Course overview ^

PHYS 4P51 is a quantum mechanics course at the 4th-year undergraduate level. It will be your last course in quantum mechanics before graduate school, and thus it should prepare you for graduate-level study and research.

My goal is that by the end of this course, you will gain a deep and intuitive understanding of the foundations of quantum theory, from the modern point of view of 21st-century theoretical physics - as it is currently understood by researchers in cutting-edge fields such as quantum foundations, quantum information, quantum computation, quantum field theory, and quantum gravity. Such an understanding will be absolutely crucial if you want to be a theorist, and will also be extremely useful if you want to be an experimentalist.

Before you begin this course, you should forget everything you learned about quantum mechanics before! We will re-learn quantum theory from scratch, developing it in an axiomatic and mathematically rigorous way from first principles. We will see that there is nothing particularly complex or mysterious about quantum mechanics (with the crucial exception of its philosophical interpretations), and obtain insight that will allow us to understand how it makes the universe works at the most fundamental level.

There is no textbook for this course. My lecture notes will contain everything you need to know. During the lectures I may sometimes teach bonus material (e.g. in reply to a student's question), but the exams will only cover the material that is in the notes. This will allow students who missed a lecture to make up the material by reading the notes without missing anything relevant to the exams.

Course syllabus ^

The course website also doubles as the course syllabus. If you need the syllabus in PDF format, simply click here to print it and choose "Save to PDF".

About the professor ^

The professor for this course is Dr. Barak Shoshany (ħe/ħim). I did my BSc in mathematics and physics at Tel Aviv University in Israel and my MSc and PhD at Perimeter Institute for Theoretical Physics in Waterloo, Ontario. I then taught at the University of Toronto for a short time. I joined Brock University as Assistant Professor in September 2020, and I also regularly teach scientific computing at McMaster University.

I am a theoretical, mathematical, and computational physicist. My research focuses on the nature of time and causality in general relativity and quantum mechanics, as well as symbolic and high-performance scientific computing. I'm always happy to talk about my research, and theoretical physics in general, so please feel free to ask me about it, both in and out of class!

I also love teaching. I developed 10 full-term undergraduate and graduate courses from scratch since 2020, including 5 physics courses, 3 astronomy courses, 1 scientific computing course, and 1 mathematics course. My devotion to teaching won me the Brock University Faculty of Mathematics & Science Award for Excellence in Teaching in 2023.

When I'm not teaching or doing research, I love composing music, playing video games, board games, and tabletop role-playing games, and reading or watching science fiction and fantasy. Please see my personal website for details on my research, teaching, talks, media interviews, music compositions, and more.

My office is located in room E219 in the Mackenzie Chown Complex (MC). I do not have fixed office hours. You are welcome to drop by my office unannounced whenever you want, but I'm not there too often. If you would like to meet, please email me at bshoshany@brocku.ca, and I would be happy to schedule a meeting, either online or in my office.

Schedule and lectures ^

The course will take place during the Fall 2023 term, from September 6 to December 5, 2023. The deadline for withdrawal without academic penalty is November 7. There will be two 1.5-hour lectures every week:

• Tuesdays 12:00-13:30,
• Wednesdays 15:30-17:00.

There will be no lectures on Reading Week, October 9-15, 2023. We will have 12 weeks of 2 lectures each, for a total of 24 lectures and 36 hours. Note that classes at Brock end 10 minutes ahead of the hour or half hour.

IMPORTANT: The lecture on Wednesday, November 15 is canceled, and instead we will have a makeup lecture on Wednesday, December 6 at the usual time, 15:30-17:00.

The lectures will take place in the physics "library", MC B209, right next to the physics office. Please note that the timetable incorrectly lists a different room; don't come to the wrong room!

The course will also have a Microsoft Teams site, where students can have discussions and ask the professor questions. The professor will also use Teams to make announcements, and it is crucial that you follow these announcements closely and enable notifications.

Lecture notes ^

The official course lecture notes are available here. They will be under constant revision throughout the term, so always make sure you have the latest version!

Download the lecture notes
(PDF file)
Last updated: December 15, 2022
Licensed under CC BY 4.0

These lecture notes will expand on lecture notes from a course I previously taught at the University of Toronto. Video lectures from that course are also available for those who are interested. However, in our course we will learn a larger amount of material, and at a more advanced level.

Possible advanced topics that I hope to cover, which are not currently in the lecture notes, include: applications of group theory and representation theory, a rigorous treatment of continuous states and operators, density matrices, measurements in quantum information, quantum cryptography, interpretations of quantum mechanics in depth, and more. We won't have time to learn all of these topics, so I will choose which ones to cover based on the students' interests. If there is any specific topic you would like to learn, whether or not it is in this list, please let me know!

Homework problem sets ^

There will be a homework problem set every week, which will include problems related to the material learned that week. Each problem set will be posted on Teams some time after the last lecture of the week. The homework problem sets will not be marked and will not contribute to your final grade directly, but solving them will be crucial for your success in the exams.

The problem sets can be solved either alone or together with other classmates, and discussion of the problem sets with other students, whether on Teams or in private, is strongly encouraged. I will provide solutions to each problem set two weeks after its release.

Each problem set will involve a subset of the exercises and problems in my lecture notes for the subsections we learned that week. If you want more practice, you should solve all the exercises and problems in the lecture notes. Detailed solutions to problems that are not in the homework sets will not be provided, but you can always ask about them on Teams if you are not sure if your solution is correct.

Exams and grading ^

There will be 3 exams during the term, roughly one per month. Each exam will test the students' understanding of the material learned up to the exam date. The exams will be scheduled for a time that works for all of the students; we will schedule them together during the lectures.

The exams will be given in person, at a room which will be booked once the exams are scheduled. I will be present in the exam room for the duration of the exam in case clarification is needed for any of the exam questions.

The exams will contain questions similar to the exercises and problems in the lecture notes. This means there will be both calculation and proof questions. The level will be the same as the questions in the notes - not harder, but also not easier. Some questions may be taken directly from, or be variations of, questions from the lecture notes, while other questions will be completely new.

In your answers, you may make use of any results derived or stated explicitly in my lecture notes, and only them. If you wish to use any non-trivial result that is not in the lecture notes, you must prove it directly from the material in the lecture notes. If you make any assumptions beyond what's in the lecture notes, your question will be marked as incomplete.

Since notes are allowed, you do not need to memorize anything! The exam is not meant to test your memory. It will test your level of understanding of the physics and math concepts you learn in the course, and your ability to apply them correctly and efficiently to concrete problems.

Once the timer starts, you will have exactly 2 hours to solve the exam (unless you have extra time accommodations). If you are late to the exam, you will not get any extra time, so please make sure to be at the exam room at least 15 minutes before the beginning of the exam.

Each exam will be worth a third of the final grade. After the average is calculated, it will be rounded to the nearest integer, with .5 rounded up. A final grade of 50% or more is required to pass the course.

Allowed material and academic integrity ^

During the in-person exams, you may use my full lecture notes, and in addition, up to 42 normal-sized double-sided papers containing any other material of your choice, handwritten and/or printed.

Computers, phones, tablets, smart watches, and other digital devices cannot be used, but you can use a calculator. Any students found in possession of a digital device of any kind (other than a calculator) during the exam will be considered as having used the device.

Cheating in any of the exams will result in a minimum penalty of zero grade in the course, even for first offenses. Students are expected to fully comply with Brock University's academic integrity policy. Please see this page for more information about academic integrity.

How to succeed in the exams ^

To succeed in the exams, please make sure to:

• Attend all the lectures and actively participate in them. If something is unclear, ask for a clarification. If a topic inspires you to ask a followup question, ask it. If I ask the class (or you personally) a question, do your best to answer it. In my experience, the students who participate the most in class are also the students who get the highest grades in the exams!
• Thoroughly read and understand my lecture notes in order to revise and get a better understanding of what I said in the lectures. This is especially important if you missed a lecture. Also, please note that anything in the lecture notes can appear in the exam, even if I did not cover it directly in the lectures, unless explicitly stated otherwise.
• Make an honest effort to solve the weekly problem sets in their entirety. Don't just read my solutions without solving the problems yourself. If you do that, you will never learn how to solve problems on your own, and you will not succeed in the exams! If you are stuck on a particular question, you should discuss it with your classmates.
• Read my solutions to the weekly problem sets very carefully. I try to make sure the solutions are as clear and detailed as possible. Your solutions to the exam questions should ideally look like my solutions to the weekly problem sets in terms of clarity, detail, and mathematical rigor.
• Solve as many as possible of the exercises and problems from my lecture notes corresponding to the sections we learned each week - preferably all of them! The exams are designed such that any student who successfully solved all the problems and exercises in the notes should be able to get 100%.
• Make use of your greatest resource in this course: the professor. If you don't interact with me in any way, then you might as well just read a textbook or watch lectures on YouTube. I am available to you during the lectures, on Teams, and by email. You are always welcome to drop by my office. Don't be shy to ask for help if you need it - that's what I'm here for!

Missed exams and extra time accommodations ^

Missed exams

If you miss an exam due to medical issues, you must email me the Brock University Medical Verification Form within 7 days of the exam. The form must filled out in its entirety and signed by both you and a health professional. Please note that the Medical Verification Form is the only form that will be accepted; the Medical Self-Declaration Form cannot be used for missed exams, even if the duration of your illness was less than 72 hours.

If you miss an exam due to any other issues, please email me within 7 days of the exam. Your email should explain why you missed the exam and include any necessary proof.

If your Medical Verification Form or other proof is acceptable, we will schedule a day and time for you to take the exam in my office. Of course, you will be forbidden from asking other students about the contents of the exam; if you do, you will be charged with academic misconduct.

Extra time accommodations

If you have any extra time accommodations from Student Accessibility Services, please email me your Approved Accommodations Summary letter before the exam date. Please make sure you appear on the OASIS portal, and that you have a valid Approved Accommodations Summary letter, before emailing me. If you don't know what these things mean, please ask your case manager.

If you have extra time accommodations, you will take the exam in the same room with everyone else, but you will have more time to solve it. Do not attempt to take the exam at the SAS exam center - they will not have the exam in the first place, and being able to ask me questions directly during the exam is extremely important for your success.

Accommodations ^

Brock University is committed to fostering an inclusive and supportive environment for all students and will adhere to the Human Rights principles that ensure respect for dignity, individualized accommodation, inclusion, and full participation. The University provides a wide range of resources to assist students, as follows:

• If you need any accommodations related to exams, such as extra time, because of a disability or an ongoing health or mental health condition, please contact Student Accessibility Services (SAS) at askSAS@brocku.ca or (905) 688-5550 ext. 3240 as soon as possible to arrange your accommodations.
• If you require academic accommodation on religious grounds, you should make a formal written request to the professor during the first two weeks of the term, or as soon as possible after a need for accommodation is known to exist. Religious accommodations are not granted automatically, and will be considered on a case-by-case basis.
• If you are experiencing mental health concerns, contact the Student Wellness and Accessibility Centre. Good2Talk is a service specifically for post-secondary students, available 24/7, 365 days a year, and provides anonymous assistance: visit the website or call 1 866 925-5454. For information on wellness, coping, and resiliency, click here.
• If you have been affected by sexual violence, the Human Rights & Equity Office offers support, information, reasonable accommodations, and resources through the Sexual Violence Support & Education Coordinator. For information on sexual violence, visit Brock's Sexual Assault and Harassment Policy or contact the Sexual Violence Support & Response Coordinator at humanrights@brocku.ca or (905) 688-5550 ext. 4387.
• If you have experienced discrimination or harassment on any of the above grounds, including racial, gender or other forms of discrimination, contact the Human Rights and Equity Office at humanrights@brocku.ca.

Intellectual property notice ^

Any and all course materials created by the instructor in this course, including but not limited to notes, slides, homework problems, homework solutions, exams, exam solutions, and photo, audio, and/or video recordings, are the intellectual property of the instructor.

Any student who, without the instructor's express consent, publicly posts or sells the instructor's work, or takes a photo, audio, and/or video recording of the instructor's lectures, will be charged with misconduct under the university's Academic Integrity Policy and/or Code of Conduct, and may also face adverse legal consequences for infringement of intellectual property rights.