Elementary aspects of probability theory will first be explained as an introduction to statistical mechanics. Next introduced are the concepts of energy levels and the number of these levels, from which the microcanonical ensemble will be defined. The first and second laws of thermodynamics are explained since they play vital roles in the foundation of statistical mechanics. The introduction of canonical ensemble and its applications are the most important part of this course. Properties of heat capacity of solids and black-body radiation are explained as typical applications of canonical ensemble.
Elementary concepts in statistical mechanics are taught, including statistical description of physical phenomena, microcanonical and canonical ensemble. Simple applications of these concepts are also expected to be mastered.
Students are expected to understand the basic concepts of statistical mechanics and thermodynamics including microcanonical and canonical ensemble and the fist and second laws of thermodynamics. In particular it is important to be able to apply these concepts to realistic problems such as harmonic oscillator, ideal gas, heat capacity of solids, and black-body radiation.
Elements of probability theory and quantum mechanics. First and second laws of thermodynamics. Microcanonical and canonical ensemble. Partition function. Debye model. Black-body radiation.
Intercultural skills | Communication skills | Specialist skills | Critical thinking skills | Practical and/or problem-solving skills |
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Most part of the course will be given in a lecture style. I will frequently ask questions and stimulate students to answer them, and then further ask questions based on the answers. Student involvement will be strongly encouraged.
Course schedule | Required learning | |
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Class 1 | Basic concepts and goals of statistical mechanics | Read Chap. 2 of the text. |
Class 2 | Elementary probability theory | Exercises of Chap. 2 |
Class 3 | Quantum mechanics of free particles | Exercises of Chap. 3, first half. |
Class 4 | Number of states and their asymptotic form of free particles | Exercises of Chap. 3, second half. |
Class 5 | First law of thermodynamics | Problems written in the lecture note. |
Class 6 | Second law of thermodynamics | Problems written in the lecture note. |
Class 7 | Midterm examination. | |
Class 8 | Derivation of canonical ensemble | Exercises of Chap. 4 |
Class 9 | Analyses of harmonic oscillators and two-level systems by the canonical ensemble | Exercises of Chap. 5, first half. |
Class 10 | Canonical ensemble of classical systems and its appllications | Exercises of Chap. 5, second half. |
Class 11 | Eigenmodes of lattice vibration | Exercises of Chap. 6, first half. |
Class 12 | Einstein and Debye models of heat capacity of solids | Exercises of Chap. 6, second half. |
Class 13 | Historical background of black-body radiation | Problems written in the lecture note. |
Class 14 | Electromagnetic field and harmonic oscillator | Exercises of Chap. 7. |
Class 15 | Quantum theory of black-body radiation | Problems written in the lecture note. |
Statistical Mechanics I (Hal Tasaki, Baihu-kan)
Lecture notes in thermodynamics and a few other topics
By the scores of midterm and final examinations. Additional points may be given reflecting interactive communications during the lectures.
Basic concepts of probability and quantum mechanics will be explained as needed.