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Module -1
Simple harmonic motion: Preliminary concepts,
Superposition ofS.H.Ms in two mutually perpendicular
directions: Lissajous figure
Damped
vibration: Differential
equation
and its solution,
Logarithmic decrement,
Quality factor.
Forced vibration: Differential equation and its solution, Amplitude and Velocity resonance, Sharpness
of
resonance. Application in L-C-R Circuit
Module -2
Interference of electromagnetic waves: Conditions for sustained interference, double slit as
an example. Qualitative idea of Spatial and Temporal Coherence, Conservation of energy
and intensity distribution,
Newton’s ring
Di fraction of
light: Fresnel and Fraunhofer class. Fraunhofer diffraction for single slit and double slits. Intensity distribution of N-slits and plane transmission grating (No deduction of the intensity distributions
for N-slits is necessary), Missing orders. Rayleigh criterion, Resolving power of grating and microscope. (Definition and formulae)
Module -3
Polarization:
General concept of Polarization, Plane of vibration and plane of polarization, Qualitative discussion on Plane, Circularly and Elliptically
polarized light, Polarization through reflection and
Brewster’s law, Double refraction (birefringence) -Ordinary and Extra-ordinary
rays .Nicol''s Prism, Polaroid. Half wave plate and Quarter wave plate
Laser : Spontaneous and Stimulated
emission of radiation, Population inversion, Einstein’s A & B co-efficient (derivation of the mutual relation), Optical resonator and Condition necessary for active Laser
action, Ruby Laser, He-Ne Laser- applications of laser.
Holography: Theory of holography, viewing the hologram, Applications
Module -4
Concept of dependence of mass with velocity, mass energy equivalence, energy- momentum relation (no deduction required). Blackbody radiation: Rayleigh Jeans’ law (derivation without the calculation of number of states), Ultraviolet catastrophe, Wien’s law, Planck’s radiation law (Calculation of
the average
energy of the oscillator), Derivation of
Wien''s displacement law and Stephan''s law
from Planck''s radiation
law.
Rayleigh Jean''s law
and Wien''s law as limiting cases of Planck''s law. Compton Effect (calculation of
Compton wavelength is required).
Wave-particle duality
and de Broglie’s hypothesis, Concept of matter waves, Davisson-Germer
experiment, Concept of wave packets and Heisenberg’s uncertainty principle.
Module -5
Elementary ideas of crystal structure : lattice, basis, unit cell, Fundamental types of lattices – Bravais
lattice, Simple cubic, f.c.c. and b.c.c. lattices, (use of models in the class during teaching is desirable]
Miller indices and miller planes, Co-ordination number and Atomic packing factor.
X-rays : Origin of Characteristic
and Continuous X-ray, Bragg’s law ( (No derivation), determination of
lattice constant
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Module -1
Physical significances of grad, div, curl. Line integral, surface integral,
volume integral- physical examples in the context of electricity and magnetism
and statements of Stokes theorem and Gauss theorem [No Proof]. Expression of
grad, div, curl and Laplacian in Spherical and Cylindrical co-ordinates.
Module -2
Electricity 2.1 Coulumbs law in vector form. Electrostatic field and its curl. Gauss’s
law in integral form and conversion to differential form . Electrostatic
potential and field, Poisson’s Eqn. Laplace’s eqn (Application to Cartesian,
Spherically and Cylindrically symmetric systems - effective 1D problems) Electric
current, drift velocity, current density, continuity equation, steady current.
2.2 Dielectrics-concept of polarization, the relation D=ε0E+P,
Polarizability. Electronic polarization and polarization in monoatomic and
polyatomic gases.
Module -3
Magnetostatics & Time Varying Field: 3. Lorentz force, force on a
small current element placed in a magnetic field. Biot-Savart law and its
applications, divergence of magnetic field, vector potential, Ampere’s law in
integral form and conversion to differential form. Faraday’s law of
electro-magnetic induction in integral form and conversion to differential
form.
Module -4
4.1 Concept of displacement current Maxwell’s field equations, Maxwell’s wave
equation and its solution for free space. E.M. wave in a charge free conducting
media, Skin depth, physical significance of Skin Depth, E.M. energy flow, &
Poynting Vector
Module -5
5.1 Generalised coordinates, Lagrange’s Equation of
motion and Lagrangian, generalised force potential, momenta and energy.
Hamilton’s Equation of motion and Hamiltonian. Properties of Hamilton and
Hamilton’s equation of motion. 4L Course should be discussed along with
physical problems of 1-D motion
5.2 Concept of probability and probability density, operators,
commutator. Formulation of quantum mechanics and Basic postulates, Operator
correspondence, Time dependent Schrödinger’s equation, formulation of time
independent Schrödinger’s equation by method of separation of variables,
Physical interpretation of wave function ψ (normalization and probability
interpretation), Expectation values, Application of Schrödingerequation -
Particle in an infinite square well potential (1-D and 3-D potential well),
Discussion on degenerate levels.
Module -6
Statistical Mechanics: Concept
of energy levels and energy states. Microstates, macrostates and thermodynamic
probability, equilibrium macrostate. MB, FD, BE statistics (No deduction
necessary), fermions, bosons (definitions in terms of spin, examples), physical
significance and application, classical limits of quantum statistics Fermi
distribution at zero & non-zero temperature, Calculation of Fermi level in
metals, also total energy at absolute zero of temperature and total number of
particles, Bose-Einstein statistics - Planck’s law of blackbody radiation.
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Module-I
Quantum mechanics:
• Generalized co-ordinates, Lagrange’s equation
of motion and Lagrangian, generalized force potential, moment and energy.
Hamilton’s Equation of motion and Hamiltonian. Properties of Hamilton and
Hamilton’s equation of motion.
• Concept of probability and probability density,
operator, Commutator, Formulation of quantum mechanics and Basic postulates,
Operator correspondence, Time dependent Schrödinger’s equation, formulation of
time independent Schrödinger’s equation by method of separation of variables,
Physical interpretation of wave function Ψ(normalization and probability
interpretation), Expectation values, Application of Schrödinger
equation-Particle in an infinite square well potential (1-D and 3-D potential
well), Discussion on degenerate levels.
Module-II
Statistical mechanics:
• Concept of energy levels and energy states.
Microstates, Macrostates and thermodynamic probability, equilibrium macrostate.
MB, FD, BE statistics (no deduction necessary), fermions, bosons (definitions
in terms of spin, examples), physical significance and application, classical
limits of quantum statistics. Fermi distribution at zero and non –zero
temperature.
Module-III
Dielectric Properties:
• Dielectric Material: Concept of Polarization,
the relation between D, E and P, Polarizability, Electronic, Ionic, Orientation
& Space charge polarization, behavior of Dielectric under alternating
field, Dielectric losses. The Magnetic properties:
• Magnetization M, relation between B, H & M.
Bohr megneton, Diamagnetism-Larmor frequency & susceptibility, Curie law,
Weiss molecular field theory & Curie-Weiss law, Hysteresis loss,
Antiferromagnetism, Ferromagnetism & Ferrites (analitative).
Crystal structure
• Crystal structure- Bravais lattice, Miller
indices
• Crystal diffraction (qualitative), Bragg's law
and reciprocal lattice,Brillouin zone. (Qualitative description)
• Free electron theory of metal – calculation of
Fermi energy, density of states.
• Band theory of solids- Bloch theorem, Kronig
Penny model.
• Electronic conduction in solids-Drude’s theory,
Boltzmann equation, Wiedemann Frantz law.
• Semiconductor-Band structure, concept of
electron and holes, Fermi level, density of states.
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