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Unformatted text preview: 1 I. SYLLABUS AND INTRODUCTION Let us start with a brief overview of the items that will (hopefully) be covered in this course and to give a guideline of what we are trying to learn. Quantum mechanics 560 and 561 are advanced quantum mechanics courses designed for graduate students. The courses will be treated as a one-year course. It will be assumed that students have already some background in quantum mechanics (the concepts of waves, quantization, expectation values, etc.). An advised introductory text- book is Introduction to quantum mechanics by Griffiths. A number of things will, however, be repeated albeit in a more mathematical fashion. Also some basic knowledge in Fourier analysis, differential equations and linear algebra (calculation of eigenvalues and eigenstates) will be expected. All the information you need to know are in the lecture notes. However, the lecture notes are relatively concise and further reading is recommended. The book that was used last year was Liboff, Introductory Quantum Mechanics , fourth edition. However, a lot of other books treat the material of 560 in a similar fashion, so pick a book that you like best. Some of the material is not covered in Liboff (the older editions dont have relativistic quantum mechanics and quite a bit of the material of 561 is not in there). The course is developed from a physicists point of view. Some concepts and mathematical techniques will be intro- duced along the way (such as matrix techniques) under the assumption that most of you are already somewhat familiar with them (after all, there are also 3 and 4 hundred level quantum mechanics courses). For a more comprehensive view of those things, I will refer to the textbook. The subjects that will be covered are History , Plancks quantum hypothesis, photoelectric effect,specific heat, atomic physics. The introduction is somewhat different from what is usually given in textbooks. However, since most of you have already followed a quantum mechanics course and since this is a graduate course, I think it is interesting to do it this way. Quite some time will be devoted to Plancks hypothesis. The physical language is quite different from that of the rest of the course (it is more thermodynamics than quantum mechanics). Some of these things are treated in the exercizes of Chapter 2 of Liboff. Other things will be mentioned more briefly. Wave mechanics , Schr odinger equation, probability density, free particles, Heisenbergs uncertainty principle. This section tries to show some of the thinking that led to the Schr odinger equation. As soon as you leave the idea of a particle as a billiard ball behind you, a number of other things follow directly, such as Heisenbergs uncertainty principle....
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