Physics 203  Introduction to Statistical Mechanics
Objectives and Goals
Statistical Mechanics is the physics of systems containing a
large number of particles. The main subject is to connect
macroscopic observable properties to microscopic properties of
matter. The goals of this course are, first, to explain the
foundations of statistical mechanics and, second, to work
through most of the classic examples of statistical mechanics,
as well as some current ones, so that the student develops
familiarity and facility with the topic. At the end of the
course, the student will be able to tackle the statistical
mechanics questions that come up in all areas of experimental
and theoretical physics and have a good foundation for further
study in statistical physics.
The course provides exposure to the following topics:
 laws of thermodynamics and simple applications
 density matrices in quantum mechanics
 ensemble approach to statistical mechanics  principles
for choosing ensembles
 derivation of microcanonical, canonical and grand
canonical ensembles
 interpretation of entropy
 fluctuations in the different ensembles and the
correspondence between the ensembles
 paramagnets
 ideal classical gas, including rotational and vibrational
internal structure
 ideal quantum gas  occupation numbers
 BoseEinstein condensation
 blackbody radiation
 electrons in metals  specific heat and spin
magnetization
 nonideal gases and virial coeficients
 phase transitions  van der Waals equation of state and
mean field theory
 selected advanced topics as time permits
Methods and Approach
 Prerequisites:

Undergraduate courses in classical mechanics, quantum
mechanics, and thermal physics are prerequisites. Some
graduate quantum mechanics would be helpful.

In classical mechanics, the main topics needed are (1) the
concept of phase space and (2) Liouville's Theorem. Though
they are briely reviewed in this course, for real
comprehension the student should have seen them before.

In quantum mechanics, the examples used in this course depend
on the student knowing the solution to certain simple quantum
mechanical problems. These are the harmonic oscillator, an
arbitrary spin in a magnetic field, the rigid rotator, and a
single particle in a magnetic field (Landau levels). In
addition, the concept of a mixed state and density matrices
are important in statistical mechanics  these will be
developed in this course in order to explain quantum
statistical mechanics, but any previous exposure would
certainly be helpful.
 Format:

This course is taught through 75minute lectures (2 per week)
and weekly homework sets. Lectures generally involve
blackboard presentations by the professor, but student
participation is encouraged. Homework sets generally consist
of about 35 problems designed to take 68 hours of
concentrated effort to complete. Students are encouraged to
discuss the homework with their peers, but are required to
write solutions independently. Students are responsible for
all material covered in the lectures and in the homework
problems. Some concepts and applications that are important
are covered only in the homework.
 Texts:

There is no good textbook for a graduate course in this
subject, and as a result there is no consensus about what text
to use in this course. Currently the recommended texts are:
 Thermodynamics and Statistical Mechanics,
1st edition, by W. Greiner, L. Neise and H. Stoecker
(Springer, New York, 1995)
 Statistical Mechanics, 2nd Edition, by
R.K. Pathria (Butterworth and Heinemann).
In addition, useful texts are:
 C. Kittel and H. Kroemer, Thermal Physics, 2nd ed.

Landau and Lifshitz, Statistical Physics, 3rd ed. part
1.
Kittel and Kroemer is used mainly for its many excellent
problems. Landau and Lifshitz is excellent for the more
advanced topics and for theoretically inclined students.
 Exams and Grades:

There is one midterm exam taken in class and a final exam in this
course. Exams are designed to test each student's grasp of the
fundamental concepts and ability to solve problems. Grades for
the course are determined by homework (45%), midterm (25%),
and the final exam (30%).
Sample Syllabus
 Introduction
 Thermodynamic quantities and relations
 Statistical Mechanics: microstates and entropy
 Ideal gas: density of states and Gibbs factor
 Classic ensembles and Liouville's theorem
 Microcanonical ensemble
 Canonical ensemble
 Boltzmann factor
 Partition function
 Helmholtz free energy
 Ideal gas and equipartition theorem
 Paramagnetism
 Grand canonical ensemble
 Chemical potential
 Grand partition function
 Quantum statistics
 Density matrix in the canonical ensemble
 Density matrix in the coordinate basis
 Thermal wavelength
 Bosons and Fermions
 Multiparticle wavefunctions
 Ideal gas in the GCE
 Ideal Bose systems
 Thermodynamics
 Bose condensation
 Blackbody radiation
 Ideal Fermi systems
 Occupation numbers
 Fermi pressure
 Electron gas in metals
 White Dwarfs
 Interacting systems
 Cluster expansion
 Virial expansion
 Phase transitions
 van der Waals gas
 Ising model
 Critical Indices
 Phase Transitions in Nuclear Physics
 Kinetic theory
 Maxwell velocity distribution and pressure
 Transport coefficients
 Htheorem