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Saturday, January 1, 2011

M.Sc. Physics


M.Sc Physics Entrance Syllabus for admission to P.G.Programme Physics – 2013.

UNIT I
Classical Mechanics: Review of laws of Motion, Components of Velocity and Acceleration in Cartesian Coordinates, Spherical Polar and Cylindrical Coordinates, Inertial & Non-inertial Frames, Uniformly Rotating Frame, Centripetal Acceleration, Coriolis Force and its applications.
Special Theory of Relativity: Reference Systems, Inertial Frames, Galilean Transformation, Conservation Laws, Propagation of light, Michelson-Morley Experiment, Search for ether. Postulates of Special Theory of Relativity, Lorentz Transformation, Length Contraction, Time Dilation, Velocity Addition Theorem, Variation of Mass with Velocity, Mass-Energy Equivalence, Particles with zero rest mass.

UNIT II
Motion in a Central Force Field: Kepler’s Laws and their derivation, Gravitational Law and Field, Potential due to a Spherical Shell, Sphere and Disc.
Systems of Particles: Centre of Mass, Equations of Motion, Conservation of Linear and Angular Momentum, Conservation of Energy, Principle of Rockets and its equation.
Rigid Body Motion: Rotational Motion, Moments of Inertia and their products (Angular Momentum, Torque) Principle Moments and Axes, Euler’s equations.
Elasticity and Small Deformations: Hooke’s Law, Elastic Constants for an Isotropic Solid, Beams supported at both the ends, Cantilever, Torsion of a cylinder, Bending Moments and Shearing Forces.
Kinematics of Moving Fluids : Equations of Continuity (Differential form), Euler’s equations, Bernoulli’s theorem, Viscous Fluids, Streamline and Turbulent Flow, Reynold’s number, Poiseuelle’s equation and its derivation.

UNIT III
Harmonic Oscillations: Differential equation and its solutions, Kinetic and Potential Energy, examples of Simple Harmonic Oscillations, Spring and Mass System, Simple and Compound Pendulum, LC circuit, Oscillations of two Masses connected by a Spring.
Superposition: Superposition of two Mutually Perpendicular Simple Harmonic Vibrations of the Same Frequency, Lissajous figures, Case of Different Frequencies.
ForcedOscillations: Damped Harmonic Oscillator, Power Dissipation, Quality Factor, Driven Harmonic Oscillator, Transient and Steady States.

UNIT IV
Vector Calculus: Scalar and Vector Fields, Triple Vector Product, Gradient of a Scalar Field and its geometrical interpretation, Divergence and Curl of Vector Field, Line, Surface and Volume
integrals, Physical interpretation of Curl and Divergence, Gauss’s Divergence Theorem, Green’s and Stoke’s Theorem.
Integral Calculus: Repeated Integrals of a Function of more than one Variables, Definition of a Double and Triple integral, Evaluation of Double and Triple Integrals as Repeated Integrals.
Electrostatics: Multipole Expansion of E for Distribution of Charge at Rest, Dipole and Quadrupole Fields, Electrostatic Field Energy, Force per unit area on the surface of a conductor in an electric field, Point Charge in front of a Grounded Plane Infinite Conductor.
Dielectrics: Parallel Plate Capacitor with a Dielectric, Dielectric Constant, Polarization and Polarization Vector P, Displacement Vector D, Relation Between E, P & D, Boundary Conditions Satisfied by E and D at the Interface Between Two Homogenous Dielectrics, Illustration Through Simple Examples.

UNIT V
Current Electricity: Steady Current, Current Density J, Non-Steady Currents and Continuity Equation, Rise and Decay of Current in LR and RC circuits, Decay Constants, Transients in LCR Circuits, AC circuits, Complex Numbers and their applications in solving AC circuit problems, Complex Impedance and Reactance, Series and Parallel Resonance, Q factor, Power Consumed by an AC circuit, Power Factor.
Magnetostatics: Multipole Expansion of B, Magnetic Dipole Moment, Biot and Savart’s law, Ampere’s Circuital Law .B = 0, x B = 0 J, Magnetization Current, Magnetization Vector, H Field (magnetizing field), Calculation of H in Simple Geometrical Situations (Hystersis Loop, Rowland ring) Susceptibility and Magnetic Permeability (linear cases).
Electromagnetic Theory: Faraday’s Laws, Integral and Differential Forms, Energy in a Static Magnetic Field, Maxwell’s Displacement Current, Maxwell’s Equations, Electromagnetic Field Energy Density. The wave equation satisfied by E and B, Plane Electromagnetic Waves in Vacuum, Poynting Vector and Theorem, Reflection
and Refraction at a Plane Boundary of Dielectrics.

UNIT VI
Basic concepts in Kinetic Theory of Matter: degrees of freedom, equipartition of energy, specific heat of monatomic gas, extension to di- and tri -atomic gases, behaviour at low temperatures, adiabatic expansion of an ideal gas, application to atmospheric physics.
Transport phenomena in gases : molecular collisions, mean free path and collision cross section, Estimates of molecular diameter and mean free path, transport of mass, momentum and energy and inter-relationship, dependence on temperature and pressure. Vander Waals gas: equation of states, nature of Vander Waals forces, comparison with experimental P-V curves, the critical constants, Joules expansion of ideal gas and of a Vander Waals gas, Joule coefficient, estimates of J-T cooling.
Liquefaction of gases: Boyles temperature and inversion temperature, principle of regenerative cooling and of cascade cooling, liquification of hydrogen and helium, refrigeration cycles, meaning of efficiency.
Review of laws of thermodynamics: Zeroth, Ist. & 2nd laws, concept of thermal equilibrium, internal energy, Carnot theorem. Entropy, Principle of increase of entropy, the thermodynamic scale of temperature, its identity with the perfect gas scale, impossibility of attaining the absolute zero,
third law of thermodynamics.

UNIT VII
Thermodynamic relationships: Thermodynamic variables, extensive and intensive, Maxwell’s general relationship. Clausius-Clapeyron heat equation, thermodynamic potentials and equilibrium of thermodynamical systems, relation with thermodynamical variables. Cooling due to adiabatic demagnetization.
The Statistical basis of thermodynamics: probability and thermodynamic probability, principle of equal a priori probability, probability distribution and its narrowing with increase in number of particles. The expressions for average properties, constraints , accessible and inaccessible states, distribution of particles with a given total energy into discrete set of energy states, microstates and macrostates.
Probability and entropy: Boltzmann entropy relation, Statistical interpretation of the second law of thermodynamics, Boltzmann Canonical distribution law and its application, the rigorous form of equipartition of energy.
Maxwellian distribution of speeds in an ideal gas: distribution of speed and of velocities, experimental verification, distinction between mean, rms and most probable speed values.

UNIT VIII
Waves in media: speed of transverse waves on a uniform string, speed of longitudinal waves in a fluid, energy density and energy transmission in waves, Waves over liquid surface, concept of gravity waves and ripples. Group velocity and phase velocity.
Standing waves: standing waves as normal modes of bounded systems, examples, Production and detection of ultrasonic waves and their applications.
Acoustics: Limits of human audibility, intensity and loudness, bel & decibel, the musical scale, transducers and their characteristics (microphone, piezoelectric system), Reverberation, Sabine’s formula.
General theory of image formation: cardinal-points of an optical system, general relationships, thick lens formula and lens combinations. Lagrange equation of magnification.
Aberration in images: chromatic aberrations, achromatic combination of lenses in contact and separated lenses. monochromatic aberrations and their reductions. aspherical mirrors and Schmidt corrector plates, aplanatic points. Common types of eye pieces: Huygens and Ramsden eye pieces.

UNIT IX
Interference of light: the principle of superposition, two-slit interference, coherence requirement for the sources, optical path retardation. lateral shift of fringes, colours of thin films.
Interferometry: Michelson interferometer, its application for precision determination of wavelength, wavelength difference and width of spectral lines. multiple beam interference, Fabry-Perot interferometer and etalon.
Frensel diffraction: Frensel half-period zones, zone Plate, straight edge, rectilinear propagation.
Fraunhofer diffraction: diffraction at a slit, the intensity distribution .Diffraction at a circular aperture resolution of images, Rayleigh criterion, resolving power of telescopic and microscopic systems.
Diffraction gratings: diffraction at N parallel slits, intensity distribution at an N parallel slits.Plane diffraction grating, resolving power of a grating.
Polarization: Polarization by refraction, Mall’s law, Refraction in Uniaxial crystals. Rotation of plane of polarization, origin of optical rotation in liquids and in crystals.
Laser Systems: Purity of spectral line, coherence length and coherence time,
spatial coherence of a source, Einstein A and B coefficients, Spontaneous and induced emission, conditions of laser action, population inversion simple application laser.

Unit X
Origin of quantum theory: Black body radiation, failure of classical physics to explain (a) UV catastrophe (b) photoelectric effect, Planck’s radiation law.
Wave- particle duality: de-Broglie’s hypothesis of matter wave, the concept of wave packets and group velocities, evidence for diffraction and interference of particles, Davison-Germer Experiment, Heisenberg’s uncertainty relation for p and x, its extension to energy and time, consequences of uncertainty relation to particle in a box.
Schrödinger equation: postulates of quantum mechanics, operators, expectation values, transition probabilities, applications to particle in a one and three dimensional box.
Hydrogen atom, natural occurrence of n, l and m quantum numbers, related physical quantities, comparison with Bohr’s theory.

Unit XI
Atomic Physics: associated magnetic moment, Spin –orbit coupling, quantum number j, spatial quantization, Stern-Gerlach experiment, Pauli’s exclusion principle. Spectra of hydrogen and sodium, spectral terms, doublet fine structure, screening constants for sodium for s, p, d, f states, selection rules. Singlet and triplet fine structure in alkaline earth spectra, LS coupling and J-J coupling., weak and strong field Zeeman effects, Lande g factor, X-ray spectra, Continuous X-ray spectrum, characteristic X-ray, Moseley’s law, X-ray absorption spectra.
Discrete set of electronic energies of molecules: Quantization of vibrational and rotational energies, determination of inter-nuclear distances, pure rotational and rotation-vibration spectra, Dissociation limit for the ground and other electronic states, transition rules for pure vibration and electronic-vibration spectra.
Raman effect: Stokes and anti-Stokes lines, complimentary character of Raman and infrared spectra, experimental arrangements for Raman Spectroscopy.

Unit XII
Structure of Nuclei: Basic properties, (angular momentum, magnetic momentum, quadrupole
moment and binding energy). Deuteron Problem, concept of nuclear forces Beta decay, Parity violation. Range of alpha particles, Gieger-Nuttel law, Gamow’s explanation of alpha decay.
Nuclear Models: shell model, liquid drop model. compound nucleus, fission and fusion, energy production in stars by p-p and carbon nitrogen cycles.
Interaction of particles and detectors: interaction of charged particles and neutrons with matter, working of nuclear detectors, G. M. Counter, Proportional Counter, Cloud Chambers, Spark Chambers, Emulsions.

Unit XIII
Crystal Structure: periodicity, lattice and bases, fundamental translation vectors, unit cell, Wigner-Seitz cell. Laue’s theory of X -ray diffraction, Laue’s theory and Bragg’s law, Laue patterns. allowed rotations, lattice types, lattice planes, Reciprocal lattice.
Bonding: Potential between a pair of atoms, Lennard-Jones potential, concept of cohesive energy, covalent, Vander Waals, ionic and metallic crystals.
Magnetic Properties: Atomic magnetic moment, magnetic susceptibility, Langevin theory of diamagnetism and paramagnetism, ferromagnetism, ferromagnetic domains.
Thermal Properties: Lattice vibrations, vibrations of one dimensional monatomic chain under harmonic and nearest neighbour interaction approximation, concept of phonons, density of modes(1-D),Debye model,lattice specific heat, low temperature limit.
Motion of electrons: quantum mechanical free electron theory. fermi energy, Fermi velocity, Fermi sphere, conductivity and Ohm’s law (explanation on the basis of displacement of fermi sphere).

Unit XIV
Band Structure: electrons in periodic potential, Kronig- Penney model, concept of brillouin zones and explanation to energy bands, energy gap, metals, insulators,and semiconductors.
Semiconductors: intrinsic semiconductors, electrons and holes, Fermi level. temperature dependence of electron and hole concentration. Doping, impurity states, n and p- type semiconductors, conductivity, mobility, Hall effect, Hall coefficient.
Semiconductor device: metal –semiconductor junction, p-n junction, energy level diagrams, majority and minority carriers, Tunnel diode, Light emitting diode(LED),solar cell.
Field effect Transisitor: JFET volt-ampere characteristics, biasing JFET, ac operation of JFET,FET as variable voltage resistor.
MOSFET: Depletion and Enhancement mode MOSFET, biasing MOSFET, digital MOSFET circuits (NAND & NOT gates)

Unit XV
Power supply: Diode as a circuit element ,load line concept, rectification, ripple factor.Zener diode, voltage stabilization. Electronic voltage regulation, characteristics of a transistor in CB, CE, CC mode, graphical analysis of the CE configuration ,Low frequency equivalent circuits, h-parameters, transistor biasing techniques(Voltage divider), bias stability, thermal runaway.
Small signal Amplifiers: General principles of operation, classification, distortion, RC coupled amplifier, gain-frequency response, derivation of gain, input and output impedance at mid-frequencies. Transformer coupled amplifiers, expression of gain at mid-frequency. Emitter follower, determination of gain at low frequencies. Common source JFET amplifier with expression for voltage gain at mid-frequency.
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