PAPER H 301 CLASSICAL MECHANICS, THEORY OF RELATIVITY Total Marks : 60 Pass marks : 12 Group A : Classical Mechanics Const...
PAPER H 301
CLASSICAL MECHANICS, THEORY OF RELATIVITY
Total Marks : 60
Pass marks : 12
Group A : Classical Mechanics
Constraints, Classification of constraints with examples. Generalised coordinates, Generalised velocities and generalized momenta.
Principles of virtual work, D’ Alembert’s principle and its derivation.
Lagrange’s equation for conservative and nonconservative system of forces from D’ Alembert principle. Conception of Lagrangian. Application of Lagrange’s equation for calculation of Lagrangian and derivation of equation of motion for a simple physical system ( Compound pendulum, linear harmonic oscillator).
Motion under central force : Central force and its examples. Reduction of motion of two bodies to the motion of single body by introducing the concept of reduced mass. Lagrangian of aparticle under central force. Differential equation of orbit of a particle under central force, Kepler’s laws planetary motion and its deduction.
Hamiltonian formulation : Concepts of phase space, Principle of variation, Deduction of Hamiltion’s canonical equations from variational principle.Concept of Hamiltonian and its physical interpretation. Deduction of Hamiltion’s principle from D’ Alemberts principle, Basic idea of Hamiltionian in quantum mechanics, Hamiltonian of simple pendulum, compound pendulum. Deduction of Hamiltion’s canonical equations in above cases.
Group B : Special Theory of Relativity
The principle of Gallilian transformation, Transformation of Newton’s Laws, departure from Newtonian relativity, Absolute rest, absolute motion, Concept of ether, Michelson-Morley experiment, negation of ether concept. Einstein’s postulates and Lorentz-Einstein transformation, Derivation of Lorentz transformation equations, Consequence of Lorentz
Transformation--- length contraction, time dilation, life time of cosmic ray muons, twin paradox, simultaneity, velocity addition rule, finite velocity of light, relativistic formula for momentum and energy.
Minkowski diagram, space-time, time-like, space-like and light like intervals, Energy momentum four vector,
PAPER H 302
COMPUTATIONAL PHYSICS
Total Marks : 60 Pass Marks : 12
GroupA: Statistical distributions and Errors
Probability: Mutually exclusive events, theorem of total probability, compound events and theorem of compound probability.
Probability distributions: Gaussian (continuous) distribution, its mean & standard deviation. Binomial distribution, its mean & standard deviation. Poisson distribution, its mean & standard deviation.
Theory of Errors: Definitions, classification of errors. Random error of a measured quantity. Propagation of error.
Group B : Numerical Techniques
Solution of Algebraic equations by Bisection Method, Newton-Raphson’s method, Numerical Integration—Simpsons rule. Numerical solution of non-liner equations –Picard’s Method, Runge Kutta Method (up to2nd order)
Group C: Operating systems and programming
Programming Languages : FORTRN and C
PAPER H 303
MATHEMATICAL PHYSICS – II
Total Marks:35 Pass Marks : 12
Group A Differential Equations
Differential equations and special functions : Ordinary differential equations, Homogeneous equations, solutions in power series, series solution of second order, differential equation by the Froebenius method.
Legendre’s differential equation, Legendre polynomial, Rodrigue’s formula, Generating function of Legendre polynomial, orthogonal properties of Legendre polynomial, Recurrence relation for Pn(X).
Bessel’s Differential Equation and its solution, Bessel’s function of first kind. Recurrence relation, spherical Bessel’s function, Generating function in connection with Bessell’s function.ter of physic
Group B Tensors and Complex Numbers
Tensors: Transformation of coordinates, tensorial character of physical quantities ,symmetric and antisymmetric tensors, rules for combination of tensors, additions ,subtractions, outer multiplications, contractions and inner multiplications, differentiation of tensors and kronekar Delta
Complex Variables:- Complex number and their graphical representation, roots of complex numbers, functions of complex variables, concepts of neighbor-hood, limit and continuity, analytical function, Cauchy-Rieman conditions and their applications.
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