Course Name- Classical and Statistical Mechanics

Code(Credit)-CUNT2460(3-0-1)

Course Objectives

• To learn the discipline-specific knowledge in classical mechanics, which includes
reduction of two body problem to one body problem, central force problem,
planetary motion etc.
• To understand the properties of macroscopic systems using the knowledge of the
properties of individual particles
• To learn the different types of statistical distribution function in order to study the
macro and microscopic behaviors.

Learning Outcomes

Upon successful completion of this course, students will be able to:
• Understand the equation of motion for different system.
• Understanding the different transformations and their applications.
• Know the concepts of classical mechanics and apply these concepts in the area of
science.

Course Syllabus

Module-I

Central force problem: Laboratory and centre of mass frames, Reduction of two-body
problem to one-body problem, Non inertial frames and pseudo forces, Central force and motion
in a plane, Differential equation for an orbit, Kepler’s laws of planetary motion, virial theorem

Module II

Lagrangian and Hamiltonial Dynamics: Constraints, D’Alembert’s principle, Lagrange’s
equations from D’Alembert’s principle, generalized coordinates, Hamilton’s equations,
Hamilton’s equations in different coordinate systems, variation principle, Euler-Lagrange’s
equations,

Module III

Canonical transformations and Poisson Bracket: Canonical transformations, Legendre
transformations, Generating Functions, Application of canonical transformations, properties of
Poisson brackets, Lagrange brackets, Invariance of Poisson bracket under canonical
transformations, phase space, Invariance and Noether theorem, Liouville’s theorem.

Module IV

Hamiltonian-Jacobi Theory and Small Oscillation: Hamiltonian-Jacobi equation, harmonic
oscillator problem, Kepler’s problem, Action and angle variables. General theory of small
oscillations: normal modes, normal coordinates and normal frequencies of two coupled
pendulum, double pendulum and vibrations of linear triatomic molecule.

Module-V

Relativistic classical mechanic: Postulates, Special theory of relativity-Lorentz
transformations, relativistic kinematics and mass–energy equivalence, Doppler’s effect of light

Module-VI

Classical statistical mechanics:
Phase space, ensembles, and partition functions. Free energy and its connection with
thermodynamic quantities. MB statistics and applications.

Module-VII

Quantum statistical mechanics:
BE statistics and FD statistics and their applications, Bose Einstein condensation. first and
second order phase transitions, phase equilibria, critical point. Blackbody radiation and
Planck's distribution law, Ising model.

Text Book:
1. Classical Mechanics by J C Upadhyaya, Himalaya Publishing House, 2014.
2. Statistical Mechanics by R.K Pathria, Oxford

Reference Books:
1. Classical Mechanics by H Goldstein, Pearson, 3rd Edition, 2011.
2. Classical Mechanics by Landau &Lifshitz, 7th Ed, CBS Publishers, New Delhi, 2010.
3. Differential Equations, Dynamical Systems and an Introduction to Chaos, MW Hirsch, S
Smale, RL Devaney.

Session Plan

Session-1

centre of mass frames

https://www.youtube.com/watch?v=oivxjoHy8s4&list=PLb2lQ33Kj040FSiv2YoiN6W0IfUgQ8Gj_&index=2

Session-2

Reduction of two-body problem to one-body problem

Session-3

Non inertial frames and pseudo forces, Central force and motion
in a plane

Session-4

Differential equation for an orbit, Kepler’s laws of planetary motion, virial theorem

Session-5

Constraints, D’Alembert’s principle, Lagrange’s equations from D’Alembert’s principle

Session-6

generalized coordinates, Hamilton’s equations

Session-7

Hamilton’s equations in different coordinate systems, variation principle

Session-8

Euler-Lagrange’s equations

Session-9

Canonical transformations, Legendre transformations, Generating Functions

Session-10

Application of canonical transformations, properties of Poisson brackets, Lagrange brackets