Physics Syllabus Of Admission Tests For Admission to M.SC. (PHYSICS) / MCA / B.Ed.
Mechanics : Inertial and non-inertial frames, Conservation Laws, Centre of mass and its kinematics. Rotational Motion, Coriolis force, Moment of inertia and elated Theorems. Harmonic, Damped and Forced oscillations, resonance. Wave phenomenon and its properties. Gravitational field and potential, Kepler’s laws. Galilean transformation, Lorentz transformations, Relativistic Doppler effect.
Electricity and Magnetism : Vector Fields and Electrostatics, Stoke’s theorems, Gauss’s law and its applications, Laplace and Poisson equations. Dielectric Medium, Gauss’s law, Clausius-Mossotti relation, Langevin-Debye equation, Capacitors. Continuity equation, LCR circuts, Kirchoff’s laws, circuits theorems. Laws of magnetic Effects of current and magnetic Properties. Electromagnetic induction, self and mutual inductance. Alternating current, LCR circuits, Power in AC circuits.
Optics and Electromagnetic Theory : Fermat’s principle and its application, cardinal points of an optical system, aberrations. Maxwell’s equations and their significance, gauge transformations and gauge condition, Poynting vector, plane e.m. waves in free space, nonconducting medium and conducting media.
Polarization : Brewster’s law, Malus law, elliptically and circularly polarized light, polaroids. Interference of polarized light. Interference, Coherence, Fresnel’s biprism, Newton’s rings, Michelson’s interferometer, Fabry – Perot interferometer.
Fraunhoffer and Fesnel diffraction, diffraction grating, diffraction at circular aperture, Lasers and its applications, Holograpy, Optical fibre.
Electronics : p-n junction diode, its characteristics and applications, LEDs, Zener diode and its application, capacitor filter, Power supply, BJT as an aimplifier, BJT biasing, Q-point and its temperature dependence, Hybrid parameters, Classification of amplifiers, RC coupled amplifier and its frequency response characteristics, negative feedback in amplifiers and its advantage, JFET, MOSFET and their characteristics, Basic logic gates, Boolean algebra and De Morgan’s theorem, Wein’s bridge, Hartley oscillators. Multivibrators, RC differentiator and integrator, Operational amplifier and its ideal applications, Modulation, Cathode Ray Oscilloscope.
Mathematical Method : Cauchy – Riemann differential equations, Green’s theorem, Cauchy’s integral theorem, Cauchy’s integral formula, Taylor and Laurent series, Cauchy’s residue theorem. Curvilinear Coordinates : Gauss’s theorem, Stroke’s theorem. Basel Functions, hermite Polynomials, Legendre, Associated Legendre and Laguerre Functions, their properties, generating functions, orthogonality relation. Fourier series, its properties and applications.
Laplace and Poission equations and their simple applications. Classification of integral equations. Forier integral, Fourier transforms, Kernels and their properties.
Classical Mechanics and Special Relativity : Lagrangian and Hamiltonian formulation, Lagrange’s equations and Hamilton’s equations of motion and applications. Seymmetry and conservation Laws. Two body central force problem. Kepler’s laws, Virial theorem, integrals of motion. Scattering cross section. Rutherford formula. Tensors, four vectors and their transformations, Lagrangian of a relativistic particle. Equation of motion. Relativistic formulae for kinematical variables, Kinematics of two body reaction Maxwell’s equation, equation of continuity in covariant form.
Quantum Mechanics : Necessity of new formalism for microparticles, Physical observables as mathematical operators, postulates of quantum mechanics, expectation values and Ehrenfest theorem, Heisenberg uncertainly principle. Schrodinger Equation, wave functions. Particle in one dimensional infinite and finite square well, potential step, potential barrier, linear harmonic oscillator. Orbital angular momentum operators and their commutation relations, eigenvalues and eigenfunctions of L2 and LZ, rigid rotator, central potential, hydrogen like atoms. Stern-Gerlach experiment, Zeeman splitting, Spin angular momentum operators and their algebra, Total angular momentum, its commutation relation. Idea of perturbation, time independent and dependent perturbation. Scatering amplitude and cross sections, scattering by spherically symmetric potential, scattering of identical particles.
Thermal and Statistics Physics : Kinetic Theory of Gases, principle of equipartition of energy, specific hearts of gases, Andrew’s experiment, collision cross section and mean free path, transport phenomena. Laws of thermodynamics, Carnot’s cycle, entropy, T-S diagrams, Gibb’s paradox. TdS equations, porous plug experiment, regenerative cooling, helmboltz and Gibb’s functions, maxwell’s equations. First and second order phase transitions. Phase space, microand macro-states, definition of entropy. Fermi-Dirac and Bosc Einstein distributions. Maxwell-Boltzmann distribution, partition function, Planck’s formula and other related laws. Monatomic ideal gas, Maxwell’s formula for the distribution of velocities, the law of equipartition of energy, specific heat. Atomic, Molecular, Laswer and Solid State Physics.
Atomic Physics : Spin – orbit interaction, Relativistic correction and Lamb Shift, fine structure of hydrogen, excitation and ionization potentials. L.S. and jj coupling scheme, Pauli’s exclusion principle, Breit’s scheme, Zeeman effect for sodium doublets. Molecular Physics : Rotation and vibration of diatomic molecules, Aligarh Muslim University vibrating rotator and its spectrum, infrared spectrum of diatomic molecules, classical theory of Raman effect, rotational Raman spectra. Electronic spectra of diatomic molecules, Frank-Condon principle, electronic structure of N2 and O2, modes of vibration HCN, CO2 and H2O.
Laser Physics : Einstein’s A and B coefficients, population inversion, ammonia maser, vibtational modes of a resonator, Quality factor, Schawlow – Townes conditions, Properties of Laser beams, Ruby, He-Ne and N2 lasers. Crystalline and Amorphous Structures, Symmetry Operations, Index System, Defects and Dislocations, Quasi – crystals, Crystal Binding, Cohesive energy of Ionic and Noble gas crystals, Bragg and Laue diffraction, Reciprocal lattice, Normal modes of one dimensional monatomic and diatomic lattices, Dispersion curves and their features, Free electron theory, Drude model of electrical conductivity, Mathiessen’s rule, Hall effect. Variation of Fermi-Dirac distribution with temperature, Sommerfeld model of free electron gas, Band theory of solids, Periodicity, Bloch theorem, Kronnig Penny model, Band gap for a linear monatomic crystal in nearly free electron model. Simple properties of superconductors.
Nuclear Physics, Particle and Astrophysics : General Properties of Atomic Nuclei, Nucler angular momentum, magnetic dipote moment, g-factor, Schmidt lines, electric quardrupole moments, Nuclear force and its properties. Bainbridge and Aston man spectrograph, mass defect and binding energy, fission and fusion. Radioactive Series, bateman equations and their application to activation analysis, Alpha, beta and gamma decays. Nuclear Reactions : Energy balance, Q-value and threshold, reaction cross section. Interaction of radiations with matter and radiation detectors.
Particle Physics : Basic interactions and their mediating quanta, classification of particles; conservation rules, determination of spin and parity of pions, strange particles quark model. Cosmic Rays Primary cosmic rays, its energy and charge spectrum, secondary cosmic rays, its composition, intensity variation, Rossi transition curve, electromagnetic cascade showers and extensive air showers. Astrophysics : Sun and its atmosphere, energy source, solar activities, stars and their temperatures and magnitudes, H-R diagram, Birth and death of stars, Chandrashekhar mas limit, pulsars, Schwarzschild radius.
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