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63

Module -1

Simple harmonic motionPreliminary concepts, SuperpositioofS.H.Ms in two mutually perpendicular directions:  Lissajous figure

Damped  vibrationDifferential  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, Newtons 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 Brewsters 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, Einsteins 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, Wiens law, Plancks 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 Broglies 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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Prof. (Dr.) Tripti Guin Biswas
tripti.biswas@skf.edu.in
(+91)9143052583
Mr. Swarup Mukherjee
swarup.mukherjee@skf.edu.in
(+91)9831924792
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