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 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.
Basic ideas of statistical mechanics, canonical ensemble in particular, will be explained.
Students are expected to understand the basic concepts of statistical mechanics and thermodynamics including microcanonical and canonical ensemble. 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. 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 the relevant part of the textbook and distributions in advance, and solve the problems given in the exercise class. |
Class 2 | Elementary probability theory | Read the relevant part of the textbook and distributions in advance, and solve the problems given in the exercise class. |
Class 3 | Quantum mechanics of free particles | Read the relevant part of the textbook and distributions in advance, and solve the problems given in the exercise class. |
Class 4 | Number of states and its asymptotic form of free particles | Read the relevant part of the textbook and distributions in advance, and solve the problems given in the exercise class. |
Class 5 | Derivation of the canonical ensemble | Read the relevant part of the textbook and distributions in advance, and solve the problems given in the exercise class. |
Class 6 | Elementary applications of canonical ensemble (1) | Read the relevant part of the textbook and distributions in advance, and solve the problems given in the exercise class. |
Class 7 | Midterm exam | |
Class 8 | Elementary applications of canonical ensemble (2) | Read the relevant part of the textbook and distributions in advance, and solve the problems given in the exercise class. |
Class 9 | Canonical ensemble of clasical systems | Read the relevant part of the textbook and distributions in advance, and solve the problems given in the exercise class. |
Class 10 | Applications of classical canonical ensemble | Read the relevant part of the textbook and distributions in advance, and solve the problems given in the exercise class. |
Class 11 | Eigenmodes of lattice vibration | Read the relevant part of the textbook and distributions in advance, and solve the problems given in the exercise class. |
Class 12 | Einstein and Debye models of heat capacity of solids | Read the relevant part of the textbook and distributions in advance, and solve the problems given in the exercise class. |
Class 13 | Historical background of black-body radiation | Read the relevant part of the textbook and distributions in advance, and solve the problems given in the exercise class. |
Class 14 | Electromagnetic field and harmonic oscillator | Read the relevant part of the textbook and distributions in advance, and solve the problems given in the exercise class. |
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.
It is strongly recommended to have finished the course of thermodynamics.