Mechanics

Inertial and non-inertial frames, examples, Transformation of displacement, velocity and acceleration between different frames of reference involving translation in uniform motion, Galilean transformation and invariance of Newton’s laws, Transformation equations of displacement velocity and acceleration for rotating frames, Fictitious forces (Coriolis force and centrifugal force), effects of Centrifugal and Coriolis forces due to earth’s rotation, Focault’s pendulum.

Centre of mass of a two particle system, motion of centre of mass and reduced mass conservation of linear momentum, elastic and inelastic collision of two particles in laboratory and center of mass frames, motion of a system with varying mass, Angular momentum conservation with examples, charged particle scattering by nucleus.

Motion under central forces, gravitational interaction, general solution under gravitational interaction, discussion of trajectories, cases of elliptical and circular orbits, Keplers laws.

Special theory of relativity:                                                                     

 Postulates of special theory of relativity, Lorentz transformations, length contraction, Time dilation, transformation and addition of velocities

Elastic constants: Young’s Modulus, Bulk Modulus, Modulus of Rigidity, Poisson’s ratio. Relations between the elastic constants, torsion of a cylinder.

Bending of beams: Bending moment, Cantilever, Potential energy and oscillation of a loaded cantilever, cantilever loaded at one end (i) when weight of beam is negligible (ii) When weight is considered, Beam supported at both ends and loaded in the middle, Experimental determination of elastic constants (Y, η ,σ).

Duality of radiation and matter, De broglie’s hypothesis, justification for the relation, Experimental confirmation of λ = h/p (Davission and Germer experiment).

Uncertainty principle relating to position and momentum, relating to energy and time, its applications to various quantum mechanical problems such as:

     i.Non-existence of electrons in nucleus

    ii.Ground state energy of H-atom

  iii.Ground state energy of Harmonic oscillator

  iv.Natural width of spectral line

Schrodinger equation:

Wave function and its interpretation, Schrödinger time dependent and time independent one-dimensional equation, three-dimensional  Schrödinger wave equation, probability current density, physical meaning of  ψ, conditions to be satisfied by  ψ.