ravenshaw university cuttack master of … nuclear physics 4 ... laplace transform, ... application...

RAVENSHAW UNIVERSITY

CUTTACK

MASTER OF SCIENCE

PHYSICS

SYLLABUS

2013-2015

SYLLABUS FOR M Sc PHYSICS

REVISED CURRICULUM – 2012

Semester I

Course

No.

COURSE No. of hours per

week

Durn. of Exam

in hours

Classes Per

Student

Credit

Point LECT LAB.

Paper-1.1 Classical Mechanics 4 - 3 4

20

Paper-1.2 Mathematical

Methods-I

4 - 3 4

Paper-1.3 Quantum Mechanics-

I (N.R.)

4 - 3 4

Paper-1.4 Electrodynamics 4 - 3 4

Paper-1.5 Practical(Optics) - 8 6 4

TOTAL 16 8 20

Semester II

Course

No.

COURSE No. of hours per

week

Durn. of Exam

in hours

Classes Per

Student

Credit

Point LECT LAB.

Paper-2.1 Plasma Physics

(Elementary)

4 - 3 4

20

Paper-2.2 Basic Electronics 4 - 3 4

Paper-2.3 Quantum Mechanics-

II (Applied)

4 - 3 4

Paper-2.4 Mathematical

Methods II

4 - 3 4

Paper-2.5 Practical - 8 6 4

TOTAL 16 8 20

Semester III

Course

No.

COURSE No. of hours

per week

Durn. of Exam

in hours

Classes Per

Student

Credit

Point LE

CT

LAB.

Paper-3.1 Advanced Quantum

Mechanics

4 - 3 4

20

Paper-3.2 Solid State Physics 4 - 3 4

Paper-3.3 Statistical Physics 4 - 3 4

Paper-3.4 Special Paper

-Electronics I /

-Plasma I/

Astroparticle Physics I

4 - 3 4

Paper-3.5 Practical (Modern

Physics )

- 8 6 4

TOTAL 16 8 20

Semester IV

Course

No.

COURSE No. of hours

per week

Durn. of Exam

in hours

Classes Per

Student

Credit

Point LE

CT

LAB.

Paper-4.1 Nuclear Physics 4 - 3 4

20

Paper-4.2 Quantum Field Theory

and Particle Physics

4 - 3 4

Paper-4.3 Special Paper

-Electronics II

-Plasma II

Astroparticle Physics II

4 - 3 4

Paper-4.4 Project and Seminar - 4

Paper-4.5 Practical (Special Paper

Paper) (Electronics /

Plasma/Astroparticle

Physics)

8 6 4

TOTAL 16 8 20

SEMESTER I

PAPER – 1.1

CLASSICAL MECHANICS

F.M.- 50 CP-04 Time : 3 Hrs

Unit – I

The Kinematics of Rigid Body Motion: Definition of rigid body, degrees of freedom,

orthogonal transformation and properties of transformation matrix. The Euler angles, Euler

Theorem on the motion of a rigid body. Finite and infinitesimal rotations. Rate of change of

vector. The Coriolis force effect.

The rigid body equations of motion: Angular momentum and kinetic energy of motion

about a point. Tensors and diadics. The inertia tensor and the moment of inertia. The eigenvalues

of the inertia tensor and the Principal axis transformation. Euler’s equations of motion. Torque

free motion of a rigid body. The heavy symmetric top with one point fixed.

Unit-II

The Hamilton equations of motion: Legendre transformation and the Hamilton equations

of motion. Cyclic coordinates and conservation theorem. Routh’s procedure and oscillation about

steady motion. Derivation of Hamilton’s equations from a variational principle. The principle of

least action.

Canonical Transformation: The equations of canonical transformation and examples.

Poisson’s brackets and other canonical invariants. Poisson’s brackets and other canonical

invariants. Equations of motion, infinitesimal canonical transformations and conservation

theorems in the Poisson bracket formulation. The angular momentum Poisson bracket relations

Unit-III

Hamillton-Jacobi Theory: Hamilton-Jacobi equations for i) principal function ii)

characteristic functions. Harmonic oscillator problem as an example of the Hamilton – Jacobi

method, separation of variables in the H-J equation. Action angle variables. The Kepler problem

in action angle variables.

Small oscillations: Potential energy in quadratic approximation, conditions of

oscillation, Lagrange’s equation for degrees of freedom, oscillating systems, T matrix, V matrix

and similarity transformation, normal frequencies and normal modes, normal coordinates with

examples, free vibration of a linear tri atomic molecule.

Reference Books:

1. Classical Mechanics: H. Goldstein , safko and Phoole (Pearson)

2. Mechanics : L.D. Landau and K.M. Lifshitz(Elsevier)

3. Particle Dynamics : J.B. Marion (Cengage)

4. Classical Mechanics : Rana and Joag (TMH)

PAPER –1.2

MATHEMATICAL METHODS I


Unit- I

Differential equations and their solutions: Bessel’s differential equation, power series

solution, Bessel function, Recurrence relations, generating function. Integral representation of

Jn’, Orthogonality Condition, Bessel functions of half odd order, Neumann function Nn’ and

Properties, Asympototic forms of Jn and Nn.. Spherical Bessel function j1 and n1, Rayleigh’s

formula for j1 and n1, orthonormality of spherical Bessel functions.

Laguerre differential equation and its solution, Laguerre polynomial, Generating function

for Laguerre, Rodrigue’s formula, Recurrence relations, orthonormality condition, integral

representation. Associated Laguerre differential equation and its solution, generating function,

associated Laguerre polynomials, orthonormality relations,.

Unit-II

Hypergeometric equation, solutions and properties, Gauss formula, Linear relationships

of hypergeometric functions, Confluent hypergeometric function and properties, Integral

representation, Relation of confluent hypergeometric functions with other special functions

Solution of non-homogenous equation : Green’s function. Symmetry of Green’s

functions, Green’s functions in 1D, 2D and 3D problems, eigenfunction expansion technique.

Complex variable : Residue theorem, it’s application to evaluate definite intergrals.

Unit-III

Definition, Properties and Representations of Dirac Delta Function, Laplace transform,

Properties and examples of Laplace Transform, Convolution theorem and its applications,

Laplace transform method of solving differential equations

General tensor analysis : Contravariant and covariant vectors, Tensor of rank two. Tensor

algebra (addition, subtraction, outer product, inner multiplication) relative tensors, Kronecker

delta and Levi-civita tensor density. Symmetry property of tensors, Pseudotensors, Metric tensor

and properties.

Reference Books:

1. Mathematical methods for Physicists : G.B. Arfken and H.J. Weber and Harris(Elsevier)

2. Mathematical Methods of Physics : J Mathews and R.L. Walker (Pearson)

3. Mathematical Physics : P.K. Chattopadhyay (New Central)

4. Mathematics for Physicists and Engineers: Pipes.( Mc Graw Hill)

PAPER –1.3

QUANTUM MECHANICS-I (NON RELATIVISTIC)


Unit –I Abstract representation of quantum states as vectors in linear vector space (Hilbert space)

Dirac’s ket vectors, bra vectors, scalar product , norm of a ket vector.Schwartz in-equality in

vector space, concept of ortho-gonality of ket-vectors.

Operators and their properties- a review, Operators representing observables. Expectation values

of operators, Hermitian operators, Eigen values and eigen vectors of Hermitian operators,

Complete set of eigen vectors of a Hermitian operator, a basis set, Expansion theorem,

Completeness and closure property. Expansion of an arbitrary ket ψ using complete set of co-

ordinate eigen kets and identification of the co-efficient of expansion ψx as the wave

function ( )xψ in co-ordinate representation such as momentum, energy etc. Unitary

transformation of basis vectors and operators. Matrix representation of ket vectors and bra-

vectors and operators.canonical commutation relation and dimensionality of Hilbert space.

Time-evolution of quantum states,Time-evolution operator.Time-dependence of quantum states

and observables in Schrodinger, Heisenberg and Interaction (Dirac) picture. Equations of motion.

Solution of Harmonic Oscillators problem in Heisenberg picture.

Unit-II

Rotational symmetry under rotation of co-ordinate system. Orbital angular momentum prLrvr

×=

as the generator of transformation under rotation. Transformation of scalar operator and a vector

operator under rotation leading to various commutation properties of

,xL yL ,zL and 2L with other vector or scalar operators. Raising and lowering operators ,+L _L .

Lie-Algebra for the components of orbital angular momentum operator. Eigen values and

eigenfunctions of ( )zLL ,2

by operator method. Matrix representations of ,xL yL ,zL and 2L .

Spin angular momentum of spin 2

1 particles- Pauli spin operators ( )zyx σσσ ,, and their

properties.Eigenvalues and eigenfunctions. Spinor transformation under rotation of co-ordinate

system.

Total angular momentum SLJrrr

+= . Lie-Algebra for the components ,, +JJr

and _J ,Eigen value

problem of 2J and

ZJ . Angular momentum matrics.

Addition of angular momenta and C.G. coefficients for states with (i) 21 2

1 jj == and (ii)

21,1 21 == jj

Unit- III

Harmonic oscillator problem in Fock-space, Creation operator †

( )aΛ

, annihilation operator

)(+Λ

a and number operator )(Λ

N and solution of one-dimentional Harmonic oscillator by operator

method. Matrix elements of † 2

, , , , , ,x X

N a a x p X PΛΛ Λ Λ Λ Λ Λ

etc between any two states in Fock-space. Time

evolution of †

,a aΛΛ

.Eigen states of annihilation operators Λ

a and Co-herrent states.

Motion in a spherically symmetric field. Central Force problem.Reduction of two-body problem

into equivalent one body problem.Maximum set of mutually commuting operators

ΛΛΛ

ZLLH ,,

2

for the central force problem, separation of radial motion and angular motion and

their solutions with appropriate boundary conditions at 0=r and ∞→r .Particle in a spherical

box i.e. bound state problem for particles in spherical box.

Bound state problem of hydrogen atom eigen values,eigenfunctions, degeneracy.

Radial probability distributions. Harmonic oscillator in 3-dimensions, eigenvalues,

eigenfunctions, degeneracy.

Reference Books:

1. Quantum Mechanics : Sakurai (Pearson)

2. Quantum Mechanics : Schiff(Mc Graw Hill)

3. Quantum Physics : Gasiorowicz (Wiley)

4. Quantum Mechanics : Merzbacher (Wiley)

5. Introduction to Quantum Mechanics : Bransden & Joachain(Pearson)

6. Quantum Mechanics : Liboff(Pearson)

7. Quantum Mechanics : Ghatak & Lokanathan (Mc Millan)

8. Quantum Mechanics : Greiner (Springer)

PAPER –1.4

ELECTRODYNAMICS

F.M.- 50 CP-04 Time :-3Hrs

Unit- I

Field of a point charge near a dielectric-dielectric interface using method of images,

Conservation Laws: Charge and Energy, Continuity Equation, Poynting’s theorem,

Newton’s third law in electrodynamics, Maxwell’s stress tensor, conservation of momentum.

Electromagnetic waves: Reflection and transmission of plane electromagnetic waves at

the boundary of two linear media (oblique incidence),

Dispersion: The frequency dependence of permittivity, Dispersion in non conductors.

Kramers- Kronig relations, Cauchy’s formula

Unit – II

Guided waves : Wave guides, TE waves in a rectangular wave guide, The co-axial

transmission line.

Potential formulation of electrodynamics: Magnetic vector and scalar potential,

The wave equation for the potentials, Gauge transformations, Coulomb gauge and

Lorentz gauge.

Retarded potentials, Lienard Wiechert potentials, The fields of a point charge in uniform

and accelerated motion, Power radiated by an accelerated point charge, Radiation reaction and its

physical basis.

Unit-III

Dipole radiation: Electric dipole radiation, Magnetic dipole radiation, Radiation from an

arbitrary distribution of charges and currents.

Relativistic electrodynamics: Lorentz transformation as an orthogonal transformation,

covariant form of electromagnetic equations, Electromagnetic field tensor, Transformation law

for electromagnetic field, The field of a uniformly moving point charge.

Reference Books:

1. Foundations of electromagnetic theory : Ritz, Milford and Christy (Pearson)

2. Introduction to electrodynamics (PHI) : David J Griffiths (Pearson)

3. Classical Electrodynamics: (Wiley)

4. Introduction to Electromagnetic Fields and Waves: Corson and Lorrain (CBS)

PAPER –1.5

PRACTICAL (OPTICS)

F.M.-100 CP-04 Time : 6Hrs

1. Determination of

(i) λ of Na light.

(ii) ∆λ of Na doublet.

(iii) Thickness of mica film using Michelson interfermometer.

2. Verification of Brewster’s Law

3. Study of rotativity of quartz

4. Verification of Fresnel’s laws of reflection of polarized light.

5. Determination of numerical aperature of optical fibre.

6. Determination of thickness of air film between half silvered plates by measurement of

Fabry – perot rings.

7. Analysis of elliptically polarized light using Babinet compensator

8. Determination of Rydberg constant by the use of prism spectrograph/plane transmission

grating.

9. Measurement of wavelength of Laser Source.

10. Verification of Malus Law

11. Study of variation of transmittance of glucose solution of different concentration.

Semester II

PAPER – 2.1

Plasma Physics (Elementary)


Unit-I

Definition; Quasineutrality, Collective Behaviour, Occurrence; Plasma properties. Debye

Shielding, Plasma parameter, Plasma frequency, Criteria for plasmas, Application of Plasma

Physics; Gaseous Electronics, Controlled Thermonuclear Fusion, Space Physics, Modern

Astrophysics, MHD Energy Conversion and Ion Propulsion, Solid State Plasmas, Gas LASERs

Mobility of charge particles, effect of magnetic field on the mobility of electrons,

diffusion of electrons and ions, ambipolar diffusion, diffusion in a magnetic field, thermal

conductivity, electron and ion temperature, dielectric constant of a plasma, Plasma as a refracting

medium, Optical properties of plasma, magnetic susceptibility of a plasma.

Unit-II

Motion of charged particles in electromagnetic field: Energy conservation, motion of

charged particles in uniform (i) electrostatic field.(ii) magneto static field. Magnetization current,

Motion of charged particle in uniform electrostatic and magneto static field. Drift due to an

external force.

Kinetic pressure in a partially ionized gas, Basic concepts related to collision of Particles in

Plasma: Collision cross section, mean free path, Collision frequency, Collision between charged

particles, Inelastic collisions: charge transfer, electron attachment, recombination.

Unit –III

Plasma as fluid: Relation Plasma Physics with ordinary electro magnetic, the fluid

equation of motion; The Convective Derivative, The stress tensor, collisions, comparison with

ordinary hydrodynamics, equation of continuity, equation of state, the complete set of fluid

equations, fluid drifts perpendicular to B, Fluid drifts Parallel to B, the plasma approximation.

Reference Books:

1. F.F.Chen, Introduction to Plasma Physics & controlled Nuclear Fusion,(Vol-I) (springer

(2/e) 2006.)

2. S.Sen Plasma Physics, (Pragati Prakashan.)

3. Waves in Plasma, T.H.Stix (AIP New York, 1992)

4. Plasma waves, D.G.Swanson (Academic Press, Bosson, 1989)

5. Principle of plasma physics, N.A.Krall & H.W. Trivelpiece, (McGrawHill New York,

1973.)

6. Elementary Plasma Physics, L.A.Arzimovich Blaisdell,( NewYork,1968.)

7. Plasma Physics, J.L.Delcroix, (Wiley New York, 1965.)

8. Introduction to Plasma Physics BM. Smirov, (Mir Publication, Moscow 1977.)

9. Fundamentals of Plasma Physics, J.A.Bittencourt, (Springer, 2004.)

10. Hydrodynamics and Hydromagnetic Stability, S. Chandrasekhar,( Dover, 1981.)

PAPER--2.2

BASIC ELECTRONICS

F.M.-50 CP-4 Time : 3 Hrs

Unit-I

Power electronics. SCR, FET, MOSFET,DIAC, TRIAC (Principle, construction,

operation with characteristics and application)

Oscillators: Klystron oscillator (principle, description, and operation) Multivibrator,

Astable, Monostable, Bistable (Principle, Description and Operation)

Operational amplifier: Differential amplifier (Circuit configuration and properties, ideal

operational amplifier input and output impedances)

Application of OP-AMP : Inverting amplifier, Non-inverting amplifier, adder,

substractor, integrator, differentiator, logarithmic amplifier, comparator (Principle, basic circuit

operation and theory)

Unit-II

Single equation loops, voltage, source, constant voltage source, constant current source.

Maximum power transfer theorem. Thevnins theorem, Nortons theorem.(Digital Electronics)

Number system :

Binary, Octal and hexadecimal numbers (basic characteristics and inter-conversion) gray

Code (inter-conversion between gray code and binary code) binary algebra-addition, subtraction,

multiplication and division.

Logic operations : Nor gate : NAND gate. Exclusive OR gate, Exclusive NOR gate

(Logic symbol, truth table and circuit with operation)

Logic families: RTL, DTL, TTL (Description and operation) CMOS, Sequential circuit-

SR flipflop clocked SR flipflop. JK flipflop, master, slave, JK flipflop (Principle and operation)

Unit-III

Different types of radiowave propagation – Description and basic theory AM

and FM transmitter (Block diagram study) with emphasis on function of limiter and

discriminator

Antenna: Basic antenna action, current and voltage distribution in linear antenna, diplole

antenna, power radiator, radiation resistance and directional pattern.

Different types of antenna: (Only descriptive study of practical antenna) Hom antennas,

Reflector antennas, Yagi antenna.

Reference Books:

1. Handlook of Electronics : Gupta Kumar (Ptragati)

3. Digital Electronics : Gothmann

4. Modern Digital Electromnics : R.P.Jain (TMH)

5. Digital Principles and Applications: Malvino, Leach, Saha (TMH)

PAPER 2.3

QUANTUM MECHANICS – II

F.M. – 50 CP-4 Time : 3 Hrs.

Unit-I

Stationary state perturbation theory, Rayleigh-Schrodinger method for nondegenerate case. First

and second order perturbation, anharmonic oscillator, general theory for the degenerate case. Removal of

degeneracy, linear and quadratic Stark effect. Normal and anamolous Zeeman effect. Fine structure of

spectral lines for H. like atoms

Unit-II

Variational method, the ground state of He-atom, Born-Openheimer Approximation for molecules, H2-

molecule ion. W.K.B. method. Connection formula, Bohr-Sommerfeld quantiazation rule, Harmonic

oscillator and cold emission. Time-dependent perturbation theory : Transition probability constant and

harmonic perturbation. Fermi’s golden rule, electric dipole radiation and selection rules.

Unit-III

Definition of scattering amplitude and scattering crossection, Formulation of scattering problem

and solution by Green’s function method. Concepts of in and out states. Neumann’s series for out

Ψ ,

Born Approximation .Application to Coulomb and screened Coulomb potential. The free particle

problem, expansion of plane wave in terms of spherical waves. Partial wave analysis for elastic and

inelasctic scattering, Black disk scattering, scattering from a hard sphere, resonant scattering from a

square well potential. Optical theorem as a consequence of conservation of probability.

Reference Books

1. Quantum Mechanics : Sakurai (Pearson)

2. Quantum Mechanics : Schiff(Mc Graw Hill)

3. Quantum Physics : Gasiorowicz (Wiley)

4. Quantum Mechanics : Merzbacher (Wiley)

5. Introduction to Quantum Mechanics : Bransden & Joachain(Pearson)

6. Quantum Mechanics : Liboff(Pearson)

7. Quantum Mechanics : Ghatak & Lokanathan (Mc Millan)

8. Quantum Mechanics : Greiner (Springer)

MATHEMATICAL PHYSICS II

PAPER-2.4

F.M. 50 CP-4 Time:3Hrs

Unit-I

Matrices:Eigenvalue Problem, determination of eigenvalues, eigenvectors and their properties,

diagonalization of a matrix, eigen vectors of commutating matrices, Cayley-Hamilton theorem, conditions

of diagonalizability, functions of a diagonalizable matrix, powers of a matrix, roots of a matrix,

exponential of a matrix, logarithm of a matrix, evaluation of functions using Cayley-Hamilton theorem.

Unit-II

Group theory : Representation of a group, Homomorphism and isomorphism continuous groups :

Lie groups, generators and structure constants, SO(2), SO(3) and SU(2) groups. Their generators and

irreducible representations, SU(2) and SO(3) homomorphism.

Unit-III

Tensor Calculus: Differentiation of a tensor, Covariant derivative of Contravariant and covariant

vectors and tensors, Tensor forms of gradient, divergence, curl and the Laplacian, geodesic

equation, Einsteins law, Parallel displacement, Curvature of Riemannian space, commutation law of

covariant differentiation, covariant curvature tensor, symmetries of curvature tensor, Bianchi identity.

Reference Books:

1. Matrices and tensors in Physics: A.W.Joshi (Phi)

2. Mathematical methods for Physicists: Arfken , Weber &Harris (Elsevier)

3. Gravitation and Cosmology: S.Weinberg. (Wiley)

4. Vector Analysis: Spiegel (Schaum) (TMH)

PAPER –2.5

PRACTICAL (ELECTRICITY)

F.M.-100 CP-04 Time : 6Hrs

1. Power supply with and without zener.

2. Study of R.F.coil characteristics

3. Study of triode as amplifier

4. Study of coupled oscillating circuit

5. Maxwell’s A.C. Bridge and determination of inductive capacitative and ohmic impedance.

6. Characteristics of LED

7. Characteristics of a photo diode.

8. Basic Logic gates

9. Rectifier with different filters

10. Transistor as Amplifier

11. Study of Hartely oscillator

12. Calibration of oscilloscope

13. Wave shaping

14. Characteristics of a light dependant Resistor/Operation of photo voltaic cell/operation of

opto-coupler.

15. Study of colpitt’s oscillators.

SEMESTER – III

PAPER -3.1

ADVANCED QUANTUM MECHANICS

F.M.-50 CP-4 Time: 3Hrs

Unit-I

Klein- Gordon equation, Non-relativistic limit, K.G equation for a spinless particle of charge q in

electromagnetic field, Lorentz invariance of K.G.equation, K.G.Equation in Schrodinger form, stationery

state solution, solution of K.G.Equation for 1/r potential. Unusual features of K.G.equation.

Unit-II

Dirac equation, Probability density and continuous equation, Non-Relativistic limit, magnetic

moment of electron, covariant form of Dirac equation, Algebraic properties of gamma matrices, Proof of

covariance, Bilinear covariants, Free particle solutions of Dirac equation, projection operators for energy

and spin.

Unit-III

Physical interpretation of free particle solutions and packets, Zitterbwegung, hole theory,

Symmetry properties of Dirac equation, (a) Parity, (b) Time reversal, (c) charge conjugation.

Dirac equation with central potential, commutation of the total angular momentum operator with

the Hamiltonian in a spherically symmetric potential.

Reference Books:

1. Relativistic Quantum Mechanics: Bjorken and S.D, Drell (Mc Graw Hill)

2. Advanced Quantum Mechanics: J.J.Sakurai (Pearson)

3. Quantum field Theory: Itzykson and Zuber (Mc Graw Hill)

4. Quantum Mechanics (Vol-II) : Messiah

PAPER – 3.2

SOLID STATE PHYSICS


Unit-I

Elastic waves-Elastic stain, stiffness constants, Elastic stiffness for cubic crystals

Defects-point defect, line defect and diffusion

Lattice dynamics-monoatomic, diatomic lattice, Einstein and Debye model for specific heat of insulators

Free electron model-Sommerfeld model of free electrons, Specific heat of metals, Wiedmann-Frank law,

Hall effect

Band theory-Kronig-Penney model, reduced, extended and periodic zones, origin of band gap.

UNIT-II

Semiconductors-intrinsic and impurity semiconductors, law of mass action, pn junction.

Dielectric properties of insulators- Local field, Claussius-Mossotti relation, Theory of polarizability,

Optical properties in the infrared, Lydanne-Sachs-Teller relations, zeros and poles of the dielectric

function.

Screening-static dielectric function, Thomas-Fermi theory of static screening, Lindhard theory of

dynamical screening, Friedel oscillations, plasma oscillations

Unit-III

Quantum theory of Diamagnetism and paramagnetism, derivation for susceptibility,

paramagnetism of conduction electrons, Ferromagnetism and anti-ferromagnetism, Ferrimagnetism, Neel

temperature, Spin waves, Magnons, Bloch law.

Superconductivity: Experimental survey, Meissner effect, Type-I and Type – II superconductors,

Thermodynamics of super conductors, London’s theory, Josephson effect, flux quantization, Microwave

quantum interference. BCS theory, High temperature superconductors (elementary ideas).

Reference books

1. Introduction of Solid State Physics : C.Kittel (Wiley)

2. Solid State Physics : A Omar (Pearson)

3. Solid State Physics : Ashcroft and Mermin (Cengage)

4. Solid state Physics : A.J. Dekker

PAPER – 3.3

STATISTICAL MECHANICS

F.M.- 50 CP-4 Time : 3 Hrs.

Unit – I :

Classical Statistical Mechanics : Postulate of classical statistical mechanics,

Liouville’s theorem, Microcanonical ensemble. Derivation of thermodynamics, equipartition

theorem, Classical ideal gas, Gibb’s paradox.

Canonical ensemble and energy fluctuation, Grand canonical ensemble and density

fluctuation. Equivalence of canonical and grand canonical ensemble.

Unit-II : Quantum Statistical Mechanics

The density matrix ensembles in quantum statistical mechanics, ideal gas in

macro canonical and grand canonical ensemble. Equation of state for ideal Fermi gas, Theory of

white dwarf stars. Ideal Bose gas, Photons and Planck’s law Phonons and Debye’s theory of

specific heat, Bose Einstein condensation.

Unit-III

Phase Transition : Thermodynamics description of phase transistions, Phase

transitions of second kind, Discontinuity of specific heat, change in symmetry in a phase

transition of second kind. Continuous Phase transitions, Ising Model (one dimensional), Mean

field theory, Order Parameter, Landau Theory, Symmetry breaking field, Critical Exponents.

Fluctuations, Mean – Square deviations, One dimensional random walk, applications to

Brownian Motion.

Books

1. Statistical Mechanics : K. Huang (Wiley)

2. Introductory statistical Mechanics: R.Bowley and M. Sanchez (Oxford)

3. Statistical Mechanics: R.K.Pathria (Elsevier)

4. Statistical Mechanics – B.K. Agrawal & M. Eisner. (New Age)

5. Fundamentals of statistical Mechanics – B.B. Laud.(New Age)

PAPER-3.4

SPECIAL PAPER (ELECTRONICS)-I


UNIT-I

Network and Network theorems : Mesh and node circuit analysis, Reduction of complicated

network, Conversion between T and TT section, Bridged T- network, Lattice network, Superposition

theorem, Reciprocity theorem, Thevenin’s theorem, Norton’s theorem, Maximum power-transfer

theorem.

Resonant Circuit: Series resonance and parallel resonance. Microwave Source: Reflex Klystron,

Magnetron and Traveling wave tube.

UNIT-II

Transmission line: Calculation of line parameters of parallel wire lines and coaxial line. Voltage

and current relations on Radio Frequency Transmission line in terms of traveling waves, Propagation

constant attenuation constant, Phase constant. Line distortion and alternative line termination for zero

load, finite load and infinite load, Standing wave ratio.

Wave guides and cavity resonators: Rectangular wave guides, circular wave guides, standing

wave ratio in wave guides, wave guide behavior at wave lengths greater than cut off, wave guide coaxial

coupling, Resonators :- Rectangular resonator, cylindrical resonator, (modes and Q of all resonators)

Excitation and coupling of cavities. Application of resonators.

UNIT-III

Wave shaping circuit: Linear wave shaping – R.C. circuit. High pass and low pass R-C with

different input voltage, Non linear wave shaping-shunt diode clippers, Series diode clippers, Double

ended clippers (PN junction diode & Zener diode), D-C Resistor clamping circuit.

Voltage and current sweep generator: Transistor constant sweep generator, Miller integrating

sweep circuit, Boot strap sweep generator current time base generator, Blocking oscillator, Triggered

transistors, Blocking oscillator.

Reference Books :

1. Networks, lines and fields :- J.D. Ryder (PHI)

2. Microwave circuits and passive devices : M.L. Sisodia & G.S. Raghuvanshi (Willy Ester Ltd.)

3. Handbook of Electronics : Gupta and Kumar (Pragati Prakashan)

PAPER 3.4

SPECIAL PAPER (PLASMA PHYSICS)-I


Unit I:

Degree of Ionisation and Saha Ionisation formula, Methods of Plasma Production:

Classical Townsend Mechanism and Electrical Breakdown in Gases, Streamer mechanism and

micro discharges, Electrical discharges (Arc discharge, Glow discharge), Radio frequency (RF)

discharges, Di-electric Barrier and Corona discharge, Other methods (Ohmic heating, heating by

LASER, heating with particle beams).

Unit II:

Plasma Equlibrium Models: Thermal Equilibrium(TE), Local Thermal Equilibrium

(LTE), Corona Equilibrium (CE), Collisional Radiative Equlibrium (CRE).

Plasma Diagnostics: High frequency current measurement(Rogowski Coil), Magnetic Probe,

Electric Probes: Single Probe, Double Probe, Emissive Probe, Plasma Spectroscopy: Radiations

from Plasmas (Line radiation and Continuum Radiation), Use of external radiation for plasma

diagnostics: Scattering by Laser radiation by Plasma Electrons; Thomson Scattering, X-ray

scattering, microwave method.

Unit III:

Motion of charged particle in non Uniform magnetic (B) field; Spatial variation of

magnetic field; Divergence term, Gradient and Curvature term, Shear terms, Equation of motion

in 1st order approximation, Average force over one Gyration Period ; Parallel Force,

Perpendicular Force, Total average force, Gradient Drift, Parallel Acceleration of the guiding

centre; Invariance of the orbital magnetic moment and magnetic flux, magnetic mirror effect,

curvature drift , combined gradient-curvature drift, Time varying E and B field, Adiabatic

Invariants (µ, J, Φ).

Reference Books:

1. The Plasma State by E. J. Hellund , Reinhold Publishing Co., 1961.

2. Plasma Spectroscopy by Hans. R. Griem, Mc-Graw Hill, 1964.

3. Plasma Diagnostic Techniques by Richard H. Huddlestone, Academic Press, 1965.

4. Introduction to Plasma Physics and controlled Fusion Vol: 1, by Francis F. Chen, (2/e),

Springer, 1974.

5. Principles of Plasma Diagnostics by I. H. Huchinson, Cambridge (2/e), 2005.

6. Fundamentals of Plasma Physics by J. A. Bittencourt, Springer, 2004.


Springer, 1974.

PAPER 3.4

SPECIAL PAPER (ASTROPARTICLE PHYSICS)-I


UNIT – I

Contents of the Universe, The cosmic distance hierarchy and the determination of galactic

densities, Parallax, Distance from velocity measurements, Distance from apparent luminosity,

Weighing galaxies, The red shift and the expansion of the universe;

Physical basis of general relativity:

The need for relativistic ideas and a theory of gravitation, Difficulties with Newtonian

mechanics: gravity, inertial frames and absolute space, Inadequacy of special relativity, Mach's

principle and gravitational waves, Einstein's principle of equivalence.

UNIT – II

Boltzmann’s formula, Saha’s equation of thermal ionization, Spectral classification, Importance

of ionization theory in Astrophysics – The H-R Diagram, Fourier transform –Infrared

Spectroscopy. Masses and radii of stars, Origin of Binary stars, Stellar masses and Mass

luminosity relation, Description of binary system, detectors and image processing, Hubble’s

Law.

UNIT – III

Principle of general covariance, Tensor densities, Geodesic equation, Geodesic equation as

representing gravitational effect, Newtonian Limit, Energy Momentum tensor – Covariant

divergence of the energy momentum tensor, Einstein Field Equation, The Cosmological

constant. Robertson Walker metric and field equation.

Text Books:

1. Gravitation and Cosmology: Principles and Applications of General Theory of Relativity

– Steven Weinberg, John Wiley & Sons.

2. Principles of Cosmology and Gravitation – Michael Berry – Cambridge University Press.

3. Lectures on Gravitation – Ashok Das.

4. An Introduction to Astrophysics – Baidyanath Basu – PHI

PAPER-3.5

PRACTICAL (MODERN PHYSICS-I)

F.M.-100 CP-4 Time: 6 Hrs

1. Determination of Planck’s constant-optical Pyrometer.

2. e/m of an electron using magnetron value.

3. Hall effect

4. Ultrasonic studies.

5. Study the variation of resistance with temperature

6. Frank Hertz experiment

7. Study of Gamma-ray Spectrometer

8. Study of Energy gap

9. G.M. Counter characteristics.

10. Single slit diffraction using Laser beam

11. Measurement of Lande’s g-factor using ESR apparatus.

SEMESTER IV

NUCLEAR PHYSICS

PAPER-4.1

FM-50 CP-4 TIME-3Hrs Unit-I (Nuclear structure and Nuclear force)

Electron scattering, Hofstadter form factor and charge distribution of the nucleus, Nuclear magnetic

moments and Schmidt lines. Magic numbers and shell model.

Electric quadrupole moment, Liquid drop model, mirror nuclei and Bohr-Wheeler theory of nuclear

fission.

Fermi gas model, . Nuclear force and the two neutron system. Yukawa meson field theory-hard core,

central and non-central forces, charge independence and charge symmetry of the nuclear force- pp, np

and nn-scattering. Deuteron, its quadrapole and magnetic moments

Unit-II (Nuclear decay)

Alpha decay, Q value, Gamow theory of alpha decay. Beta decay-Fermi theory of beta decay- shape of

the beta spectrum, Selection rule-allowed and forbidden transitions, Parity violation in beta decay, helicity

operator, Gamma decay-selection rule.

Unit-III (Nuclear reactions)

Energetics of nuclear reaction, compound nucleus theory, resonance scattering, Breit-Wigner formula,

Optical model potential- Kapur-Peirls theory, Direct reaction-cross section in the first Born

approximation.

Reference books

1. Theoretical Nuclear Physics - J. M. Blatt and V. F. Weisskopf,

(Wiley, New York, 1952)

2. Nuclear Physics - R. R. Roy and B. P. Nigam

3. Nuclear Physics - V. Devanathan (Narosa, 2011)

4. Introductory Nuclear Physics-Samuel S. Wong (Prentice Hall

international Inc., 1990)

QUANTUM FIELD THEORY AND PARTICLE PHYSICS

PAPER-4.2

FM-50 CP-4 Time-3Hrs

Unit I

Fields: The canonical formalism and Quantization procedure for particles, Fields and

Lagrangian formulation of Fields, Quantization of Fields, Quantization of Relativistic

Schrodinger equation, The meaning of Field Quantization, Two particle system, Covariant

description of free fields, Covariance of the field equation, Noethers theorem, Symmetry and

conservation laws.

Unit II

Particle Physics I: Quantization of real Klein-Gordon field, Covariant commutation

relations, microscopic causality and the meson propagator.

Classical and Quantum pictures of interactions, electromagnetic interactions, Strong

interactions, Weak and electroweak interactions, Gravitational interactions, The interaction

cross-section, Decays and resonances.

Unit III

Particle Physics II :Basic forces, classification of elementary particle, spin, parity,

isospin, strangeness, lepton and baryon number. Conservation laws, Gellmann-Nishijima

scheme, Meson and baryon octet, elementary ideas of SU(3) symmetry. Quark model.

Reference Books :

1. Quantum field theory: F. Mandl, G. Shaw (Inter Science New Work)

2. An Introduction to Quantum Field Theory- Peskin, Schroeder (Levant)

3. Introduction to Particle Physics: M.P.Khanna (PHI)

4. Introduction to High Energy Physics: D.H.Perkins(Cambridge University Press)

5. Introduction to Elementary Particles: D.Griffiths. (Pearson)

PAPER- 4.3

SPECIAL PAPER, ELECTRONICS - II


UNIT – I

Application of OPAMP: Scale changing, Phase shifting, Voltage follower, RC-active

filters, Instrumentation amplifier, Analog computation, Logarithmic amplifier, Antilogarithmic

amplifier, Bridge amplifier, Voltage regulator, Saw-tooth wave generator, Voltage comparator,

Schmitt trigger, Monostable and Bistable multivibrator, 555 IC timer.

UNIT-II

Half adder, full adder, Half subtractor, Full subtractor, Adder as subtractor, BCD adder,

Simplification of Boolean expressions using Kamaugh maps, (Two, three, four variables), Don’t care

condition, Decoder, Encoder, BCD to 7 segment decoder, Digital comparator, Multiplexer,

Demultiplexer, D/A converter, A/D converter.

Computer Memory: Memory cell, memory organization, read only memory, random access

memory, characteristics of memories.

Microprocessor: Basic concepts of Microprocessor, Microprocessor architecture, qualitative idea on

8085, Motorola M6800 microprocessors.

UNIT-III

Quantum Electronics: Basic principle of Laser, spontaneous and stimulated emission,

Einstein’s A and B co-efficients, Population inversion, laser scheme in two and three level systems,

Optical resonator, Light amplification and threshold condition, Ruby laser, He-Ne laser,

Semiconductor laser.

Transducers: Position, Pressure, Temperature, Piezoelectric, Optical, Acoustic

transducers.

Reference Books:-

1. Integrated Circuits and Semi conductor devices : Deboo/ Burrous Theory and Application : G.J.C.

N. (McGraw Hill)

2. Digital Electronics : Willium H. Gothmann (PHI)

3. Fundamental of Computers : V. Rajaraman (PHI)

4. Introduction of Microprocessor : Aditya P. Mathur (McGraw Hill)

5. Modern Digital Electronics : R.P. Jain, M.M.S. Anand

6. Electronics Fundamentals & Application : D.Chattopadhya & Rakhit

7. Handbook of Electronics : Gupta Kumar

8. Optoelectronics an Introduction : J.Wilson, J.H. B. Hawkes. Eastern economy edition (Prentice

Hall)

9. Optical electronics –Ajay Ghatak & K. Tyagarajan. (Cambridge University Press.)

PAPER- 4.3

PLASMA PHYSICS (SPECIAL )- II


Unit I:

Elements of Plasma Kinetic theory: Phase Space; single particle phase space, many

particle phase space, volume elements, Distribution function, Number density and Average

velocity, The Boltzmann equation; Collision less Boltzmann equation, Jacobian of the

transformation in phase space, Effect of particle interactions, Relaxation model for the collision

term, BBGKY theory- the Vlasov Equation, Correction to Vlasov Equation, Effect of particle

interaction, Relativistic form of Vlasov equation, Moment Equations, Plasma oscillations and

Landau damping.

Unit II:

Waves in Plasmas: The wave equation, Solution in Plane waves, Harmonic waves,

Polarisation, Energy flow, Wave packets and group velocity, Electron Plasma waves, Ion waves,

Electrostatic Electron Oscillations Perpendicular to B, Electrostatic Ion Waves perpendicular to

B, The Lower Hybrid Frequency, Electromagnetic waves perpendicular to B0 = 0,

Electromagnetic waves perpendicular to finite B0, Cut offs and resonances, Electromagnetic

waves parallel to finite B0, Magneto-sonic waves, Magneto hydrodynamic waves (Alfven

waves, sound waves, Magnetosonic waves).

Unit III:

Equilibrium and stability: Introduction, Hydromagnetic Equilibrium, The Concept of β,

Classification of Instabilities, Two-stream instability, The Gravitational Instability, Resistive

Drift Waves, The Weibel Instability.

Nonlinear effects: Sheaths, Ion Acoustic Shock waves, Pondermotive Force, Parametric

instabilities (Coupled Oscillators, frequency matching, Instability threshold, The oscillating two-

stream instability, The parametric decay instability).

Magnetic Confinement: Condition for fusion, The need for magnetic confinement, The

Mirror Machine, Toroidal Confinement, Magnetic Surfaces and Toroidal equilibrium,

Confinement in TOKAMAKs, Theory of TOKAMAK Equilibrium.

Reference Books:

1. The Plasma State by E. J. Hellund , Reinhold Publishing Co., 1961.


Springer, 1974.

3. Fundamentals of Plasma Physics by J. A. Bittencourt, Springer, 2004.

4. Waves in Plasma, T.H.Stix, AIP New York, 1992.

5. Plasma waves, D. G. Swanson, Academic Press, Boston, 1989.

6. Elementary Plasma Physics, L. A. Arzimovich Blaisdell, NewYork,1968.

7. Plasma Physics, J.L.Delcroix, Wiley New York, 1965.

8. Introduction to Plasma Physics BM. Smirov, Mir Publication, Moscow 1977.

9. Hydrodynamics and Hydromagnetic Stability, S. Chandrasekhar, Dover, 1981. PAPER- 4.3

ASTROPARTICLE PHYSICS (SPECIAL )- II


UNIT – I

Basic units in particle physics, Natural Units, Relativistic Kinematics. Time ordered product, Normal

ordered product, Wick’s theorem. The S-matrix expansion, First order terms in S-matrix, Feynman

diagrams in configuration and momentum space, Feynman Rules in QED, Differential cross section

and decay width, Compton Scattering, Bhaba Scattering.

UNIT – II

Classification of weak interactions, V – A form of interaction. Charged Leptonic Weak Interactions,

Decay and lifetime of Muon, Neutron and Pion, Charged Weak Interactions of Quarks, Neutral

Weak Interactions, Cabibbo hypothesis.

UNIT – III

Lagrangian Formulation of Classical Particle Mechanics, Lagrangians in Relativistic Field Theory,

Local Gauge Invariance, Yang-Mills Theory, The Mass Term, Spontaneous Symmetry-Breaking,

The Higgs Mechanism. Brief introduction to the Standard Model (SM) in particle physics. Particle

formation in the early Universe.

Text Books:

1. Particle Kinematics - E. Byckling and K. Kajantie, Wiley, New York, 1973

2. Elementary Particle Physics- D. J. Griffiths

3. Introduction of High Energy Physics- D.H. Perkins

4. Quarks and Leptons - F. Halzen and A. D. Martin

5. Introduction to Quantum Field Theory - Michael E. Peskin and Daniel V. Schroeder

6. A First Book of Quantum Field Theory - Amitabha Lahiri and Palash B. Pal

7. Quantum Field Theory F. Mandl and G. Shaw

Reference Books:

1. Review of Particle Physics”, Particle Data Group, available on the website http://pdg.lbl.gov

2. Concept of Particle Physics - V. Weisskopf G.K. Gottfried

3. Particles and Nuclei - Bogdan Povh, Klaus Rith, Christoph Schloz and FranK

1. Zetsche

4. Quantum Field Theory - Lewis H. Ryder

5. The Quantum Theory of Fields - Steven Weinberg

6. Quantum Field Theory - Claude Itzykson and Jean-Bernard Zuber

PAPER-4.4

PROJECT AND SEMINAR F.M. – 50 CP-4

PAPER-4.5

PRACTICAL ELECTRONICS (SPECIAL)

F.M. – 100 CP-4 Time : 6 Hrs

1. Study of characteristics of operational amplifier. (inverting, non inverting, scale changing, unity

follower; summing and difference op AMP)

2. Study of characteristics of diac.

3. Study of feedback amplifier.

4. Study of given multivibrator, multi-stage (ERC) coupled amplifier.

5. Study of Multiplexer and verification of Truth Table.

6. Study of De-multiplexer and Truth Table.

7. Study of truth tables different types of flipflop circuit

8. Study of input and output impedance of an amplifier

9. Study of characteristics of optoelectronic devices. (Phototransitor, Photodetector, Photovalatic

cell and opto couples)

10. Study of chipping and clamping circuits.

11. Study of wave shape (frequency) of op-AMP based Wien Bridge oscillator.

12. Study of voltage regulation by Zener Diode

13. Study of Quality factor of the given coil.

14. Study of Gain and bandwidth of R-C coupled amplifier with varied load.

15. Calibration of electronic voltmeter for A.C. and D.C.

16. Study of characteristic of class A and AB amplifier.

17. Study of characteristic of given triac.

18. Study of wave forms (and frequency) of blocking oscillator

19. Study of FET characteristics.

20. Verification of Truth Table of different Logic gates (AND, OR, NOT, NAND, NOR)

21. Verification of Truth Table of Half Adder and Full Adder

22. Verification of Truth Tables of Half and Full Subtractor.

PAPER-4.5

PRACTICAL PLASMA PHYSICS (SPECIAL)

F.M.- 100 CP-4 ` Time : 6 Hrs.

1. Determination of critical spark length and verification of Paschen’s law

2. Measurement of Ion density of Plasma by using a single probe.

3. Study of hall-effect in plasma

4. Measurement of electron, temp, of plasma using double probe.

5. Measurement of electron density of a moving plasma

6. Measurement of electrons density of plasma using single probe.

7. Measurement of Ion density of Plasma using double probe.

8. Study of Arc plasma parameters using single moving probe.

9. Measurement of collision cross section of electrons in plasma

10. Use of a Rogoswki coil.

PAPER-4.5

PRACTICAL ASTROPARTICLE PHYSICS (SPECIAL)

F.M.- 100 CP-4 ` Time : 6 Hrs.

1 Gamma Ray Spectrometer

2 GM Counter: Measurement of thickness and attenuation parameter using different types

of sources.

3 Electron Spin Resonance

4-7 Study of four scattering processes using simulation experiments.

8-10 Study of decay by using Hijing software.

11-12 Analysis of stellar spectrum using Glass Spectrograph.

13 Visit to Ion Beam Laboratory and Scattering Laboratory any research institute.

14 Measurement of density and temperature of given plasma using single probe.

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