This is a one-semester course on advanced undergraduate quantum mechanics. In the course, we will develop the full theory of non-relativistic quantum mechanics in a mathematically complete way. That is, we will start from the basic underlying principle that distinguishes quantum mechanics from classical physics, namely, that the state of a system is an element of a complex vector space and not, as in classical physics, an element of a set. We will then discuss the basic postulates that form the basis of the theory of non-relativistic quantum mechanics. After developing this basic understanding, we will then discuss the wave function formalism as a representation of an infinite dimensional complex vector space. We will spend some time describing the properties of angular momentum. We will solve the quantum simple harmonic oscillator with raising (creation) and lowering (annihilation) operators. We will then discuss entanglement and Bell's inequality. We will conclude, as time permits, with a discussion of quantum information, relativistic quantum mechanics and quantum field theory. A previous background in quantum mechanics will be useful but not essential. I will approach the subject as if this were your first exposure to quantum mechanics.
I have been monitoring what Prof. Somalwar is covered in Physics 361 and I will select material for Physics 417 that is, in general, complementary to that in Physics 361. Some will have been covered in Physics 361, but it will be good to go over it again in a somewhat different style. It's important that you leave the course with a good understanding of quantum mechanics. I will do my best to tailor the level and pace of the course so that it is suitable for, at least, most of you. Feedback will be very valuable for this. If something is covered too quickly for you, please come to a weekly study session described below where we can go over it more thoroughly.
My office is Serin 328 W. If you want to contact me, please send email to me at physics.rutgers.417@gmail.com. This is a special email account that I've set up for this course to keep the email separate from all my others. Please use this email for communications having to do with this course. Please do NOT use my physics.rutgers.edu email.
Lectures will be on Tuesdays and Thursdays from 2:00 pm to 3:20 pm in ARC, Room 107. In lecture, I'll emphasize the basic principles using only the amount of math that is necessary. I very much encourage you to ask questions and initiate discussions. That is the best way to make the lectures effective. I'll post lecture notes on the Canvas website after each lecture. These notes will consist of summaries of the main points of the lecture. They aren't meant to be self contained and you'll probably find them difficult to understand if you don't attend the lecture to see them in context.
The text book for the course is Quantum Mechanics: A Mathematical Introduction by Andrew Larkoski. This is a new book that has just been published. I haven't had experience using it yet, but it seems to be very good. It covers material similar to what I'll discuss in lecture and it is at a similar level. My lectures, though, will be independent and won't strictly follow this book. I will post notes on my lecture material that you can use for studying and reviewing the lectures. Use the textbook as a complement to my notes.
Here are some additional books that you might find useful.
You can find the syllabus for the course here. This syllabus is meant to be flexible and I will likely modify it as appropriate as the course proceeds. In particular, we might not get to the lectures on relativistic quantum mechanics and field theory. If so, we shouldn't be too disappointed by that. These topics are rarely covered in an undergraduate course.
There will be about ten homework assignments during the semester. These will in general consist of a range of problems from straight forward to challenging. Making an attempt at the homework problems is very important. The homework will count for a larger percentage of your grade than in most courses. Even if you do well on the exams, if you don't do the homework, you will not get a good grade. Remember, though, the main point of the homework is to help you to learn the material.
The homework assignments will be due at midnight on Sunday evenings. They are to be submitted electronically through Canvas. Before the first homework assignment is due, I'll post a list of rules that must be followed when submitting.
During the first week of the course, I'll survey the class to find a good time for a weekly study session. These sessions are completely voluntary. Depending on the interests of those attending, we will go over homework problems, review material presented in lecture, discuss lecture material in greater depth or discuss topics not covered in lecture. No material discussed in these sessions that is not discussed in lecture will be on the exams.
In addition to the weekly study sessions, please don't hesitate to come to see me about any questions you might have concerning the lecture material, homework or related physics. If you would like to meet with me, simply email me at physics.rutgers.417@gmail.com listing three times that you are available. I will then get back to you within 24 hours letting you know which of those times would be good for me. Please do not phone or drop by my office unexpected.
There will be an 80-minute, in-class, mid-term exam and a 3-hour, final exam.
The course grade will be based on the following criteria:
| Exams (in-class and final combined): | 50% |
| Homework: | 40% |
| Lecture (attendance and participation): | 10% |
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This page is maintained by Prof. Steve Schnetzer.