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B.S. STATISTICAL MECHANICS [PHYS-632] SYLLABUS
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Formulation of Statistical Methods: Specification
of the state of a system, concept of ensembles, elementary probability
calculations, distribution functions, statistical interpretation of
entropy (Boltzmann theorem)
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Statistical Ensembles: Microcanonical ensemble,
canonical ensemble and examples (e.g., paramagnet), calculation of
mean values, calculation of partition function and its relation with
thermodynamic quantities, the grand canonical ensemble and examples
(e.g. adsorption), calculation of partition function and thermodynamic
quantities
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Simple Applications of Ensemble Theory: Monoatomic
ideal gas in classical and quantum limit, Gibb’s paradox and
quantum mechanical enumeration of states, equipartition theorem and
examples (ideal gas, harmonic oscillator), specific heat of solids,
quantum mechanical calculation of paramagnetism
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Quantum Statistics: Indistinguishibility and symmetry
requirements, Maxwell-Boltzmann statistics, Bose-Einstein and photon
statistics, Fermi-Dirac statistics (distribution functions, partition
functions). Examples: polyatomic ideal gas (MB), black body radiation
(photon statistics), conduction electrons in metals (FD), Bose condensation
(BE).
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Systems of Interacting Particles: Lattice vibrations
in solids, van der Waals gas, mean field calculation, ferromagnets
in mean field approximation
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Recommended Text:
1. W. Brewer, F. Schwabl, “ Statistical Mechanics”,
Springer Verlag (2002).
2. F.Reif, Fundamentals of Statistical and Thermal Physics McGraw
Hill, (1965).
3. T. L. Hill, “ Statistical Mechanics”, World Scientific
Publishing Company, (2004)
4. K. Huang, “Statistical Mechanics”, John Wiley and Sons
(1988).
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