Part I:
Module I : Mathematical Methods of Physics
Curinlinear coordinates, circular cylindrical and spherical polar coordinates Victor algebra and Victor calculus,
Matrices – Cayley Hamilton Theorem, Eegin values and Eegin vectors. Special Functions (Gama, Beta, Hermite, Bessel, Laguerre, Legendre)
Complex Analysis – Analytic function, Taylor and Laurent expansions, poles, residue and evaluation of integrals. Fourier Series, Fourier and Laplace transforms. Tensors, Introductory group theory, representation of groups. Irreducible representation SU (2),SU(3).
Module II: Classical Mechanics
Newtons laws, Lagrangian and Hamiltonian formalism. Canonical Transformation and Poison
Bracket
Hamilton Jacobi Theory
Rigid body Dynamics-
Small oscillations
Special theory of relativity
Non leniar Dynamics – logistic map – bifurcation – attractors – fractal, fractal dimension.
Module III: Quantum Mechanics
Wave particle duality, Fundamental postulates of Q.M., Schrodinger picture & Heisenberg picture
Eigen value problem (particle in a box, harmonic ocillator). Tunneling through a barrier.
Heisenberg uncertainly principle. Algebra of linear vector space, Dirac notation, Angular Momentum algebra (spin, addition of angular momentum).
Time independent perturbation theory and applications : Variational method.
Time dependent perturbation theory and Fermi Golden Rule.
Elementary theory of Scattering phase shifts, partial waves, Born approximation.
Relaturistic Quantum Mechanics : Klein Gordon – Dirac equations.
Module IV: A) Electro Dynamics & Statistical Physics
Review of Electrostatics and Magnetostatics
(Gausi's law, Biot Savart Law, Amperes theorum)
Maxivells equation in free space and linear isotropic media – boundary conditions on the fields at interfaces. Sealar and vector potentials.
(Retarded potential Lienard Wiehirt potential, field of a moving point charge)
Electromagnetic waves in free space. Dielectrics and conductors. Reflection, refraction, polarisation Transmission lines and Wave guides.
Statistical Physics
B) Laws of thermodynamics. Thermodynamic potentials
Phase space, micro and macrostates, Micro canonical, canonical and grand canonical ensembles and partition funtions. Classical and quantum statistics, Ideal Bose and Fermi gases.
First and second order phase transitions. Diamagnetism, paramagnetism an ferromagnetism.
Module V: Spectroscopy and Condensed Matter Physics
A) Spectroscopy
Introduction to Atomic Spectroscopy :- LS coupling, - J J coupling, - Zeeman effect, - Stark
effect, Lande - g factor
Electronic, rotational, vibrational and Raman Spectra of diatomic molecules, selection rules.
Spin Resonance Spectroscopy : NMR, ESR, Mossbauer Spectroscopy.
Laser : Spontaneous and stimulated emission, Einstein coefficients. Optical pumping, population inversions, rate equation. Modes of resonators and coherence length.
B) Condensed Matter Physics
Bravais lattice, Reciprocal lattice. Diffraction and the structure factor. Brillouin zone.
Vibractions of crystals with monoatomic and diatomic basis – Phonon heat capacity – Density of states in one an three dimensions – Einstein and Debye models
Free electron theory and electronic specific heat.
Hall Effect
Super conductivity Type I and Type II superconductors.
Josephson functions, BCS theory
Module VI: Nuclear and Particle Physics & Electronics
A) Nuclear Properties : size shape and charge distribution, spin and parity – Binding energy, semi empirical mans formula, liquid drop model, Nature of nuclear force. Elmentary ideas of alpha, beta and gamma decay and their selection rules. Fission and fusion. Nuclear for reactions. Reaction crossection, Q valve.
Elementary particles and their Quantum numbers.
Quark Model
A) Electronics :
Semi conductor devices (diodes, functions, transistors, FET) Amplifuro, Oscillators.
Opto electronic devices (solar cells, photo detection, LED), Operational amplifiers and their applications. Digital techniques and applications (registers, counters, comparators) A/D and D/A converters.
Module VII: Recent Developments in Physics
Nanotechnology
Properties of metal, semi conductor, rare gas and molecular nanoclusters – superconducting fullerene – quantum confined meterials – quantum wells, wires, dots and rings – meta materials – graphene
Non Linear Dynamics
Soliton – Effect of nonlinearity and dispersion.
Non Conventional Energy Resources
Wind Energy, Solar Energy, Tidal energy, Bio.
Evolution of Universe
Big Bang Theory : Spontaneous symmetry breaking, Higgs Boson.
Basis of Quantum Computing
Part II: General Knowledge,
Module I : Mathematical Methods of Physics
Curinlinear coordinates, circular cylindrical and spherical polar coordinates Victor algebra and Victor calculus,
Matrices – Cayley Hamilton Theorem, Eegin values and Eegin vectors. Special Functions (Gama, Beta, Hermite, Bessel, Laguerre, Legendre)
Complex Analysis – Analytic function, Taylor and Laurent expansions, poles, residue and evaluation of integrals. Fourier Series, Fourier and Laplace transforms. Tensors, Introductory group theory, representation of groups. Irreducible representation SU (2),SU(3).
Module II: Classical Mechanics
Newtons laws, Lagrangian and Hamiltonian formalism. Canonical Transformation and Poison
Bracket
Hamilton Jacobi Theory
Rigid body Dynamics-
Small oscillations
Special theory of relativity
Non leniar Dynamics – logistic map – bifurcation – attractors – fractal, fractal dimension.
Module III: Quantum Mechanics
Wave particle duality, Fundamental postulates of Q.M., Schrodinger picture & Heisenberg picture
Eigen value problem (particle in a box, harmonic ocillator). Tunneling through a barrier.
Heisenberg uncertainly principle. Algebra of linear vector space, Dirac notation, Angular Momentum algebra (spin, addition of angular momentum).
Time independent perturbation theory and applications : Variational method.
Time dependent perturbation theory and Fermi Golden Rule.
Elementary theory of Scattering phase shifts, partial waves, Born approximation.
Relaturistic Quantum Mechanics : Klein Gordon – Dirac equations.
Module IV: A) Electro Dynamics & Statistical Physics
Review of Electrostatics and Magnetostatics
(Gausi's law, Biot Savart Law, Amperes theorum)
Maxivells equation in free space and linear isotropic media – boundary conditions on the fields at interfaces. Sealar and vector potentials.
(Retarded potential Lienard Wiehirt potential, field of a moving point charge)
Electromagnetic waves in free space. Dielectrics and conductors. Reflection, refraction, polarisation Transmission lines and Wave guides.
Statistical Physics
B) Laws of thermodynamics. Thermodynamic potentials
Phase space, micro and macrostates, Micro canonical, canonical and grand canonical ensembles and partition funtions. Classical and quantum statistics, Ideal Bose and Fermi gases.
First and second order phase transitions. Diamagnetism, paramagnetism an ferromagnetism.
Module V: Spectroscopy and Condensed Matter Physics
A) Spectroscopy
Introduction to Atomic Spectroscopy :- LS coupling, - J J coupling, - Zeeman effect, - Stark
effect, Lande - g factor
Electronic, rotational, vibrational and Raman Spectra of diatomic molecules, selection rules.
Spin Resonance Spectroscopy : NMR, ESR, Mossbauer Spectroscopy.
Laser : Spontaneous and stimulated emission, Einstein coefficients. Optical pumping, population inversions, rate equation. Modes of resonators and coherence length.
B) Condensed Matter Physics
Bravais lattice, Reciprocal lattice. Diffraction and the structure factor. Brillouin zone.
Vibractions of crystals with monoatomic and diatomic basis – Phonon heat capacity – Density of states in one an three dimensions – Einstein and Debye models
Free electron theory and electronic specific heat.
Hall Effect
Super conductivity Type I and Type II superconductors.
Josephson functions, BCS theory
Module VI: Nuclear and Particle Physics & Electronics
A) Nuclear Properties : size shape and charge distribution, spin and parity – Binding energy, semi empirical mans formula, liquid drop model, Nature of nuclear force. Elmentary ideas of alpha, beta and gamma decay and their selection rules. Fission and fusion. Nuclear for reactions. Reaction crossection, Q valve.
Elementary particles and their Quantum numbers.
Quark Model
A) Electronics :
Semi conductor devices (diodes, functions, transistors, FET) Amplifuro, Oscillators.
Opto electronic devices (solar cells, photo detection, LED), Operational amplifiers and their applications. Digital techniques and applications (registers, counters, comparators) A/D and D/A converters.
Module VII: Recent Developments in Physics
Nanotechnology
Properties of metal, semi conductor, rare gas and molecular nanoclusters – superconducting fullerene – quantum confined meterials – quantum wells, wires, dots and rings – meta materials – graphene
Non Linear Dynamics
Soliton – Effect of nonlinearity and dispersion.
Non Conventional Energy Resources
Wind Energy, Solar Energy, Tidal energy, Bio.
Evolution of Universe
Big Bang Theory : Spontaneous symmetry breaking, Higgs Boson.
Basis of Quantum Computing
Part II: General Knowledge,
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