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Old October 30th, 2014, 05:04 PM
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Join Date: Apr 2013
Default Re: After M.Sc, info about M.Phil Entrance Exam

You are looking for M.Phil Physics entrance exam syllabus, I am giving here:

APER-I: MATHEMATICAL PHYSICS
Unit-I: Vector space and Matrices, Linear independence, Bases,
dimensionality, Inner product, Linear transformation, matrices,
Inverse, Orthogonal and Unitary matrices, Independent element of a
matrix, Eigen values and eigen Vectors, Diagonalization, Complete
orthonormal sets of functions.
Unit-II: Complex Variables: Cauchy- Riemann condition, analytic
functions,Cauchy’s theorem, Cauchy integral formula, Laurent series,
singularities, residue theorem, contour integration, evaluation of
definite integrals, problems.
Unit-III: Differential equations, first order differential equation, second order
differential equation with constant coefficients, second order linear
ODEs with variable coefficients, Solution by series expansion,
nonhomogenous differential equations and solution by the method of
Green’s functions.
Unit-IV: Special functions, Legendre, Bessel, Hermite and Laguerre functions
with their physical applications, generating functions, orthogonality
conditions, recursion relations,
Unit-V: Integral transforms, Fourier integral and transforms, inversion
theorem, Fourier transform of derivatives, convolution theorem,
Laplace Transform(LT), LT of Derivatives, Inverse LT, Fourier series;
properties and applications, discrete Fourier transform.

Unit-I Preliminaries, Newtonian mechanics of one and many particle systems,
Conservation laws,Constraints & their classification, Principle of virtual work,
Generalized coordinates, D’Alembert’s principle and Lagrange’s equations,
Velocity-dependent potentials and dissipation function, Simple applications of
the Lagrangian formulation, Hamilton’s principle, Lagrange’s equations from
Hamilton’s principle, Conservation theorems and Symmetry properties,
Energy function and the conservation of energy.
Unit-II The Hamiltonian formulation of mechanics, Legendre transformations and the
Hamilton’s equations of motion, Cyclic coordinates and Conservation
Theorems, Hamilton’s equations from Hamilton’s principle, The principle of
least action, Simple applications of the Hamiltonian formulation.
Unit-III Canonical transformations with examples, The harmonic oscillator, Poisson’s
brackets, Equations of motion and conservation theorems in the Poisson
Bracket formulation. Hamilton-Jacobi (HJ) theory: The HJ equation for
Hamilton’s principal function, Harmonic oscillator as an example of the HJ
method, The HJ equation for Hamilton’s characteristic function, The actionangle
variables
Unit –IV The Central force: Two-body central force problem and its reduction to the
equivalent one-body problem, The equations of motion and first integrals, The
equivalent one-dimensional problem and classification of orbits, The
differential equation of the orbit, Closure and stability of orbits, The Kepler
problem, Scattering in a central force field: Rutherford scattering.
Unit – V Rigid body dynamics, The Euler angles, Euler’s theorem on the motion of a
rigid body, Rate of change of a vector, The Coriolis force, Angular
momentum and Kinetic energy of motion about a point, The Euler equations
of motion of rigid bodies. Formulation of the problem of small oscillations,
The eigen-value equation and the principal axis transformation, Frequencies
of free vibration and normal coordinates, Free vibration of linear triatomic
molecule.


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Paper-III: ELECTRODYNAMICS & PLASMA PHYSICS
Unit-I Maxwell’s equations, vector and scalar potentials and the wave equation,
Gauge transformations, Lorenz gauge, Coulomb gauge, Green function for
the wave equation, four-vectors, mathematical properties of the spacetime
in special relativity, matrix representation of Lorentz transformation,
covariance of electrodynamics, transformation of electromagnetic fields.
Unit-II Radiation by moving charges, Lienard-Wiechert potential and fields for a
point charge, total power radiated by an accelerated charge- Larmor’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 in frequency and angle of
energy radiated by accelerated charge.
Unit -III Bremsstralung: emission from single-speed electrons, thermal
Bremsstralung emission and absorption, Synchrotron radiation:
spectrum of synchrotron radiation, spectral index for power law electron
distribution, transition from Cyclotron to Synchrotron emission,
Cherenkov radiation
Unit-IV Plasma: definition, Debye shielding phenomenon and criteria for plasma,
motion of charged particles in electromagnetic field; Uniform E & B
fields, Electric field drift, Non-uniform magnetostatic field, Gradient B
drift, Parallel acceleration and magnetic mirror effect, Curvature drift,
adiabatic invariants.
Unit-V Elementary concepts of plasma kinetic theory, the Boltzmann equation,
the basic plasma phenomena, plasma oscillations.
Fundamental equations of magneto-hydrodynamics (MHD),
Hydrodynamics Waves; Magneto sonic and Alfven waves, Magnetic
viscosity and magnetic pressure, plasma confinement schemes.
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