Statistical Physics II

PHYS*4240 Statistical Physics II Fall 2009 Department of Physics University of Guelph

Instructor The instructor for this course is Eric Poisson. Eric's office is MacNaughton 211, his extension is 53991, and his e-mail address is [email protected]. Eric is very much an informal guy, and he prefers to be addressed simply as ``Eric''. He does not appreciate being subjected to such pompous titles as Doctor, Professor, or His Gracious. Eric's field of research is general relativity, including black holes and gravitational waves. For additional details, please consult his research web page.

Schedule The official class times are Monday, Wednesday, and Friday from 10:30am to 11:20am. Classes will take place in MacNaughton 118. The first class will take place on Friday, September 11. The mid-term exam will be scheduled in due course; it will take place outside of regular class times. The final exam is scheduled for Thursday December 17, 2009, from 11:30am to 1:30pm.

Scope, prerequisites, and expectations This course is a continuation of PHYS*3240 (Statistical Physics I). It focuses mostly on techniques of statistical mechanics and their applications to simple physical systems (such as the ideal gas in the classical and quantum regimes, and paramagnetic systems). The prerequisites for this course are PHYS*3240 (Statistical Physics I) and PHYS*3230 (Quantum Mechanics I). It is therefore assumed that the student has a good knowledge of thermodynamics, including some notions of statistical mechanics. The course relies also on a working knowledge of classical mechanics, quantum mechanics, electromagnetism, and basic mathematics. This is a demanding course in which you will learn sophisticated methods of theoretical physics. These are useful well beyond the context of this course; statistical mechanics finds applications in virtually all areas of physics, chemical physics, and biophysics. This is physics for grownups, and it is imperative that you conduct yourself as a grown-up while taking this course. This means, most of all, taking responsibility for your own education. In practice, this means that

you will spend a considerable amount of time outside of class hours teaching yourself the material. The mastery of physics does not come easily to anyone. You must work hard at it, and the work must be done by you, and no one else. My role as your instructor is to help you in this process. I do not believe, however, that I can truly teach you the material. I can lecture on it, give you an orientation, and illustrate the basic ideas, but all this will not make you learn the material. (This may only give you a false impression that you have learned it.) What you must do in addition is teach yourself, and my role as your instructor is mostly to help you teach yourself. Knowledge and understanding will come from your own efforts; they cannot be directly transmitted from me to you. It is imperative that you come prepared to do your own learning in this course, and be willing the spend the time that this requires. My lectures will be given at a level that is comparable to, but somewhat lower than, the coverage in the lecture notes. My purpose in the lectures is to introduce the main themes and talk about them in fairly general terms. But attending the lectures will not be enough; you will be expected to master the material at the level set in the lecture notes. It will be your job to go through the lecture notes in detail, outside of class hours, following the schedule that I will give in class. You are expected to read the text carefully, go through all the mathematical steps, fill the gaps, and work through the exercises at the end of each chapter. Doing all this will prepare you very well for the midterm and final exams. If you follow this course of action you will do very well in this course. And if you follow this advice in other courses as well, your education in physics will be rock-solid. If, however, you fail to read the notes, go though the math, do the exercises, or if you rely too much on group work, then you will acquire no useful skills from this course. And if this is your general attitude, your education in physics will turn out to be useless. Physics is challenging. Live up to the challenge!

Textbook There is no required textbook for this course. However, a highly recommended text is: •

F. Reif, Fundamentals of Statistical and Thermal Physics (McGraw-Hill, 1965, QC 175.R43).

This is a fine book that will serve forever as a useful reference. Some of the problems for the homework assignments will be taken out of Reif. The lecture notes do not follow this book closely.

Lecture notes I have prepared detailed lecture notes for the course, and these will serve as the official textbook for the course. They will be available for purchase in the Quiz Room, starting early in September.

Additional references •

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D.L. Goodstein, States of Matter (Prentice Hall, 1975; Dover, 1985, QC 173.3.G66). A rather advanced text focusing on applications of statistical mechanics to all states of matter. The first chapter is a rapid summary of thermodynamics and statistical mechanics and is well worth reading. K. Huang, Statistical Mechanics, Second Edition (Wiley, 1897, QC 174.8.H83). A classic. Rather advanced, but very good. A. Katz, Principles of Statistical Mechanics: the Information Theory Approach (Freeman, 1967, QC 175.K33). Information theory provides a highly formal, but very elegant, approach to statistical mechanics. A chapter of the lecture notes is devoted to this topic, and this chapter was prepared with the help of Katz' book. C. Kittel, Elementary Statistical Physics, (Wiley, 1958, QC 175.K6). A very concise summary of all you need to know about statistical physics. C. Kittel and H. Kroemer, Thermal Physics, Second Edition (Freeman, 1980, QC 311.5.K52). A rather elementary account. L.D. Landau and E.M. Lifshitz, Statistical Physics, Third Edition, Part 1 (Pergamon, 1980, QC 175.L32). This book is just too perfect. For the theoretically minded only. F. Mandl, Statistical Physics, Second Edition (Wiley, 1988, QC 174.8.M27). This book covers roughly the same material as covered in class, with a nice, readable presentation. It is highly recommended. P.K. Pathria, Statistical Mechanics (Pergamon, 1972, QC 175.P35). This is a very good book at a level slightly more advanced than this course. Well worth consulting. M.W. Zemansky and R.H. Dittman, Heat and Thermodynamics (McGraw-Hill, 1981, QC 254.2.Z45). This book focuses mostly on classical thermodynamics, with some elements of statistical mechanics.

Grading system Grades will be based on homework assignments, a closed-book midterm exam, and a closedbook final exam. In marking scheme A the weights are assigned as follows: Assignments 25%, midterm exam 35%, and final exam 40%. In marking scheme B the weights are assigned as follows: Assignments 25%, midterm exam 25%, and final exam 50%. The final mark will be the best of the two marks calculated under the two schemes. No other marking scheme will be considered. I expect to distribute about three or four sets of homework problems to be worked out on a time scale of about two weeks. You are permitted to discuss the homework problems with your colleagues while trying to solve them. However, and this is important, after the discussions you must write up the solutions yourself, independently of anyone else. Cheating will not be tolerated. After each assignment has been handed in, the solutions will be posted on these web pages. The midterm and final exams will be written outside of normal class times. These will be closedbook exams, meaning that you will not be allowed to consult your notes nor any other sources

during the exams. You will, however, be provided with relevant material such as a formula sheet. The scheduling of the midterm exam will be decided during the first few weeks of class.

Course content Chapters 1-3, 4-7 constitute the core of this course. No lectures will be given on Chapter 4. Lectures will be given on Chapter 8 if time permits. The last couple of lectures will be devoted to Chapter 9. 1. 2. 3. 4. 5. 6. 7. 8. 9.

Review of thermodynamics Statistical mechanics of isolated systems Statistical mechanics of interacting systems Information theory Paramagnetism Quantum statistics of ideal gases Black-body radiation Heat capacity of solids Thermodynamics of black holes