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.
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
To prepare for class, students should read the course schedule section and check what topics will be covered. Required learning should be completed outside of the classroom for preparation and review purposes.
Course schedule | Required learning | |
---|---|---|
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. |
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
統計力学 (長岡洋介著, 岩波基礎物理シリーズ 7)
No prerequisites are necessary
Students’ course scores are based on final exams.
Basic concepts of probability and quantum mechanics will be explained as needed.