule and logistics ^

Lectures will be given every Monday and Wednesday from 1:00pm to 3:00pm, from May 4th to June 15th, 2020. There will be no lecture on May 18th, due to Victoria Day.

Tutorials will be given every Monday and Wednesday from 3:00pm to 4:00pm, with the same schedule as the lectures. There will be a total of 24 hours of lectures and 12 hours of tutorials. The students will split into two groups for the tutorials.

The course will be taught online via Zoom, due to the ongoing COVID-19 pandemic. Students will receive information on how to attend the Zoom meetings via email, and the information will also be on Quercus. The meetings will be protected by a password to prevent Zoombombing. Please do not share the meeting ID or password with anyone who is not a student in this course.

The live lectures will be recorded and made available to watch at your leisure. However, it is highly recommended to attend the live lectures if possible, so that you can ask questions and interact with the lecturer.

Any interaction with students will be edited out unless you explicitly ask to be included in the recording. Therefore, please feel free to ask as many questions as you want during the lectures; your questions will not be made public.

Please click here for the course listing on the University of Toronto website.

Lecturer and teaching assistants ^

The lecturer for this course is Barak Shoshany. I received my PhD in theoretical physics from Perimeter Institute in Waterloo, where I also work as a postdoctoral researcher. I had research internships at Tel Aviv University and Weizmann Institute of Science in Israel and CERN in Switzerland. My research interests currently include general relativity, quantum gravity, and scientific computing.

My office hours are every Tuesday from 11:00am to 1:00pm. These will be virtual office hours, held via Zoom using the same meeting ID and password as the lectures. Please feel free to come to the office hours with any questions or concerns.

Outside of the office hours, you are always welcome to email me at barak.shoshany@utoronto.ca. I will do my best to reply to all student emails as soon as possible. In addition, if you wish to schedule a 1-on-1 video chat, please do not hesitate to email me.

The teaching assistants are Aaron Goldberg and Jyotirmoy Roy. Both of them would be happy to answer any questions you may have by email. They will also hold virtual office hours before the mid-term and the final assessment. If needed, you may ask the teaching assistants to schedule 1-on-1 video chats by emailing them.

Course outline ^

This course will serve as a comprehensive introduction to the foundations of quantum mechanics, from the modern point of view of 21st century theoretical physics. It will be somewhat different from a traditional first course in quantum mechanics, in that we will develop the theory from scratch in an axiomatic and mathematically rigorous(ish) way. There will be less emphasis on doing calculations, and more on a deep conceptual understanding of the theory.

First, a short non-technical overview of quantum mechanics will be provided. We will discuss the failures of classical mechanics that prompted the development of the quantum theory, and list the major differences between classical and quantum mechanics.

Next, we will learn the necessary mathematical background, including complex numbers, linear algebra, and probability. Even if you took courses on these subjects before, you should still pay careful attention, since we will learn the material from the quantum point of view and introduce important notation that is unique to quantum mechanics.

Once we have a firm grasp of the mathematical background, we will use it to define quantum mechanics axiomatically. We will learn about fundamental concepts such as Hilbert spaces, states, operators, observables, superposition, probability amplitudes, and expectation values.

Then, we will begin studying simple discrete quantum systems known as qubits, which are the quantum analogue of bits, and are used in quantum computers. We will learn about Schrödinger's cat, quantum entanglement, Bell's theorem, the uncertainty principle, unitary evolution, quantum measurements, and quantum teleportation.

In the remainder of the course we will study simple continuous quantum systems and related phenomena, including Hamiltonians, the Schrödinger equation, the quantum harmonic oscillator, wavefunctions, the wave-particle duality, quantum interference, and scattering and tunneling in one dimension.

If time permits, we will touch on exciting advanced topics such as canonical quantization, path integrals, quantum algorithms, particle physics, quantum field theory, and/or quantum gravity.

By the end of the course, the students should expect to have a fairly good understanding of quantum mechanics, and to develop an intuition for this very strange and unintuitive theory. They will also be adequately prepared to dive deeper into the subject, whether by taking more advanced courses or by doing research.

Grading ^

There will be 6 weekly homework assignments, consisting of a subset of the problems provided in the lecture notes. Submitted solutions will be marked as "pass" or "fail" only. The homework assignments have a strict deadline, and late submissions will not be accepted. I will post the correct solutions shortly after the deadline.

You are strongly encouraged to solve all of the homework assignments in order to make sure you understand the material. Collaboration with other classmates is allowed, as long as it is clearly specified exactly which students worked together and how much each of them contributed. Please note that questions from the homework may appear in the assessments.

There will be a midterm and a final assessment, both in the form of oral assessments via 1-on-1 Zoom meetings with the lecturer. The oral assessments will be recorded for grading purposes, but will not be posted anywhere. Dates for the mid-term and the final will be posted later; the final will take place sometime between June 17th and June 25th.

The midterm will be 10 minutes long, and the final will be 15 minutes long. During both, I will simply ask you a few questions to see if you understand the material. One of the goals of the midterm will be to introduce you to the oral assessment format and prepare you for the final assessment.

As some of the students currently live in different time zones, attendance at the live online lectures or tutorials will not affect the final grade. The final grade will consist of:

• 18%: homework assignments (3% for each "pass"),
• 22%: midterm oral assessment,
• 60%: final oral assessment.

Homework assignments ^

The homework assignments will be given as selected exercises and problems from the course lecture notes. However, you are strongly encouraged to solve all of the exercises and problems in the notes, even those that were not given as homework! Also, it is highly recommended to typeset your homework solutions using LyX.

Homework solutions should be submitted through Quercus.

• Homework 1 (due by Saturday, May 23rd, noon Eastern Time): Exercise/Problem no. 3.2, 3.20, 3.21, 3.23, 3.26, 3.27, 3.29, 3.30, 3.31, 3.32, 3.34, 3.39.

• Homework 2 (due by Saturday, May 30th, noon Eastern Time): Exercise/Problem no. 3.41, 3.44, 3.45, 3.46, 3.47, 3.52, 3.55, 3.56, 3.61, 3.62, 3.63, 3.64. Problem 3.65 is optional, but if solved correctly will give an automatic "pass" on this assignment.

• Homework 3 (due by Saturday, June 6th, noon Eastern Time): Exercise/Problem no. 4.4, 4.6, 4.10, 4.12, 4.13, 4.16, 4.20, 4.21, 4.22, 4.23, 4.24, 4.25.

• Homework 4 (due by Saturday, June 13th, noon Eastern Time): Exercise/Problem no. 4.28, 4.33, 4.34, 4.35, 4.37, 4.42, 4.46, 4.47, 4.50, 4.51, 4.52, 4.53. Problem 4.54 is optional, but if solved correctly will give an automatic "pass" on this assignment.

• Homework 5 + Final Project (due by Thursday, June 25th, noon Eastern Time): Exercise/Problem no. 5.8, 5.9, 5.12, 5.13, 5.15, 5.16, 5.20, 5.21, 5.22, 5.23, 5.25, 5.26, 5.27, 5.28.