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11th September 2015, 12:41 PM
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Join Date: Mar 2013
Re: Uniraj Msc Syllabus

University of Rajasthan is a public and state university and one of the oldest university in Rajasthan. It was established on 8 January 1947.

University of Rajasthan M. Sc. Physics previous Syllabus

Paper-I : Clasical Mechanics and Mathematical Method in Physics
Paper-II : Classical Electrodynamics
Paper-III: QuantumMechanics,Atomic and Molecular Physics
Paper-IV : Electronics, Numerical Methods and Computer Programming

PAPER - I:

Classical Mechanics and Mathematical Methods in Physics

Max.Marks :100 Duration : 3hrs.

Note:Five qustion are to be set taking one from each unit ( each question will have an internal choice).Student will attempt all the five question 40% weightage will be given to problems and numericals.

Unit - I

Holonomic and nonholonomic constraints: D-Alembert's Principle, Generalized.coordinates,Lagrangian, lagrange's equation and its applications, Velocity dependantotential in Lagaragian formulation.Generalized momentum, Legendre transfomation, Hamiltonian, Hamilton's Canonical equation.
Calculus of variations and its ilpplication to simple problems, Hamilton's variational principle, Derivation of Lagrange's and Hamilton. Canonical equation from Hamiltons variational principle. Extension of Hamilton's Principle for nonconservative and nonholonomic systems. Method of Lagrange's multipliers,

Unit - II

Conservation principle and Noether's theorem. Conservation of energy, linear momentum and angular momentum as a consequence of homogencity of time and scope and isotropy of space respectively.
Canonical transformation, integral in variants of poincare: Lagrange's and Poisson brackets as canonical invariants. Equation of motion in Poisson bracket formulation, Infinitesimal contact transformation and generators of symmetry, Liouville's theorem, Hamilton Jacobi equation and its applications.

Unit - III

Action angle, variable adiabatic invariance of action variable : The Kepler problem in action angle variables,theory of small oscillation in Lagrangian formulation,normal coordinates and its applications,Orthgonal transfonnation,Eulerian angles,Euler theorem, Eigen values of the inertia tensor, Euler equations. Force free motion of a rigid body.
Laplace transforms, and their properties, Laplac transform of derivatives and integrals of laplac transform, Laplace, Convolution theorem,Impulsive function Application of laplace transform in solving liner differential equations with constant coefficient with variable coefficient and liner partial differential equation.

Unit - IV

Fourier Transforms: Development of the Fourier integral from the Fourier seriese, 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, Convoluation theorem, intensity in term of spectral density for quasi-monochromatic EM waves, momentum representation. Application of Hydrogen Atom and Harmonic Oscillator problems. Application of Fourier Transform to Differaction Theory; Diffaction patternof one two slits.

Unit - V

Coordinate transformation in N-dimesional space: Contravriant and covariant tensor, Jacobian. Relative tcnsor, pseudo tensors (Example: change density, angu1ar momentum) Algebra of tensors, Metric theorem, Associated tensors,Reimannian space (Example: Euclidian space and 4-D Mmkowski space), Christoffelas symbols, transformation of Christoffelas symbols,
Covariant differentiation. Ricci's theorem, Divergence, Curl and Laplacian in tensor form. Stress-and Strain tensors. Hook's law in tensor form. Lorentz Covariance of Maxwell equation.

Group of transformations. (Example: symmetry transformation of 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 representation, Crystallo-graphic point groups. Irreducible representation of
C4v Translation group and the reciprocal lattice.

Reference Books:

1. Goldstein - Classical Mechanics.
2. Landau.and Lifshitz - Classical Mechanics.
3. A. Raychoudhary - Classical Mechanics.
4. Mathematical Methods for Physicists: George Arkfen (AcademicPress). .
5. Applied Mathematics for Engineers and Physicists: L. A. Pipe (McGraw Hill)
6. MathematicalMethods-Potter and Goldberg (Prentice Hall of fudia).
7. Elements of Group Theory for Physicists: A. W. Joshi (Wiley Eastern Ltd.)
8. VectorAnalysis (Schaum Series) (Mc Graw Hill).

Contact address

University of Rajasthan
JLN Marg
Jaipur, Rajasthan 302004

Map Location

[MAP]University of Rajasthan[/MAP]


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