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• 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.
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
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
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
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.
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.
Relativistic classical mechanic: Postulates, Special theory of relativity-Lorentz
transformations, relativistic kinematics and mass–energy equivalence, Doppler’s effect of light
Classical statistical mechanics:
Phase space, ensembles, and partition functions. Free energy and its connection with
thermodynamic quantities. MB statistics and applications.
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.
1. Classical Mechanics by J C Upadhyaya, Himalaya Publishing House, 2014.
2. Statistical Mechanics by R.K Pathria, Oxford
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.
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
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
Canonical transformations, Legendre transformations, Generating Functions
Application of canonical transformations, properties of Poisson brackets, Lagrange brackets