चार महीने का बच्चा कैसे बना अरब़पति? जन्म के सिर्फ चार माह बाद यदि कोई बच्चा अरबपति बन जाए तो इसे उसकी किस्मत ही कहेंगे। भारत के एकाग्रह रोहन मूर्ति नाम के बच्चे की किस्मत कुछ इसी प्रकार चमकी है। देश की दूसरी सबसे बड़ी आइटी कम्पनी इंफोसिस के फाउंडर नारायण मूर्ति ने सोमवार अपने चार महीने के पोते एकाग्रह मूर्ति को 240 करोड़ रूपए के शेयरों की हिस्सेदारी का तोहफा देकर उसे शायद देश का सबसे कम उम्र का अरबपति बना दिया है। BSE की फाइलिंग के अनुसार इंफोसिस में अब एकाग्रह रोहन की 15 लाख शेयरों की हिस्सेदारी हो गई है। इसका मतलब अब एकाग्रह रोहन इंफोसिस का 0.04% का हिस्सेदार है। शेयरों के स्थानान्तरण के बाद नारायण मूर्ति के पास कम्पनी के कुल शेयरों का 0.36% हिस्सा बचा है। जिस समय नारायण मूर्ति द्वारा अपने पोते को शेयर देने की खबर बाई उस समय इंफोसिस के शेयरों में गिरावट देखने को मिल रही थी। एकाग्रह रोहन, नारायण मूर्ति तथा सुधा मूर्ति के बेट रोहन मूर्ति और उनकी पत्नि अर्पणा कृष्णन का बेटा है। आपको यह पता होगा कि नोरायण मूर्ति ने अपनी पत्नि सुधा मूर्ति से 10 हजार रूपए उधार लेकर 1981 में इंफोसिस क
M.L. SUKHADIA UNIVERSITY, UDAIPUR B.Sc. III Year Physics
PAPER-I Quantum mechanics, and Atomic and Molecular Physics
UNIT-I
- Introductory Schrodinger theory: Rise and fall of Plank-Bohr quantum theory, Duality of radiation and matter, de Broglie’s hypothesis, justification for the relation , experimental confirmation.
- Phase and group velocities of a wave: Formation of a wave packet, illustrations. Uncertainty principle relating to position and momentum, relating to energy and time, application of complementarity principle, photon interpretation of two slit interference, Einstein-de-Broglie relations as a link between particle and wave properties, general equation of wave propagation, propagation of matter waves, time dependent and time independent Schrodinger equations, physical meaning of ψ, conditions to be satisfied by Schrodinger equation as an operator equation. Postulatery approach to wave mechanics, operators, observable and measurements.
- Operators: Eigen values and eigen functions; linear operators, product of two operators, commuting and non commuting operators, simultaneous eigen functions, orthogonal functions. Hermitian operators, their eigen values, Hermitian adjoint operators, expectation values of an operator.
UNIT-II
- Simple one dimensional problem: Particle in a box with rigid walls. Concept of a potential well. Wave functions and energies for the ground and excited states; quantization of energy qualitative discussion of the solutions for a shallow potential well.
- Applications of operator method: Simple harmonic oscillator, step-up and step-down operators, eigen functions and eigen values of the ground state and excited state, zero point energy probability density and its variations with degree of excitation; orthogonality of wave functions.
- Other one dimensional problems: Step potential, penetration through rectangular barrier. Transmission coefficients, barriers of special shapes, quantum mechanical tunneling, particle in of three dimensional cubical box, degeneracy.
UNIT-III
- Angular momentum and spin Central force; orbital angular momentum, operators for its Cartesian components, commutation relations, mutual as well as with L2, operators L+ and L-, their interpretation as step operators eigen values of L2 , half integral values for quantum numbers. Angular momentum operators in spherical polar coordinates; evaluation of their eigen functions explicitly in terms of the coordinates, their degeneracy.
- Schrodinger equation for hydrogen atom in spherical polar coordinates; separations into radial and angular variation, qualitative discussion of spherical harmonics. Angular momentum and magnetic moment of electron due to orbital motion, Bohr Magneton.
UNIT-IV
- Mono valent and divalent atoms
- Back ground from quantum theory: The four quantum numbers ; spectral terms arising from L-S coupling, s, p, d, f, notation, selection rules. Half life of excited states, width of a spectral line.
- Spectra of mono and divalent atoms: Doublet fine structures of hydrogen lines ; screening constant for monovalent atoms, series limits, doublet structure for alkali spectrum. Spectra of helium and alkaline earth atoms, singlet and triplet series. Effect of magnetic field on energy levels : Gyromagnetic ratios for orbital and spin motions; vector model, Lande g factor, strong and weak field effects, illustrative cases of H, Na, Ca and Hg.
- X-ray spectra: The continuous x-ray spectrum, Duane and Hunt limit. Characteristic x-rays : Mosley’s law, doublet fine structure, H-like character of X-ray states, X-ray absorption spectra, absorption edges.
UNIT-V
- Sharing of electrons: Formation of molecular orbitals, H2+ ions, H2 molecule, electronic levels, singlet and triplet characters. Rotational energy levels, inter-nuclear distance.
- Vibrational energy levels, force constants, anharmonicity dissociation energy, isotope effects on rotational and vibrational energies. Raman effect (brief study). Spectra of diatomic molecules : Pure rotation spectra ; selection rules, vibration-rotation spectra, selection rules, vibration-rotation spectra ; selection rules, P, Q and R branches.
- Electronic band systems, sequences and progressions, Frank-Condon principle. (Statement only, no derivation)
- Recent developments in Physics including discussion of Nobel prizes in Physics (no questions to be set in the theory examination).
Recommended Book
- Quantum Mechanics, Atomic and Molecular Physics by Saraswat and Tiwari, Himanshu Publication, Delhi
- Quantum Mechanics, Atomic and Molecular Physics (Hindi) by Kalra, Kakani and Saraswat, Himanshu Publications, Delhi
PAPER-II Electrodynamics, Electromagnetic Waves and Relativity
UNIT-I
- Motion of charged particles in E and B fields: Case of cathode ray oscillograph, positive ray parabola, velocity selector, magnetic focusing, mass spectrography.
- Faraday’s law for electromagnetic induction: Faraday’s law integral and differential forms; self-inductance of a solenoid and of a straight conductor, energy stored in an inductor and in the magnetic field. Displacement current; modified Ampere’s law, Maxwell’s equation for time-dependent electromagnetic field in vacuum and in material media, boundary conditions.
UNIT-II
- Electromagnetic potentials: Magnetic vector potential A and scalar potential φ. Poisson’s equation for A in terms of current density, solutions for line surface currents. Coulomb and Lorentz gauge transformations, Lorentz law in terms of potentials.
- Maxwell’s equations and electromagnetic waves: Plane-wave solution for Maxwell’s equation; orthogonality of E, B and propagation vector. Poynting vector; energy and momentum propagation, reflection and transmission at dielectric boundaries (normal incidence), polarization by reflection, Brewster’s angle.
UNIT-III
- Electromagnetic waves in conductors: Modified field equation; attenuation of the wave, reflection at and transmission through a conducting surface. Total internal reflection.
- Radiation from accelerated charges: Modification (Conceptual only) of Coulomb’s law to include velocity and acceleration dependent terms in E field. Radiation from an oscillating dipole and its polarization. Radial and spherical power of electromagnetic radiation, Radiation pressure equation in free space and medium.
UNIT-IV
- The Lorentz transformations: Galilean transformations; Newtonian relativity, instances of their failure; electromagnetism, aberration of light, Michelson-Morley experiment; Einstein’s basic postulates and geometric derivation of Lorentz transformations; invariance of Maxwell’s equations, length contraction, simultaneity, synchronization and time dilation, Einstein’s velocity addition rule, Doppler effect in light. Relativistic gravitational Red Shift.
UNIT-V
- Relativistic dynamics: Variation of mass with velocity, mass energy equivalence, relativistic formulae for momentum and energy.
- The structure of space-time: Four vectors; invariance of an interval, time-like, space-like and light-like intervals, Minkowski space.
- Relativistic electrodynamics: Electric field of a point charge in uniform motion; transverse components, magnetism as a relativistic phenomenon, transformation of E and B fields.
- Recent developments in Physics including discussion of Nobel prizes in Physics (no questions to be set in the theory examination).
Recommended Book
- Electrodynamics, Electromagnetic waves and relativity by Vimal Saraswat, Himanshu Publication, Delhi
- Electrodynamics, Electromagnetic Waves and Relativity (Hindi) by Kalra, Himanshu Publications, Delhi
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PAPER-III Solid State, Nuclear and Particle Physics
UNIT-I
- Crystal geometry: Crystal lattice, crystal planes and Miller indices, unit cells. Typical crystal structures, coordination number, packing fraction, symmetry elements, rotation, inversion and reflection, point groups and crystal classes, space groups.
- Crystallography: Bloch functions, Bloch’s theorem, diffraction of X-rays by a crystal lattice. Laue’s formulation of X-ray diffraction, reciprocal lattice, Brillouin zones, Laue spots, rotating crystal and Debye-Scherrer methods.
- Introduction to nano particles: Definition, length scales, importance of nanoscale and Technology.
UNIT-II
- Types of binding in solids: Covalent binding and its origin, ionic binding, energy of binding, transition between covalent and ionic binding, metallic binding, Van der Waal’s binding, hydrogen bond.
- Conduction in metals: Drude’s theory, DC conductivity, AC conductivity, plasma frequency, thermal conductivity of metals, Fermi-Dirac distribution, thermal properties of free-electron gas, Sommerfeld’s theory of conduction in metals.
UNIT-III
- Conduction in semiconductors: Bands in solids, metals, insulators and semiconductors. Motion of free electrons on a chain of atoms, effective mass, electrons and holes, donor and acceptor impurities, donor impurity levels. Thermal excitation of carriers, electrical conductivity. Elementary ideas of Hall effect in metals and semiconductors and magnetoresistance.
- Charge transport in semiconductors: Ionization energy of impurity atoms, carrier concentration in doped semiconductors at high and low temperatures, control of conductivity of semiconductors by impurities and current flow in semi-conductors.
UNIT-IV
- Structure of nucleus: Discovery of the nucleus, composition. Basic properties: charge, mass, size, spin, magnetic moment, electric quadrupole moment, binding energy, binding energy per nucleon and its observed variation with mass number of the nucleus. Coulomb energy, volume energy, surface energy, other corrections, explanation of the binding energy curve. Liquid drop model of the nucleus.
- Nuclear forces: Two-nucleon system, deuteron problem, binding energy, nuclear potential well, results of p-p and n-p scattering experiments, meson theory of nuclear forces e.g. Bartlett, Heisenberg, Majorana forces and potentials (No derivations).
- Radioactivity: Decay constant and half-life, spectra of emitters, Geiger-Nuttal law, Gamow’s explanation. Beta decay: elementary Fermi’s theory (No derivations). Antineutrino. Nuclear radiation, energy levels.
UNIT-V
- Detectors for charged particles: Ion chamber, Geiger counter, resolving time, cloud chamber.
- Accelerators: Need for accelerators; cyclic accelerators, cyclotron, betatron, synchrocyclotron, variable energy cyclotron, phase stability. Brief introduction to Accelerator facilities in India.
- Rutherford scattering formula, different types of nuclear reactions.
- Artificial radioactivity: Nuclear fission, neutron reactions, Fermi and trans-uranic elements, chain reaction, criticality, moderators. Brief discussion of Reactor facilities in India.
- Discovery of cosmic rays: Hard and soft components, discovery of muon, pion, heavy mesons and hyperons, mass and life time determination for muon and pion.
- Primary cosmic rays: Extensive air showers, solar modulation of primary cosmic rays, effect of earth’s magnetic field on the cosmic ray trajectories.
- Elementary particles: Discovery and important properties, Standard Model Strangeness, conservation of strangeness in particle interactions, quark hypothesis, high energy electron scattering from protons, basic interactions of quarks and leptons, interrelation between particle physics and cosmology.
- Big Bang theory (Brief study, no derivations) Brief introduction to Larger Hadron Collider “Big Bang” experiments at CERN.
- Recent developments in Physics including discussion of Nobel prizes in Physics (no questions to be set in the theory examination).
Recommended Book
- Solid State, Nuclear and Particle Physics by Saraswat and Mandot, Himanshu Publication, Delhi
- Solid State, Nuclear and Particle Physics (Hindi) by Kalra, Himanshu Publications, Delhi
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