Back

Unit-I     
Vector space and Matrices; linear independence: Bases; Dimensionality; Inner product; Linear transformation; Matrices; Inverse; Orthogonal and unitary matrices; Independent elements of a matrix; Eigenvalues and eigenvectors; Digonalization; Complete orthonormal sets of functions.
              
Unit-II    
Special functions; Second order linear ODES with variable coefficients; Solution by series expansion; Hermite and Lagaurre equations, Physical applications Generating function and recursion relations

Unit-III   
Special functions: Spherical harmonics, Henkel, Neumann function, Generating function and recursion relations

Unit-IV  
Fourier series; FS of arbitrary period; Half-wave expansions; Partial sums; Fourier integral and transforms; FT of delta function.

Unit-V     
 Liouville theorem. Power series Taylor’s theorem. Laurents theorem. Calculus of residues, evaluation of real definite integrals.

Text and Reference Books

1. Mathematical Methods for Physics by G. Arfken
2. Matrices and Tensors for Physicist by A.W. Joshi
3. Advanced  Engineering Mathematics by E. Kreyszig
4. Special Functions, by E.D. Rainville
5. Special Functions, by W.W. Bell
6. Mathematical Method for Physicists and Engineers by K.F. Relly, M.P. Hobson and S.J. Bence
7. Mathematics for Physicists by Mary L. Boas

Unit-I     
Preliminaries: Newtonian mechanics of one and many particles systems; Conservation laws, work-energy theorem; Open systems (with variable mass). Constraints; their classification; D’Alembert’s principal, generalized coordinates, Lagrange’s equations; gyroscopic forces; dissipative systems

Unit-II    
Jacobi integral; Gauge invariance; generalized coordinates and momenta; Integrals of motion; Symmetries of space and time with conservation laws; Invariance under Galilean transformations.
Rotating frames; Inertial forces; Terrestrial and astronomical applications of coriolis  force.

Unit-III   
Central force- Definition and characteristics; Two body problem; closure and stability of circular orbits; general analysis of orbits; Kepler’s law and equation; artificial satellites; Rutherford scattering.

Unit-IV  
Principal of least action; Derivation of equations of motion; Variation and end points; Hamilton’s principal and characteristic functions; Hamilton-Jacobi equation.

Unit-V    
Canonical transformation; Generating functions; Properties; Group property, examples; infinitesimal generators; Poisson bracket; Poisson theorems; Angular momentum PBs; Small oscillations; Normal modes and coordinates.

Text and Reference Books:

1. Classical Mechanics, by N.C. Rana and P.S. Jog (Tata McGraw-Hill, 1991)
2. Classical Mechanics, by H. Goldstein (Addison Wesley, 1980).
3. Mechanics by A. Sommerfeld (Academic Press, 1952)
4. Introduction to Dynamics by Perceival and D. Richards (Cambridge Univ. Press, 1982)

Unit-I     
Why Quantum Mechanics? Revision, inadequacy of classical mechanics, development of Schrodinger equation, continuity equation, wave-packet admissible wave functions stationary states. Formalism of wave mechanics, expectation values, quantum mechanical operators for position and momentum in the coordinate representation.

Unit-II    
Construction of quantum mechanical operators for other dynamical variables from those of position and momentum. Ehrenfest’s theorem, momentum eigen functions in the coordinate representation, box normalization and Dirac delta normalization.
               Brief revision of linear vector spaces, inner or scalar product, Schwarz inequality, state vector, general formalism of operator mechanics vector

Unit-III   
Operator algebra, commutation relations, eigen values, eigen vectors, hermitian operators degeneracy, orthogonality of eigenvectors of Hermitian operators, non-commutativity of two operators and uncertainty in the simultaneous measurements of the corresponding dynamical variables. The fundamental expansion postulate, representation of state vector, Dirac’s bra-ket notations.

Unit-IV  
Matrix representation of operators, change of basis, unitary transformations, Harmonic oscillator problem by operator method

Unit-V    
Angular momentum in QM: commutation relations, eigen values and eigen-function of L2 operator. Role of L2 operator in central force problems, radial part of eigenfunction for hudrogen atom, three dimensional square well potential, parity of wave functions and parity operator,

Text and Reference Books

1. L.I. Schiff, Quantum Mechanics (McGraw-Hill)
2. S. Gasiorowicz, Quantum Mechanics (Wiley)
3. B. Craseman and J.D. Powell, Quantum Mechanics (Addison Wesley)
4. A.P. Messiah, Quantum Mechanics
5. Mathews and Venkatesan, Quantum Mechanics.

Unit-I     
Transistors: JFET, BJT, MOSFET and MESFET: Structure, Working, Derivations of the equations for I-V characteristics under different conditions; High frequency limits.Microwave devices: Tunnel diodes, transfer electron devices (Gunn diode); Avalanche transit time devices, Impatt diodes and parametric devices.

Unit-II    
Photonic devices: Radiative and non-radiative transitions. Optical absorption, Bulk and thin film Photoconductive devices (LDR), diode photo-detectors, Solar cell-(open circuit voltage and short circuit current, fill factor). LED (high frequency limit, effect of surface and indirect recombination current operation of LED).

Unit-III   
Laser device: Diode laser (condition for population inversion in active region, light confinement factor.  Optical gain and threshold current for lasing, Fabry-Perrot cavity length for lasing and the separation.
Memory devices: Static and dynamic random access memories SRAM and DRAM, CMOS and NMOS, non-volatile – NMOS, magnetic, optical and ferroelectric memories, charge coupled devices (CCD).

Unit-IV  
Other electronic devices: Electro-optic, Magneto-optic and Acousto-optic effects.  Material properties related to get these effects. Important ferroelectric, Liquid crystal and Polymeric materials for these devices.

Unit-V    
Piezoelectric, Electrostrictive and magneto-strictive effects, Important materials exhibiting these properties, and their applications in sensors and actuator devices.  Acoustic delay lines, piezoelectric resonators and filters. High frequency piezoelectric devices-Surface Acoustic Wave Devices.

Text and Reference Books.

1. Semiconductor Devices – Physics and Technology, By S.M. Sze, Wiley (1985).
2. Introduction to semiconductor devices, M.S. Tyagi, John Wiley and Sons.
3. Measurement, Instrumentation and experimental design in Physics and Engineering by M. Sayer and A. Mansingh, Prentice Hall, India (2000).
4. Optical electronics by Ajoy Ghatak and K. Thyagarajan, Cambridge, Univ. Press.

M. Sc. Physics (II SEMISTER)
Paper-V
quantum Mechanics-iI

Unit-I     
Time dependent perturbation theory, First order perturbation theory applied to non-degenerate states, second order perturbation, Application of perturbation theory to the ground state energy of He atom (calculation given in Pauling and Wilson), Normal and anomalous Zeeman effect, first order Stark effect in the ground and first excited states of H atom and second order Stark effect of H atom, an-harmonic oscillator.

Unit- II   
Time dependent perturbation theory, transition rate, constant perturbation harmonic in time, radiative transitions, absorption and induced emission, atomic radiation, dipole approximation, Einstein’s atomic radiation, Einstein’s A and B coefficients and their calculations.

Approximation methods: W.K.B. method and its application to barrier penetration. Variational principle and its application to simple cases like ground state of He atom and deuteron in Yukawa potential.

Unit-III   
System of identical particles, exchange and transposition operators, totally symmetric and anti-symmetric wave function and their expressions for a system of non-interacting particles, statistics of systems of identical particles, Relation of statistics with spin, Ortho and para states of the helium atom and their perturbation by Coulomb repulsion.

Unit-IV  
Scattering theory, scattering cross-section in laboratory and centre of mass system, scattering by a central potential, Partial wave method, phase shifts and their importance, scattering by a square well potential and a perfectly rigid sphere, resonance scattering.

Unit-V    
Hamiltonian of a molecule, Born-Oppenheimer approximation, Heitler-London theory of the hydrogen molecule, Outline of the helium atom and their perturbation by the Coulomb repulsion.

Text and Reference Books.

1. E. Merzbacher, Quantum Mechanics (Wiley and Sons-Toppon)
2. J. L. Fowell and b. Crazemann, Quantum mechanics ( B I Publications)
3. L I Schiff, Quantum Mechanics (McGraw-Hill)
4. D. Bohm, Quantum Theory (Asia Publishing House)
5. Pauling and Wilson, Introduction to Quantum Mechanics
6. A.K. Ghatak and S. Lokanathan, Quantum Mechanics (Macmillan, India)
7. P.T. Mathews and K. Venkatesan, A text book of Quantum Mechanics ( Tata McGraw-Hill)
8. P.T. Mathews, Introduction to Quantum Mechanics (Tata-McGraw-Hill)

 

M. Sc. Physics (II Semester)
Paper-VI
Statistical mechanics

Unit-I     
Foundation of statistical mechanics; Specification of states of a system, contact between statistics and thermodynamics, Classical ideal gas, Entropy of mixing and Gibbs’s paradox. Micro-canonical ensemble, phase space, trajectories and density of states, Liouville’s theorem, Canonical and grand canonical ensembles; Patrician function, calculation of statistical quantities, energy and density fluctuations.

Unit-II    
Density matrix, statistics of ensembles, statistics of indistinguishable particles, Maxwell-Boltzmann, Fermi-Dirac and Bose-Einstein statistics, properties ideal Bose and Fermi gases, Bose-Einstein condensation.

Unit-III   
Cluster expansion for classical gas, Virial equations of states, Ising model, Mean field theories of the Ising model in three, two and one dimensions. Exact solutions in one dimension.

Unit-IV  
Landau theory of phase transition, Critical indices, Scale transformation and dimensional analysis.

Unit-V    
Correlation of space-time dependent fluctuations, fluctuations and transport phenomenon, Brownian motion, Langevin theory, fluctuation dissipation theorem.  The Fokker-Planck equation.

Text and Reference Books

1. Statistical and thermal Physics, by F. Reif
2. Statistical Mechanics by K. Huang
3. Statistical Mechanics by R.K Patharia
4. Statistical mechanics by R. Kubo
5. Statistical Physics by Landau and Lifshitz

M. Sc. Physics (II SEMISTER)
Paper-VII
Electrodynamics and plasma physics

Unit-I        
Review of Four-Vector and Lorentz transformation in four dimensional space, Electromagnetic field tensor in four dimensions and Maxwell’s equations, Duel field tensor, wave equation for vector and scalar potential and solution, Retarded potential and Lienord-Wiechert potential.

Unit-II       
Electric and magnetic fields due to uniformly moving charge and accelerated  charge, Linear and circular acceleration and angular distribution of power radiated, Bremsstrahlung, Synchrotron radiation and Cerenkov radiation, reaction force of radiation.

Unit-III      
Motion of charge particles in electromagnetic fields, uniform E and B fields, Nonuniform fields, diffusion across magnetic fields. Time varying  E and B fields, adiabatic in-variants;  first, second third adiabatic in-variants.

Unit-IV     
Elementary concepts: derivation of moment equations from Boltzmann equations, Plasma oscillations, Debye shielding, plasma parameters, Plasma confinement.
Hydromagnetic waves: magneto-sonic and Alfven waves.

Unit-V       
Wave phenomena in magneto-plasma: Polarization, Phase velocity, Group velocity, cutoffs, resonance for EM wave propagating parallel and perpendicular to magnetic field, Propagation at finite angle and CMA diagram, Applton-Hartee formula and propagation ionosphere and magnetosphere; Helicon, Whistler, Faraday Rotation.       

Text and Reference Books:
1.   Classical Electricity and Magnetism , Panofsky & Phillips
2.   Plasma Physics, Bittenciurt

1. Plasma Physics, Chen
2. Classical Electrodynamics, J. D. Jackson (second and third Addition)

  M. Sc. Physics (II Semester)

Paper-VIII
Atomic and molecular physics

Unit-I     
Quantum states of one electron atoms-Atomic orbital-Hydrogen spectrum-Pauli’s principle, Spectra of alkali elements-Spin orbit interaction and fine structure in alkali Spectra-Equivalent and non-equivalent electrons-

Unit-II    
Normal and anomalous Zeeman effect, Paschen Back effect, Stark effect.

Unit-III   
Two electron systems, interaction energy in LS and JJ Coupling, Hyperfine structure (Qualitative) – Line broadening mechanisms (General ideas)

Unit-IV  
Types of molecules, Diatomic linear symmetric top, asymmetric to and spherical to molecules, Rotational spectra of diatomic molecules as a rigid rotator, Energy levels and spectra of non-rigid, Intensity of rotational lines, Stark modulated microwave spectrometer (qualitative)

Unit-V    
Vibrational energy of diatomic molecule, Diatomic molecule as a simple harmonic oscillator, Energy levels and spectrum, Mores potential energy curve, Molecules as vibrating rotator, Vibration spectrum of diatomic molecule, PQR branches, IR spectrometer (qualitative)

Text and Reference Books

1. Introduction to atomic spectra, H.E. White
2. Fundamentals of molecular spectroscopy, C.B. Banwell
3. Spectroscopy Vol. I, II & III, Walker & Straughen
4. Introduction to molecular Spectroscopy , G. M. Barrow
5. Spectra of diatomic molecules, Herzberg
6. Molecular spectroscopy, G.M. Barrow
7. Spectra of atoms and molecules, P.F. Bemath
8. Modern spectroscopy, J.M. Holias.