IIS University - International College for Girls - ICG Courses

M.Sc. (Physics)

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Duration: 2 Years

Eligibility: Graduation

Course Structure

Course Code	Course Title
Semester – I
PHY 121	Classical Mechanics
PHY 122	Mathematical Methods in Physics
PHY 123	Quantum Mechanics
PHY 124	Electronics
PHY 125	Physics Practical
Semester - II
PHY 221	Classical Electrodynamics – I
PHY 222	Numerical Methods and Application of Matlab
PHY 223	Atomic and Molecular Physics
PHY 224	Statistical and Solid State Physics
PHY 225	Physics Practical
Semester - III
PHY 321	Classical Electrodynamics – II
PHY 322	Nuclear Physics-I
PHY 323	Advanced Quantum Mechanics
Special Paper- I
PHY 324 (a)	Condensed Matter Physics - I
PHY 324 (b)	Microwave Electronics-I
PHY 325	Physics Practical
Semester - IV
PHY 421	Solid State Physics
PHY 422	Nuclear Physics-II
PHY 423	Introductory Quantum Field Theory
Special Paper- II
PHY 424 (a)	Condensed Matter Physics – II
PHY 424(b)	Microwave Electronics-II

 

Course Syllabus

Semester - I

PHY 121  Classical Mechanics

Unit I

Holonomic and non-holonomic constraints: D-Alembert's Principle, Generalized coordinates, Lagrangian, Lagrange's equation and its applications, Velocity dependent potential in Lagrangian formulation, Generalized momentum, Legendre transformation, Hamiltonian, Hamilton's canonical equations.

Unit II

Calculus of variation and its application to simple problems: Hamilton's variational principle, Derivation of Lagrange's and Hamilton’s canonical equation from Hamilton’s variational principle. Extension of Hamilton’s Principle for nonconservative and nonholonomic systems. Method of Lagrange's multipliers.

Unit III

Conservation principle and Noether's theorem, Conservation of energy, linear momentum and angular momentum as a consequence of homogeneity of time and space and isotropy of space respectively.

Unit IV

Canonical transformation, integral invariants of poincare: Lagrange's and Poisson’s brackets as canonical invariants, equation of motion in Poisson bracket formulation, Infinitesimal canonical transformation and generators of symmetry, Liouville's theorem, Hamilton Jacobi equation and its applications.

Unit V

Action angle variable: adiabatic invariance of action variable , The Kepler problem in action angle variables, theory of small oscillations in Lagrangian formulation, normal coordinates and its applications,Orthgonal transformation, Eulerian angles, Euler’s theorem, Eigen values of the inertia tensor, Euler’s equations. Force free motion of a rigid body. 

 

PHY 122  Mathematical Methods in Physics

Unit I

Coordinate transformation in N-dimensional space: Contravariant and covariant tensor, Jacobian , pseudo tensors (Example: charge density, angu1ar momentum) Algebra of tensors, Metric tensors, Associated tensors, Riemannian space (Example: Euclidian space and 4-D Minkowski space), Christoffel symbols, transformation of Christoffel symbols.

Unit II

Covariant differentiation, Ricci's theorem, Divergence, Curl and Laplacian in tensor form,  Stress and Strain tensors, Hooke's law in tensor form, Lorentz Covariance of Maxwell equation.

Unit III

Group of transformations, (Example: symmetry transformations of a square), Generators of a finite group, Normal subgroup, Direct product of groups, Isomorphism and Homomorphism, Representation theory of finite groups, Invariant subspace and reducible representations, irreducible representations, Crystallo-graphic point groups, Irreducible representation of C4ν, Translation group and the reciprocal lattice.

Unit IV

Fourier Transforms: Development of the Fourier integral from the Fourier series, Fourier and inverse Fourier transform: Simple applications: Finite wave train, wave train  with Gaussian amplitude, Fourier transform of Derivatives, Solution of wave equation as an application, Convolution theorem, intensity in terms of spectral density for quasimonochromatic EM waves, momentum representation, Application of Fourier Transform to Diffraction Theory, Diffraction pattern of single and double slits.

Unit V

Laplace transforms and their properties, Laplace transform of derivatives and integrals of Laplace transform, Laplace convolution theorem, Impulsive function , Application of Laplace transform in solving linear differential equations with constant coefficient, with variable coefficient and linear partial differential equation.

 

PHY 123  Quantum Mechanics

Unit I

• States, Amplitude and Operators: States of a quantum mechanical system, representation of quantum-mechanical states, properties of quantum mechanical amplitude, operators and change of a state, a complete set of basis states, products of  linear operators, language of quantum mechanics, postulates, essential definitions and commutation relations.
• Observables and Description of Quantum system: Process of measurement, expectation values, time dependence of quantum mechanical amplitude, observable with no classical analogue, spin dependence of quantum mechanical amplitude on position, the wave function, super position of amplitudes, identical particles.

Unit II

Hamiltonian matrix and the time evolution of Quantum mechanical States:

Hermiticity of the Hamiltonian matrix, time independent perturbation of an arbitrary system, simple matrix examples of time independent perturbation, energy eigen states of a two state system, diagonalizing of energy matrix, time independent perturbation of two state system, the perturbation solution: weak field and strong field cases, general description of two state system, Pauli matrices, Ammonia molecule as an example of two state system.

Unit III

• Transition between stationary States: Transitions in a two state system, time dependent perturbations, The Golden Rule, phase space, emission and absorption of radiation, induced dipole transition and spontaneous emission of radiation energy width of a quasi stationary state.
• The co-ordinate Representation: Compatible observables, quantum conditions and uncertainty relation, Coordinate representation of operators, position, momentum and angular momentum, time dependence of expectation values, The Ehernfest Theorem, the time evolution of wave function, the Schrödinger equation, energy quantization, periodic potential as an example.

Unit IV

Symmetries: Compatible observables and constants of motion, symmetry transformation and conservation laws, invariance under space and time translations and space rotation and conservation of momentum, energy and angular momentum.

Unit V

Angular momentum : Angular momentum operators and their Eigen values, matrix representations of the angular momentum operators and their eigenstates, coordinate representations of the orbital angular momentum operators and their eigen states (Spherical Harmonics), composition of angular momenta, Clebsch-Gordon Coefficients, tensor operators and Wigner Eck art theorem, commutation relations of Jx, Jy, Jz with reduced tensor operator, matrix elements of vector operators, time reversal invariance and vanishing of static electric dipole moment of stationary state.

 

PHY 124  Electronics

Unit I

Operational Amplifiers: Differential amplifier, circuit configurations , dual input, balanced output differential amplifier, DC analysis , AC analysis, inverting and non inverting inputs, CMRR, constant current bias level translator. Block diagram of typical OP-Amp analysis, Open loop configuration, inverting and non-inverting amplifiers, Op-Amp with negative feedback, voltage series feedback, effect of feed back on closed loop gain, input resistance, bandwidth and output offset voltage - voltage follower, Practical Op-Amp input offset voltage, input bias current , input offset current, total output offset voltage, CMRR frequency response, DC and AC amplifier, integrator and differentiator.

Unit II

Oscillators and wave shaping Circuits: Oscillator Principle - Oscillator types, Frequency stability response, the phase shift oscillator, Wein bridge oscillator, LC tunable oscillators.

Multivibrators: Monostable and Astable multivibrators, Comparators, Square wave and triangle wave generation, clamping and clipping.

Unit III

Voltage regulators: Fixed regulators, adjustable voltage regulators, switching regulators.

Digital Electronics: Combinational logic: Transistor as a switch, circuit realization of OR, AND, OR, NOR, NAND gates, Exclusive OR gate, Boolean algebra , De- Morgan Theorems, Adder, subtractor, comparator, decoder, demultiplexer , data selector, multiplexer, encoder.

Unit IV

Sequential Logic: Flip-Flops, one - bit memory, RS flip-flop, J flip flop, JK master slave flip-flop, T flip-flop, D flipflop, shift registers , synchronous and asynchronous counters,cascade counters, Binary counter, Decade counter.

Unit V

Microprocessors:

Introduction to microcomputers: memory , input/output , interfacing device 8085, CPU Architecture, BUS timings, Demultiplexing the address bus, generating control signals , Instruction set , addressing modes , Illustrative programmes , writing Assembly language programmes, looping, counting and indexing , counters and timing delays, stack and subroutine.

 

PHY 125   Physics Practical

Note: The students will be required to perform 8 experiments in each semester:

• To study regulated power supply, using (A) Zener diode only (B) Zener diods with a series transistor (C) Zener diode with a shunt transistor.
• To study the percentage regulations and variation of Ripple factor, with load for a full wave rectifier.
• To study analog to digital and digital to analog conversion.
• To study a driven mechanical oscillator.
• Study the simulated L.C.R. Transmission line (audio frequency) and to find out the value for Zo experimentally from the graph.
• To study Compton scattering of gamma rays and verify the energy shift formula.
• To determine ultrasonic velocity and to obtain compressibility for a given liquid.
• To design a RC coupled two stage amplifier of a given gain and the cutoff frequencies.
• To study Hartley oscillator.
• To Study Transistor bias Stability.
• To design a Multivibrator of given frequency and study its wave shape.
• To study the characteristics of FET and use it to design a relaxation oscillator.
• To study the characteristics of a UJT and use it to design a relaxation oscillator and measure its frequency.
• To study the addition, integration and differentiation properties of an operational amplifier.

 

Semester - II

PHY 221  Classical Electrodynamics – I

Unit I

Electrostatics: Electric field, Gauss Law, Differential form of Gaussian law. Another equation of electrostatics and the scalar potential, surface distribution of charges and dipoles and discontinuities in the electric field and potential, Poisson and Laplace equations, Green's Theorem, Uniqueness of the solution with the Dirichlet or Neumann boundary conditions, Formal solutions of electrostatic boundary value problem with Green's function, Electrostatic potential energy and energy density, capacitance.

Unit II

Boundary Value Problems in Electrostatics: Methods of Images, Point charge in the presence of a grounded conducting sphere, point charge in the presence of a charged insulated conducting sphere, point charge near a conducting sphere at a fixed potential, conducting sphere in a uniform electric field by method of images, Green function for the sphere, General solution for the potential, conducting sphere with hemispheres at different potentials, orthogonal functions and expansion.

Unit III

Multipoles, Electrostatics of Macroscopic Media, Dielectrics: Multipole expansion, multipole expansion of the energy of a charge distribution in an external field, elementary treatment of electrostatics with permeable media. Boundary value problems with dielectrics, molar polarizability and electric susceptibility, models for molecular polarizability, electrostatic energy in dielectric media.

Unit IV

Magnetostatics: Introduction and definition, Biot and Savart Law, the differential equation of magnetostatics and Ampere's law, Vector potential and magnetic induction for a current loop, magnetic fields of a localized current distribution, magnetic moment, force and torque on and energy of a localized current distribution in an external magnetic induction, macroscopic equations, boundary conditions on B and H, methods of solving Boundary value Problems in magnetostatics, uniformly magnetized sphere, magnetized sphere in an external field, permanent magnets, magnetic shielding, spherical shell of permeable material in a uniform field.

Unit V

Time varying fields, Maxwell's equations ,conservation laws, energy in a magnetic field, vector and scalar potentials, Gauge transformations, Lorentz gauge, Coloumb gauge, Green function for the wave equation, derivation of the equations of macroscopic electromagnetism, Poynting's theorem and conservation of energy and momentum for a system of charged particles and EM fields, conservation laws for macroscopic media, electromagnetic field tensor, transformation of four potentials and four currents, tensor description of Maxwell's equations.

 

PHY 222   Numerical Methods and Application of Matlab

Unit I

• Errors in Numerical Analysis: Source of Errors, Round off error, Arithmetic error, error analysis, Condition and stability, Approximation, Functional and Error analysis, method of undetermined coefficients, use of interpolation formula, iterated interpolation, inverse interpolation, Hermite interpolation and Spline interpolation,
• Solution of Linear equations : Direct and Iterative methods, Calculation of eigen values and eigen vectors for symmetric matrices.

Unit II

• Solution of Nonlinear equation: Bisection method, Newton's method, modified Newton's method, method of iteration, Newton’s method for the case of complex roots.
• Integration of a function: Trapezoidal and Simpson's rules. Gaussian quadrature formula, Singular integrals, Double integration.

Unit III

Integration of Ordinary differential equation: Predictor-corrector methods, Runga- Kutta method. Simultaneous and Higher order equations. Numerical integration and differentiation of Data, Least- Squares Approximations, Fast Fourier Transformation.

Unit IV

Curve fitting using MATLAB: Least square line, Methods of curve fitting, Interpolation by Spline functions, Fourier series and trigonometric polynomials, Bezier curve

Unit V

Numerical Integration using MATLAB: Introduction to Quadrature, Composite trapezoidal and Simpson’s Rule, Recursive rules, Adaptive Quadrature, Gauss- Legendre Integration

 

PHY 223  Atomic and Molecular Physics

Unit I

Hydrogen Atom : Gross structure energy spectrum, probability distribution of radial and angular (l=1,2) wave functions (no derivation), effect of spin, relativistic correction to energy levels and fine structure, magnetic dipole interaction and hyperfine structure, the Lamb shift (only qualitative description).

Unit II

Interaction with External Fields : Non degenerate first order stationary perturbation method, atom in a weak uniform external electric field and first and second order Stark effect, calculation of the polarizability of the ground state of H-atom and of an isotropic harmonic oscillator, degenerate stationary perturbation theory, Linear Stark ffect for H-atom levels, inclusion of spin-orbit and weak magnetic field, Zeeman effect, strong magnetic field and calculation of interaction energy.

Unit III

Systems with Identical Particles : Indistinguishability and exchange symmetry, many particle wave functions and Pauli's exclusion principle, spectroscopic terms for atoms. The Helium atom, Variational method and its use in the calculation of ground state and excited state energy, Helium atom.

Unit IV

The Hydrogen molecule: Hitler-London method for H2 molecule, WKB method for one dimensional problem, application to bound states (Bohr Sommerfield quantization) and the barrier penetration (alpha decay problems).

Unit V

Spectroscopy (Qualitative) : General features of the spectra of one and two electron systems, singlet, doublet and triplet characters of emission spectra, general features of alkali spectra, rotation and vibration band spectrum of a molecule, PQ and R branches, Raman spectra for rotational and vibrational transitions, comparison with infra red spectra, general features of electronic spectra, Frank and Condon's principle.

 

PHY 224   Statistical and Solid State Physics

Unit I

Basic Principles, Canonical and Grand Canonical ensembles : Concept of statistical distribution, phase space, density of states ,Liouville's theorem, systems and ensemble, entropy in statistical mechanics, Connection between thermodynamic and statistical quantities, micro canonical ensemble, equation of state, specific heat and entropy of a perfect gas using microcanonical ensemble. Canonical ensemble, thermodynamic functions for the canonical ensemble, calculation of mean value, energy fluctuation in a gas, grand canonical ensemble, thermodynamic functions for the grand canonical ensemble, density fluctuations.

Unit II

Partition functions and Statistics : Partition functions and properties, partition function for an ideal gas and calculation of thermodynamic quantities, Gibbs Paradox, validity of classical approximation, determination of translational, rotational and vibration contributions to the partition function of an ideal diatomic gas. Specific heat of a diatomic gas, ortho and para hydrogen.

Unit III

Identical particles and symmetry requirement, difficulties with Maxwell-Boltzmann statistics, quantum distribution functions, Bose Einstein and Fermi-Dirac statistics and Planck's formula, Bose Einstein condensation, liquid He4 as a Boson system, quantization of harmonic oscillator and creation and annihilation of phonon operators, quantization of fermion operators.

Unit IV

Theory of Metals : Fermi-Dirac distribution function, density of states, temperature dependence of Fermi energy, specific heat, use of Fermi-Dirac statistics in the calculation of thermal conductivity and electrical conductivity, Drude theory of light, absorption in metals.

Unit V

Band Theory: Bloch theorem, Kroning Penny model, effective mass of electrons, Wigner-Seitz approximation, NFE model, tight binding method and calculation of density for a band in simple cubic lattice, pseudo potential method.

 

PHY 225  Physics Practical

Note: The students will be required to perform 8 experiments in each semester: 

• To verify Hartmann's formula using constant deviation spectrograph.
• To find e/m of electron using Zeeman effect.
• To find out dissociation energy of I2.
• Salt Analysis/Raman Effect (Atomic)
• To verify Fresnel's formula.
• Curve fitting using MATLAB.
• Numerical integration (Simpson’s rule) using MATLAB.
• Numerical integration (Trapezoidal rule) using MATLAB.
• Verification of Bragg's law using microwaves.
• To study the dynamics of a lattice using electrical analog.
• To study ESR and determine g-factor for a given spectrum.
• Michelson Interferometer.

 

Semester - III

PHY 321  Classical Electrodynamics – II

Unit I

Plane Electromagnetic Waves and Wave Equation: Plane wave in a nonconducting medium. Frequency dispersion characteristics of dielectrics, conductors and plasma, waves in a conducting or dissipative medium, superposition of waves in one dimension, group velocity, causalty, connection between D and E, Kramers- Kroning relation.

Unit II

Magneto hydrodynamics and Plasma Physics : Introduction and definitions, MHD equations, Magnetic diffusion, viscosity and pressure, Pinch effect, instabilities in pinched plasma column, Magneto hydrodynamics wave, Plasma oscillations, short wave length limit of plasma oscillations and Debye shielding distance.

Unit III

• Covariant Form of Electrodynamic Equations: Mathematical properties of the space-time special relativity, Invariance of electric charge, covariance of electrodynamics, Transformation of electromagnetic field.
• Thomson scattering and radiation, Scattering by quasi-free charges, coherent and incoherent scattering, Cherenkov radiation.

Unit IV

Radiation by moving charges: Lienard-Wiechert Potential for a point charge, Total  power radiated by an accelerated charge, Larmour's formula and its relativistic generalization, Angular distribution of radiation emitted by an accelerated charge, Radiation emitted by a charge in arbitrary extremely relativistic motion. Distribution of frequency and angle of energy radiated by accelerated charges.

Unit V

Radiation damping: Self fields of a particle, scattering and absorption of radiation by a bound system, Introductory considerations, Radiative reaction force from conservation of energy, Abraham Lorentz evaluation of the self force, difficulties with Abraham Lorentz model, Integro-differential equation of motion including radiation damping, Line Breadth and level shift of an oscillator, Scattering and absorption of radiation by an oscillator, Energy transfer to a harmonically bound charge.

 

PHY 322  Nuclear Physics-I

Unit I

Two Nucleon system and Nuclear forces : General nature of the force between nucleons, saturation of nuclear forces, charge independence and spin dependence, General forms of two nucleon interaction, Central, non-central and velocity dependent potential, Analysis of the ground state (3S1) of deuteron using a square well potential, range-depth relationship, excited states of deuteron, Discussion of the ground state of deuteron under non-central force, calculation of the electric quadrupole and magnetic dipole moments and the D-state admixture.

Unit II

Nucleon-Nucleon Scattering and Potentials : Partial wave analysis of the neutronproton scattering at low energy assuming central potential with square well shape, concept of scattering length, coherent scattering of neutrons by protons in (ortho and para), hydrogen molecule, conclusions of these analysis regarding scattering lengths, range and depth of the potential, the effective range theory (in neutron-proton scattering) and the shape independence of nuclear potential, the effective range theory (in neutron-proton scattering) and the shape independence of nuclear potential.

Unit III

Effective range theory and the shape independence of nuclear potential: effective range theory (in neutron-proton scattering) and the shape independen ce of nuclear potential, A qualitative discussion of proton-proton scattering at low energy, General  features of two-body scattering at high energy effect of exchange forces. Phenomenological Hamada-Johnston hard core potential and Reid hard core and soft core potentials, Main features of the One Boson Exchange Potentials (OBEP) (no derivation).

Unit IV

Interaction of radiation and charged particle with matter (No derivation) : Law  of absorption and attenuation coefficient, photoelectric effect, Compton scattering, pair production; Klein-Nishijima cross-sections for polarized and unpolarized radiation, angular distribution of scattered photon and electrons, Energy loss of charged particles due to ionization, Bremstrahlung energy target and projectile dependence of all three processes, Range-energy curves, Straggling.

Unit V

Experimental Techniques : Gas filled counters, Scintillation counter, Cerenkov counters, Solid state detectors, Surface barrier detectors, Electronic circuits used with typical nuclear detector, Multiwire proportion chambers, Nuclear emulsions, techniques of measurement and analysis of tracks; Proton synchrotron, Linear accelerators, Acceleration of heavy ions.

 

PHY 323  Advanced Quantum Mechanics

Unit I

Scattering (non-relativistic): Differential and total scattering cross section, transformation from CM frame to Lab frame, solution of scattering problem by the method of partial wave analysis, expansion of a plane wave into a spherical wave and scattering amplitude, the optical theorem, Applications: scattering from a delta potential, square well potential and the hard sphere scattering of identical particles, energy depen dence and resonance scattering, Breit-Wigner formula, quasi stationary states, Lippman-Schwinger equation and the Green's functions approach for scattering problem, Born approximation and its validity for scattering problem, Coulomb scattering problem under first Born approximation in elastic scattering.

Unit II

Relativistic Formulation and Dirac Equation: Attempt for relativistic formulation of quantum theory, The Klein-Gordon equation, Probability density and probability current density, solution of free particle KG equation in momentum representation, interpretation of negative probability density and negative energy solutions.

Unit III

Dirac equation for a free particle: Properties of Dirac matrices and algebra of gamma matrices, non-relativistic correspondence of the Pauli equation (inclusive of electromagnetic interaction), Solution of free particle Dirac equation, orthogonality and completeness, relations for Dirac spinors, interpretation of negative energy solution

Unit IV

Symmetries of Dirac Equation : Lorentz covariance of Dirac equation, proof of covariance and derivation of Lorentz boost and rotation matrices for Dirac spinors, Projection operators involving four momentum and spin, Parity (P), charge conjugation (C), time reversal (T) and CPT operators for Dirac spinors, Billinear covariants, and their transformations, behaviour under Lorentz transformation, P,C,T and CPT, expectation values of coordinate and velocity involving only positive energy solutions and the associated problems, inclusion of negative energy solution, Zitter bewegung, Klein paradox.

Unit V

Quantum Theory of Radiation : Classical radiation field, transversality condition, Fourier decomposition and radiation oscillators, Quantization of radiation oscillator, creation, annihilation and number operators, photon states, photon as a quantum mechanical excitations of the radiation field, fluctuations and the uncertainty relation, validity of the classical description, matrix element for emission and absorption, spontaneous emission in the dipole approximation, Rayleigh scattering. Thomson scattering and the Raman effect, Radiation damping and Resonance fluorescence. 

Special Paper- I

PHY 324 (a)  Condensed Matter Physics - I

Unit-I

Structure Factor: Static structure factor and its relation with the pair correlation function. Determination of structure factor by X-ray and neutron scattering, inelastic neutron scattering and dynamic structure factor, space time correlation function and its relation with dynamic structure factor, properties of space time correlation function, Langevin's equation for Brownian motion and its modifications, velocity autocorrelation function, mean square displacement, Relation between velocity autocorrelation function and diffusion coefficient.

Unit-II

Liquid Metals: Metallic interactions,Kinetic energy, electrostatic exchange and correlation, Pseudopotential formalism, diffraction model, structure factor, form factor for local and non-local potentials, energy eigen states, dielectric screening. Energy wave number characteristics, calculation of phonon dispersion of liquid metals, Band structure energy in momentum and direct space, Ziman's resistivity formula, Green function  method for energy bands in liquid metals.

Unit-III

Quantum Liquids : Distinction between classical and quantum liquids, criteria for freezing, phase diagram of He4, He I and He II Tisza's two fluid model, entropy filter, Fountain effect, superfluid film vehicle, Viscosity and specific heat of He4, first sound, second sound, third sound and fourth sound, Landau theory: Rotons and Phonons, t-matrix theory of superfluid He, Basic differences in superfluidity of He3 and He4.

Unit IV

Exotic Solids : Structure and symmetries of liquids, liquid crystals and amorphous solids. Aperiodic solids and quasicrystals; Fibonanccy sequency, Penrose lattices and their extension to 3-dimensions, Special carbon solids.

Unit V

Fullerences and tubules; Formation and characterization of fullerences and tubules. Single wall and multivwall carbon tubules. Electronic properties of tubules. Carbon  nanotubule based electronic based devices Definition and properties of nanostructured materials. Methods of synthesis of nanostructured materials. Special experimental techniques for characterization of nanostructured materials. Quantum size effect and its applications.

 

PHY 324 (b)   Microwave Electronics-I

Unit-I

Introduction to microwaves and its frequency spectrum, Application of

microwaves.

• Rectangular wave guides: Wave equation & its solutions, TE & TM modes. Dominant mode and choice of wave guide dimensions, methods of excitation of waveguides.
• Circular wave guide-wave equation & it solutions, TE, TM & TEM modes.
• Attenuation - Cause of attenuation in wave guides, wall current. & derivation of attenuation constant, Q of the wave guide.

Unit-II

• Resonators: Resonant Modes of rectangular and cylindrical cavity resonators, Q of the cavity resonators, Excitation techniques, Introduction to Mircostrip and Dielectric resonators, Frequency meter.
• Ferrites: Microwave propagation in ferrites, Faraday rotation, Devices employing Faraday rotation (isolator, Gyrator, Circulator). Introduction to single crystal ferromagnetic resonators, YIG tuned solid state resonators.

Unit-III

Microwave tubes: Space charge spreading of an electron beam, Beam focusing. Klystrons: Velocity Modulation, Two Cavity Klystron, Reflex Klystron, Efficiency of Klystrons.

Unit-IV

• Magnetrons: Types & description, theoretical relations between Electric & Magnetic field of oscillations, Modes of oscillations & operating characteristics,
• Traveling wave tubes: O & M type traveling wave tubes. Gyrotrons: Constructions of different Gyrotrons, Field - Particle Interaction in Gyrotron.

Unit-V

Microwave Measurement:

• Microwave Detectors: Power, Frequency, Attenuation, Impedance Using smith chart, VSWR, Reflectometer, and Directivity Coupling using direction coupler.
• Complex permittivity of material & its measurement: definition of complex permittivity,determination of permittivity of solids, liquids and powders using shift in minima method.

 

PHY 325   Physics Practical

Note: The students will be required to perform 8 experiments in each semester:

• To determine half-life of a radio isotope using GM counter.
• To study characteristics of a GM counter and to study statistical nature of radioactive decay.
• To study spectrum of β- particles using Gamma ray spectrometer.
• To calibrate a scintillation spectrometer and determine energy of γ-rays from an unknown source.
• To study absorption of particles and determine range using at least two sources.
• Practical
  
  • To study variation of energy resolution for a Nai (Tp) detector.
  • To determine attenuation coefficient (u) for rays from a given sources.
• Study the characteristics of a given Klystron and calculate the mode number, E.T.S. and transit time.
• Study the radiation pattern of a given Pyramidal horn by plotting it on a Polar graph paper. Find the half power beam width and calculate its gain.
• Find the dielectric constant of a given solid (Teflon) for three different lengths by using slotted section.
• Find the dielectric constant of a given liquid (organic) using slotted section of Xband.
• To find Dissociation energy to I.
• Study of a Heat Capacity of Solids.
• Study of lattice dispersion.
• To .stud y temperature variation of resistivity or a semi-conductor and to obtain band gap using four probe method.
• To study hall effect and to determine hall coefficient.
• To study the variation of rigidity of a given specimen as a function of the temperature.
• To study the dynamics of a lattice using electrical analog.

 

Semester - IV

PHY 421  Solid State Physics

Unit I

Lattice Dynamics and Optical Properties of Solids: Interatomic forces and lattice dynamics, simple metals, ionic and covalent crystals, optical phonons and dielectric constants, inelastic neutron scattering, Mossbauer effect. Debye-Waller factor, Anharmonicity, thermal expansion and thermal conductivity, Interaction of electrons and phonons with photons, Direct and indirect transitions, Absorption in insulators, Polarities, one-phonon absorption, optical properties of metals, skin effect and anomalous skin effect.

Unit II

Semiconductors: Law of mass action, calculation of impurity conductivity, ellipsoidal energy surfaces in Si and Ge, Hall Effect, recombination mechanism, optical transitions and Schockely-Read theory, excitations, photoconductivity, photoluminescence. Point’s line, planar and bulk defects, colour centres, F-centre and aggregate centres in alkali halides.

Unit III

Magnetism: Larmor diamagnetism. Paramagnetism, Curie-Langevin and Quantum  theories, Susceptibility of rare earth and transition metals, Ferromagnetism: Domain theory, Weiss molecular field and exchange, spin waves: dispersion relation and its experimental determination by inelastic neutrons scattering, heat capacity. Nuclear Magnetic resonance: Conditions of resonance, Bloch equations, NMR- experiment and characteristics of an absorption line.

Unit IV

Superconductivity : Experimental Results : Meissner effect, heat capacity, microwave and infrared properties, isotope effect, flux quantization, ultrasonic attenuation, density of states, nuclear spin relaxation, Giaver and AC and DC Josephson tunnelings.

Unit V

Cooper pairs and derivation of BCS Hamiltonian, results of BCS Theory (no derivation), High Tc superconductivity, introduction to theories of High Tc superconductors.

 

PHY 422   Nuclear Physics-II

Unit I

Nuclear Shell Model : Single particle and collective motions in nuclei, Assumptions and justification of the shell model, average shell potential, spin orbit coupling, single particle wave functions and level sequence, magic numbers, shell model predictions for ground state parity, angular momentum, magnetic dipole and electric quadrupole moments, and their comparisons with experimental data, configuration mixing, single particle transition probability according to the shell model, selection rules, approximate estimates for the transition probability and Weiss Kopf units, Nuclear isomerism.

Unit II

Collective Nuclear Models : Collective variable to describe the cooperative modes of nuclear motion, Parameterization of nuclear surface, A brief description of the  collective model Hamiltonian (in the quadratic approximation), Vibrational modes of a spherical nucleus, Collective modes of a deformed even-even nucleus and moments of inertia, Collective spectra and electromagnetic transition in even nuclei and comparison with experimental data, Nelson model for the single particle states in deformed nuclei.

Unit III

Nuclear Gamma and Beta decay: Electric and magnetic multipole moments and gamma decay probabilities in nuclear systems (no derivations), Reduced transition probability, Selection rules, Internal conversion and zero-zero transition.

Unit IV

General characteristics of weak interaction: nuclear beta decay and lepton capture, electron energy spectrum and Fermi-Curie plot, Fermi theory of beta decay (parity conserved selection rules Fermi and Gamow-Teller) for allowed transitions, ft-values, General interaction Hamiltonian for beta decay with parity conserving and non conserving terms; Forbidden transitions, Experimental verification of parity violation,  The V-A interaction and experimental verification.

Unit V

Nuclear Reactions: Theories of Nuclear Reactions, Partial wave analysis of reaction Cross section, Compound nucleus formation and breakup, Resonance scattering and reaction-Breit-Wigner dispersion formula for s-waves (1 = 0), continuum cross section, Statistical theory of nuclear reactions, evaporation probability and cross section for specific reactions, The optical model, Strapping and pick-up reactions and their simple theoretical description (Butler theory) using plane wave Born approximation (PWBA), Shortcomings of PWBA, Nuclear structure studies with deuteron strapping (d, p) reactions.

 

PHY 423  Introductory Quantum Field Theory

Unit I

Scalar and Vector fields, Classical Lagrangian field theory, Euler Lagrange's equation, Lagrangian density for electromagnetic field. Occupation number representation for simple harmonic oscillator, linear array of coupled oscillators.

Unit II

Second quantization of identical bosons, second quantization of the real Klein-Gordon Field and Complex Klein-Gordan field, the meson propagator.

Unit III

The occupation number representation for fermions, second quantization of the Dirac field, the fermion propagator, the em interaction and gauge invariance, covariant quantization of the free electromagnetic field, the photon propagator.

Unit IV

S-matrix, S-matrix expansion, Wick's theorem, Diagrammatic representation in configuration space, the momentum representation, Feynman diagrams of basic processes, Feynman rules of QED.

Unit V

Applications of S-matrix formalism: The Coulomb scattering, Bhabha scattering, Moller scattering, Compton scattering and Pair production.

 

Special Paper- II

(The students will choose the same special paper from (a) & (b) as in III Semester)

PHY 424 (a)  Condensed Matter Physics - II

Unit I

Phase Transformation and Alloys: Equilibrium transformation of first and second order, Equilibrium diagrams, Phase rule, Interpretation of phase diagrams, Substitutional solid solutions, Vegard's law, intermediate phases, Hume-Rothery rules, interstitial phases (carbides, nitrides, hydrides, borides). Martensitic transitions, structure factor of liquid metal alloys, behaviour of s(q), radial distribution function g(r) and relationship between s(q) and g(r)

Unit II

Disordered Systems: Disorder in condensed Matter, Substitutional, positional and topographical disorder, Short and long range order, Spinning, sputtering and ionimplantation techniques, glass Transition, glass formation ability, nucleation and growth processes.

Unit III

Anderson model for random system and electron localization, mobility edge, qualitative application of the idea of amorphous semiconductors and hopping conduction, Metal glasses, Models for structure of metal glasses, Structure factor of binary metallic glasses and its relationship with the radial distribution functions, Discussion of electric, magnetic and mechanical properties of glassy systems.

Unit IV

Structure determination/characterization: Basic theory of X-ray diffraction. Indexing of Debye-Scherer patterns for powder samples, examples from some cubic  cross section, scattering length and structure factor, Mossbauer effect, hyperfine parameters-Isomer shift, quadrupole splitting and Zeeman splitting, Application of Valence and coordination, site symmetry magnetic behaviour, Discussion in context of Fe57.

Unit V

Electronic Structure Determination: Basic principles of X-ray, photo-emission and positron annihilation techniques, qualitative discussion of experimental arrangement and typical results for both simple as well as transition metals.

 

PHY 424(b)  Microwave Electronics-II

Unit I

• Avalanche Transit Time Device: Read Diode, Negative resistance of an avalanching p-n junction diode IMPATT and TRAPATT Oscillator. 
• Transferred Electron Device: Gunn Effect, two valley, model, High field domains domains, Different modes for Microwave generation.

Unit II

Passive Devices : Termination (Short circuit and mathced terminations) Attenuator, Phase changers, E & H plane Tees, Hybride Junctions. Directional coupler.Parametric Amplifier: Varactor, Equation of Capacitance in Linearly graded & Abrupt p-n Junction, Manely Rowe relations, parametric upconvertor and Negative resistance parametric parametric amplifier, use of circulator, Noise in parametric amplifiers.

Unit III

Microwave Antennas: Intrdouction to antenna parameters, Magnetic Currents, Electric and magnetic current sheet, Field of Huygen's source, Radiation from a slot antenna, open end of a wave guide and Electromagnetic Horns. Prabolic reflectors, Lens antennas. Radiation fields of Microstrip wave guide, Microstrip wave guide, Microstrip antenna calculations, Mircrostrip design formulas.

Unit IV

Microwave Communications: Line of sight microwave system, Derivation of LOS communication range, OTH microwave systems, Derivation of fields strength of tropospheric waves, Transmission, interference and signal damping, Duct propagation.

Unit V

Satellite Communication : Satellite orbits, Satellite location with Synchronous satellites, Satellite orbits, Satellite location with respect to earth and looks angle, earth coverage and slant range, Eclipse effect, Link calculation, Noise consideration, Factors Affecting satellite communication.