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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