(A) TENSOR ANALYSIS AND GREEN FUNCTION:

(i) Tensor Analysis:

 Covariant and contravariant tensors, addition, multiplication, Contraction of tensors, Tensor density, Levi-cevita tensor density, Pseudo-tensors, Symmetry properties, Differentiation, connection and covariant differentiations, Metric tensor. 

(ii) Green Function: 

Green function properties, Integral-differential equation, Application to linear oscillator (vibrating string), Eigen function, Eigen value equation, Green function for two and three dimensions, Expansion in spherical and cylindrical coordinates, Structural green function.

(B) COMPLEX VARIABLES AND FOURIER TRANSFORM:

(i) Complex variables: 

General function of complex variable, Cauchy-Riemann differential equation and analyticity, conformal mapping (translation, rotation, inversion), Cauchy’s integral formula, Taylor’s and Laurent’s series, singularity, poles, Residue theorem, Evaluation of definite integrals (around unit circle, infinite semicircle using Jordan’s lemma with poles lying on real axis and integration involving multiple valued function-branch point).

(ii) Fourier Transform: 

Definition, Sine and Cosine transform properties: linearity, change of scale, translation, Modulation, simple applications.

(C) NUMERICAL ANALYSIS: 

Interpolation: methods of interpolation, least square curve fitting, Methods of equal intervals, unequal intervals, central differences. 

Inverse interpolation:

Iteration of successive approximation, exchange of dependent and independent variables and reversion of series. 

Numerical differentiation: 

Method based on interpolation, on finite differences operator and on undetermined coefficients. Numerical integration: Simpson’s one-third and one-eighth rule, Euler-Maclaurin formula, Quadrature formulae, Numerical solution to ordinary differential equation by Euler’s and Runge kutta methods, Solution of algebraic and transcendental equations: Newton-Raphson method, Iterative methods.

References:

1. Matrices and Tensors in Physics by A.W. Joshi (Wiley Eastern Ltd., New Delhi).

2. Mathematical methods for physicists by Arfken.

3. Mathematics for Physics by P. Dennery and A. Krzynicki (Harper and Row, New York).

4. Numerical Analysis by Balguruswamy.

5. Numerical Analysis by Harper.

6. Applied Numerical Analysis by Gerald.

(A) ELECTROMAGNETIC THEORY:

(i) Maxwell Equations:

 Microscopic and Macroscopic fields, Maxwell equations, Fields D and H, Dielectric tensor, Principal Dielectric axes.

(ii) Potential and Gauges: 

Scalar and vector potentials, Gauge transformation, Lorentz gauge and Transverse gauge, Maxwell equations in terms of electromagnetic potentials.

(iii) Four Dimensional Formulation: 

Minkowski space, Intervals, Proper time, Lorentz transformation, Transformation of velocities, addition of velocities, relativistic Doppler effect, Four vectors, Four Tensor, Principle of least action, Four-momentum of a free particle.

(iv) Propagation of Electromagnetic Waves: 

Propagation of electromagnetic waves in free space, conducting and non-conducting medium, Reflection and refraction at a plane interface between dielectrics, Polarization by reflection, dispersion (Normal and anomalous), Metallic reflection, Electromagnetic waves propagation in bound media.

(B) PLASMA PHYSICS:

(i) Plasma State & its Properties: 

Elementary ideas of plasma state of matter, Motion of charge particles in uniform E & B fields, non-uniform fields, drifting motion, electrostatic and magnetostatic lenses, Time varying E & B fields, Adiabatic invariants, Plasma confinements (Pinch effect, Mirror confinement, Van Allen Belts), Elementary idea of fusion technology.

(ii) Hydrodynamical Description of Plasmas: 

Hydroynamical description, Equation of magneto-hydrodynamics, High frequency plasma oscillations, Short wavelength limit and Debye-screening distance.

(iii) Kinetic Theory of Plasma: 

Boltzmann-Vlasov equation, Landau damping, Collision damping.

(iv) Wave Phenomenon in Magneto-Plasma: 

Electromagnetic waves perpendicular to B0, phase velocity, Polarization, Cut-off and resonances, Electromagnetic waves parallel to B0, Magnetosonic and Alfven wave.

References:

1. The Classical Theory of Fields by L.D. Landau and E.M. Lifshitz (Pergmon Press, Oxford).

2. Foundations of Electromagnetic Theory by Reitz, Milford & Christy (Narosa, Delhi).

3. Classical Electrodynamics by J. D. Jackson (Wiley Eastern Ltd., Delhi).

4. Introduction to Plasma Physics by F. F. Chen (Plenum Press, New York).

5. Plasma Physics by A. Bittencourt

(A) GROUP THEORY:

Symmetry elements and symmetry operations, Point group and their representation, Mathematical group, Matrix representation, Orthogonality theorem (statements and interpretation only), Reducible and irreducible representations, Direct product group, normal modes, symmetry characterization of electronic states and vibrational model of polyatomic molecules, character tables (C2v, D3h and D6h).

(B) MOLECULAR STRUCTURE:

H2+ ion, Born-Oppenheimer approximation and its application, H2 molecule, Heitler-London theory, Valence bond theory of diatomic molecules, exchange energy, Simple valence bond treatment of H2O and C6H6 molecules, LCAO approximation, application to H2 and other molecules, hybridization, Huckel approximation and its application to butadiene and benzene molecules.

(C) MOLECULAR SPECTROSCOPY:

(i) Rotation and Vibration Spectra: 

IR and Raman spectra of rigid rotator and harmonic oscillator, IR and Raman spectra of non-rigid rotator, anharmonic oscillator and vibrating rotator, Intensities in rotation–vibration spectra, Isotope effect in rotation and vibration spectra. 

(ii) Electronic Spectra: 

Electronic energy and total energy, vibration structure of electronic transitions, progressions and sequences, rotational structure of electronic bands, band head formation and band origin, Intensity distribution in vibrational structure, Frank-Condon principle and its quantum mechanical formulation, intensity alternation in rotational lines.

References:

1. Elements of Group theory for Physicists by A.W. Joshi (Wiley Eastern. Ltd. New Delhi).

2. Group Theory and Quantum Mechanics by M.T. Tinkham (Tata McGraw Hill, New Delhi).

3. Chemical Applications of Group Theory by F.A. Cotton (Wiley Eastern Ltd. New Delhi).

4. Molecular Spectra and Molecular Structure by G. Herzberg (Dover Publication, London).

5. Molecular orbital Theory by A. Streitweiser.

6. Valence by C.A. Coulson.

7. Introduction to Molecular Spectroscopy by G. M. Barrow.

8. Fundamentals of Molecular Spectroscopy by C. N. Banwell.

9. Quantum Theory of Molecules and Solids, Vol-I by J.C. Slater (McGraw Hill, New York).

(A) THERMODYNAMICS:

Entropy and Probability, Thermodynamic potentials – Helmholtz free energy, Gibbs free energy, Enthalpy and Internal energy; Equilibrium conditions for an isolated system, Third law of thermodynamics.  Thermodynamics of first and second order phase transition, Clausius-Clapeyron and Ehrenfest’s equations, Chemical potential and phase equilibria, thermodynamic properties of liquid Helium II, The Lambda transition, London’s theory, Quantum liquid, Tisza two fluid model, Landau structure, superfluidity, second sound.

(B) STATISTICAL MECHANICS:

Ensembles, Canonical, microcanonical and grandcanonical ensembles and their partition function, Partition function for monoatomic and diatomic gases, Gibb’s paradox, Sackur-Tetrode equation, Maxwell-Boltzman, Bose-Einstein and Fermi-Dirac statistics, Degenerate bosons and Bose-Einstein condensation, Black body radiation, electron gas and its thermodynamic properties, White dwarfs and their limiting mass, statistical (Thomas-Fermi) model of atom.

(C) FLUCTUATIONS AND COOPERATIVE PHENOMENA:

(i) Fluctuations:

 Mean square deviation, Fluctuation in ensembles; Concentration fluctuation in quantum statistics, one- dimensional random walk and Brownian motion, Fourier analysis of random functions, Wiener-Khintchine theorem, The Nyquist theorem.

(ii) Cooperative Phenomena: 

Phase transition of second kind, Ising model, Bragg-Williams approximations, Kirkwood Method, Order-disorder in alloys, structural phase change.

References:

1. A treatise on Heat by M. N. Saha and B. N. Srivastava (Indian Press Limited, Allahabad).

2. Thermodynamics for chemists by S. Glasstone (John Wiley, New York).

3. Thermal Physics by C. Kittel (John Wiley, New York).

4. Statistical Mechanics by B. K. Agrawal and Melvin Eisner (Wiley Eastern Ltd., Delhi).

5. Statistical Mechanics by R. K. Pathria (Pergmon Press).

6. Statistical Mechanics by Kerson Huang (Wiley Student Edition).

7. Statistical Physics Part I by Landau and Lifshitz (Pergmon Press, Oxford).

8. Statistical Physics Part II by Lifshitz and Pitaevskii (Pergmon Press, Oxford).

9. Fundamentals of Statistical & Thermal Physics by Reif (Mc Graw Hill, London)

(A) POWER ELECTRONICS:

(i) Power Devices: 

SCR; basic structure, I-V characteristics and two transistor model, DIAC and

TRIAC; basic structure, operation and equivalent and I-V characteristics, TRIAC as high power

switch, DIAC as triggering device of TRIAC, UJT in over voltage protection, saw tooth wave

generation using UJT.

(ii) Regulator Circuit: 

Load and line regulation, stabilization ratio, internal impedance and

temperature coefficient of voltage regulation, linear voltage regulator circuit.

(iii) Controlled rectification: 

SCR controlled half and full wave rectifier circuit and their

analysis, elements of SMPS, SCR control and stability in SMPS,

(B) OPERATIONAL AMPLIFIER:

Characteristics of Op-Amp, inverting and non-inverting inputs, input offset current and input

offset voltage, slew rate and power band width, Op-Amp as an amplifier, Bode plot and

frequency response of Op-Amp, voltage follower, current follower, Op-Amp as integrating and

differentiating circuits, frequency to voltage and voltage to frequency converter, voltage

controlled oscillator and wave shaping circuits (Triangular and square wave), Astable,

Monostable and Bistable Multivibrators, clipping and clamping circuits.

(C) DIGITAL ELECTRONICS:

(i) Number system and Codes: 

Binary, Octal and Hexadecimal system and their

interconversion, binary arithmetic, 1’s, 2’s and 9’s compliments, addition and substraction, BCD

and hexadecimal codes, signed numbers.

(ii) Boolean algebra and Gates: 

Boolean variables, Boolean algebra, composite function and

their algebraic simplification, precedence rule, De-Morgans theorem, duality in Boolean algebra,

logic gates, universality of NAND and NOR gates.

(iii) Logic circuit design: 

Standard representation of logic function, SOP and POS terms and

design of logic circuits using these terms, Karnaugh Map, simplification of Boolean expression,

half adder and full adder, serial and parallel adder, half and full subtractors.

(iv) Elements of logic family: Transistor as a switch, FAN IN, FAN OUT, noise immunity,

propagation delay, RTL, DTL, TTL logic, sourcing and sinking logic, ECL logic.

References:

1. Integrated Electronics by Milman and Halkias.

2. Hand Book of Electronics by Gupta and Kumar.

3. Operational Amplifiers and Linear Integrated Circuits by Gaykwad.

4. Digital Electronics by Malvino and Brown.

5. Digital Electronics by R. P. Jain.

Students will be required to perform at least seven experiments from group A as well as

from group B. They will have to maintain record books of experiments done for each group

separately.

GROUP A: ELECTRONICS

1. Study of R-C Coupled Amplifier

2. Study of Multivibrator

3. Study of Push-pull Amplifier

4. Study the characteristics and determination of h-Parameter of PNP transistor in CE.

5. Study of Energy band gap of Semiconductor.

6. Study of High pass and Low pass Active Filter.

7. Study of saw tooth wave generator by UJT.

8. Study of TTL gates.

9. Study of Phase Shift Oscillator.

10. Study of Linear and Square wave detector.

11. (a) Study of Bias Stabilization.

(b) Study of Temperature effect on Diode junction.

12. Study of Clipping – Clamping circuit.