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Physics 521 Syllabus Textbooks: • J. J. Sakurai, Modern Quantum Mechanics (required) • C. Cohen-Tannoudji et al., Quantum Mechanics, Vol. 1 The conceptual flavor of the course is similar to Sakurai’s book, but not identical. The main differences correspond to background material, which we cover in more detail, dealing with the mathematical framework of Quantum Mechanics, and an early extensive discussion of spin ½ and other two-level systems —the simplest systems for which the essential aspects of Quantum Mechanics are most directly visualized. Cohen-Tannoudji will be used in Homework assignment the first part of the course; the emphasis will switch almost completely to Sakurai as the course progresses. Sakurai will also be the textbook for Physics 522, where the second volume of Cohen-Tannoudji will be used as occasional reference (the latter contains many important problems worked out in great detail!) There is a new book (which is actually a strongly-revised second edition of an old book) which I like a lot, K. Gottfried and T.-M. Yan, Quantum Mechanics: Fundamentals. I have thought about adopting this book as textbook, but I eventually decided against that, as the book may seem a little too “advanced,” on a first reading. Still, I strongly recommend it, especially for those students who are more theoretically inclined. Note: I always recommend the Feynman Lectures on Physics, Vol. 3, as a most beautiful, illuminating source of Quantum Mechanics at an “elementary” level. Volume 3 of the Feynman Lectures represents a famous experiment at teaching Quantum Mechanics “correctly” at the sophomore level. (There is actually a nice story in a recent issue of Physics Today about that “experiment,” describing both the design of the course and the putting together of the three-volume masterpiece.) In addition, the old Berkeley Physics Course, Vol. 4, Quantum Physics, is a must-read piece for those who have not been trained to think about basic things such as orders of magnitude, qualitative reasoning, and other key aspects of “thinking like a physicist” —which is important for your Qualifying Exams, but even more important for your proper education as a research physicist! Overview of the course: ◊ Introduction: The Quantum Mechanical way of thinking about nature at the microscopic level. We shall condense the essence of key empirical evidence stemming from the Stern-Gerlach experiment and from a gedanken electrondiffraction experiment. ◊ The language of Quantum Mechanics: Dirac notation — bras, kets, operators, matrix elements, etc. ◊ The postulates of Quantum Mechanics: Probability amplitudes, probabilities, mean values, the measurement process, the uncertainty “principle,” time evolution. ◊ Spin 1/2 and other two-level systems. Chemical bonding by electron sharing. The systems to be considered display the beauty and practical implications —e.g., masers, lasers— of Quantum Mechanics. This is achieved with a minimum of mathematical complications (a great advantage of the two-level systems). ◊ The harmonic oscillator in Quantum Mechanics (solved by operator techniques), and applications. The Mössbauer effect. ◊ Aspects of wave mechanics: Propagation in space, the Feynman path integral, the Aharonov-Bohm effect. ◊ Theory of the angular momentum in Quantum Mechanics. ◊ The central potential problem; the hydrogen atom. Any topic from the above outline which is not covered in the Fall semester will be covered in the Spring semester. The Physics 521-522 sequence is really one course (one subject), partitioned into two because of “practical” reasons. Note: Elementary aspects of wave mechanics are assumed to be part of your background. (The first Homework assignment deals with standard one-dimensional problems.) Sakurai assumes that you have this background (he also assumes that you are familiar with typical three-dimensional wave-mechanics problems, such as the hydrogen atom, which we will cover in some detail). In Cohen-Tannoudji, Vol. 1, you will find many worked-out problems in wave mechanics. Let me know right away if you have any questions/anxieties, about this issue! 2 A proper comprehension of Quantum Mechanics is a necessary (but not sufficient!) condition for a successful research career in just about any area of physics of current interest. Thus, in doing physics, you will find that you will use Quantum Mechanics “all the time.” Homework will be assigned about once a week. It is extremely important that you view each assignment as a challenge for your understanding of the subject. Attack your homework individually, and as soon as possible. Don’t wait until the day before the assignment is due to start thinking about it —you would not learn much. I recommend that you ask for help from me, or from a classmate, only after you think about your question for a while. But to that end, you need to give yourself quality time to think. Office hours: To be determined after we agree on a final schedule for the course. Feel free to contact me also by e-mail at any time. I am setting up a class e-mailing list which I will use to send your assignments, and general information (e.g., some clarification of a Homework problem) outside class hours. Please send me an e-mail right away so that I can include you in the class list. There will be a “mid-term” and a final exam. Course Credit: 40% mid-term; 40% final; 20% homework. Note: Both exams (mid-term and final) will reflect rather closely the material covered in homework assignments, and in my lectures; there will be no big “surprises.” Thus, by doing the homework well you will not only learn the subject (which is the main point), but that you can expect to perform well in the exams! I emphasize that you should concentrate, on a daily basis, on learning the subject, with your effort, and my help. Your grade will take care of itself if you understand (as oppose to memorize) your physics! Professor Adolfo G. Eguiluz 613 Science and Engineering Building Phone: 974-9642; 574-5783 (ORNL) e-mail: [email protected] 3