This is a one-semester course on advanced undergraduate quantum mechanics. In this 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 a significant amount of time describing the properties of angular momentum which is a very important feature of quantum mechanics. We will discuss entanglement and Bell's inequality. We will solve the quantum simple harmonic oscillator with raising (creation) and lowering (annihilation) operators. We'll conclude, as time permits, with a discussion of the hydrogen atom. 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.
Lectures will be on Mondays and Wednesdays from 1:40 pm to 3:00 pm in SEC Room 207. In lecture, I will emphasize the basic principles using only the amount of math that is necessary. I encourage you very much to ask questions and initiate discussions. That is the best way to make the lectures effective. I will post lecture notes on the Sakai web site 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 textbook for the course is A Modern Approach to Quantum Mechanics by John Townsend. Of all of the the textbooks that I looked at, this one follows most closely the material I will cover in the class. Everything that I go over in class will be included in the lecture notes that I will post. In that sense, the textbook is not necessary. I think that it will be useful for those who would like an alternative description to the material covered. I have listed it as a recommended but not required text. I will cover most but not all of the material in this book.
Here are some other textbooks that you might find useful.
I'm still working on the syllabus and will post it here by the end of the year. It will follow fairly closely the outline of Prof. Binney's course that you can find here.
There will be about ten homework assignments during the semester. These will in general consist of a range of problems from straightforward 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.
Please don't hesitate to come to see me about any questions you might have concerning the lecture material, homework or related physics. I will survey the class in the first lecture and we'll set up a time for a regular office hour that will hopefully be convenient for all of the students. In addition to the regular office hour, you're welcome to come see me at other times. I will be glad to talk to with you if I'm not busy. I may sometimes have to miss my scheduled office hour. In that case, I'll do my best to notify you in advance.
There will be an 80-minute, in-class, mid-term exam and a 3-hour, final exam. The dates of these exams will be announced later.
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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