M.Sc in Physics

Bharathiar University
In Coimbatore

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  • Master
  • Coimbatore

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Starts Location
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Bharathiar University, Coimbatore, 641046., Tamil Nadu, India
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Course programme

Unit -I: Matrices and determinants
Properties of matrix addition and multiplication - different types of matrices and
their properties - Rank of a Matrix and some of its theorems - solutions to linear
homogeneous and non homogeneous equations - Cramers rule - eigenvalues and
eigenvectors of matrices - differentiation and integration of a matrix
Unit -II: Solving of differential equations
Homogeneous linear equations of second order with constant coefficients and
their solutions - ordinary second order differential with variable coefficients and their
solution by power series and Frobenius methods - extended power series method for
indicial equations
Unit-III: Special differential equations and their solutions
Legendre's differential equation: Legendre polynomials - Generating functions -
Recurrence Formulae - Rodriques's formula - orthogonality of Legendre's polynomial;
Bessel's differential equation: Bessel's polynomial - generating functions - Recurrence
Formulae - orthogonal properties of Bessel's polynomials - Hermite differential equation
- Hermite polynomials - generating functions - recurrence relation.
Unit - IV: Laplace Transforms
Laplace transforms: Linearity property, first and second translation property of
LT - Derivatives of Laplace transforms - Laplace transform of integrals - Initial and
Final value theorems; Methods for finding LT: direct and series expansion method,
Method of differential equation; Inverse Laplace transforms: Linearity property, first and
second translation property, Convolution property - Application of LT to differential
equations and boundary value problems
Unit - V: Fourier Series and integrals
Fourier series definition and expansion of a function x - Drichlet's conditions -
Assumptions for the validity of Fourier's series expansion and its theorems - Complex
representation of Fourier series - Problems related to periodic functions - graphical
representation of FS - Fourier integrals - convergence of FS - some applications of
Fourier transforms
Unit I: Lagrangian & Hamiltonian Formalism
Hamiltonian variational Principle- Lagrange's equations of motion-Application of
Lagrange's equation-Linear Harmonic oscillator-Particle moving under central force-
Single particle in space - Cartesian & plane polar coordinates - Atwood's machine-
Hamilton's equations of motion -Deduction of Hamiltonian's equation from variational
principle-Application of Hamiltonian's equations of motion- Linear Harmonic oscillator-
Particle moving under central force- A bead on a straight Wire - Atwood's Machine -
Principle of least action
Unit II - Canonical transformations and Poisson brackets
Canonical transformation - Generating function - Properties of canonical transformation
- Poisson bracket - Properties of Poisson bracket - constant of motion using Poisson
brackets - Poisson brackets of canonical variables - Poisson's Theorem. - Invariance of
Poisson bracket under canonical transformation - Motion as successive canonical
transformation (Infinitesimal generators). Harmonic oscillator problem using
infinitesimal generators
Unit III: HJ equation, Central force & Small Oscillations
The Hamilton - Jacobi equation for Hamilton's principle function - Harmonic oscillator
problem using Hamilton's - Jacobi method -Central force - definition and characteristics
- Two body problem - Equation of the orbit - Classification of orbits - Stable & unstable
equilibrium-Lagrange's equation for small oscillations-- Normal modes Normal
frequencies and Normal coordinates - Two masses and three springs - Three coupled
pendulums - Free vibrations of linear triatomic molecule.
Unit IV: Classical Statistics:
Maxwell Boltzmann Distribution Law(no derivation)- Evaluation of Constants-
Maxwell's Law of Distribution of Velocities-Most Probable, Mean, Mean Square and
Root Mean Square Speeds- Principle of Equipartition of Energy-Partition Function- -Total Internal Energy of an Ideal Gas-Molar Heat Capacity of a gas at Constant Volume-
Entropy-Helmholtz Free Energy-Pressure and Equation of State of an Ideal Gas.
Unit V: Quantum Statistics:
Bose-Einstein Distribution Law(no derivation)- B-E Energy Distribution for energies in
the range E to E+dE-Condition for B-E Distribution to approach M-B Distribution-Bose
Temperature- Bose-Einstein Condensation-Planck's Law from B-E Law- Fermi-Dirac
Distribution Law(no derivation)- F-D Law for energies in the range E to E+dE-Fermi
Energy-Effect of Temperature-Energy Distribution Curve-Free Electrons in a Metal-
Comparison of M-B, B-E and F-D Statistics.
Unit I: Equation of Motion & Application of Schrödinger's Equation:
State Vectors-Hilbert Space-Dirac Notation-Dynamical Variables as Operators-Change
of Basis-Unitary Transformation-Equation of Motion in Schroedinger Picture,
Heisenberg Picture & Dirac Picture.
Unit II: Approximate Methods:
Time Independent Perturbation Theory in Non-Degenerate Case-Ground State of Helium
Atom-Degenerate Case-Stark Effect in Hydrogen-Variation Method & its Application to
Hydrogen Molecule-WKB Approximation.
Unit III: Time Dependent Perturbation Theory:
Time Dependent Perturbation Theory-First and Second Order Transitions-Transition to
Continuum of States-Fermi Golden Rule-Constant and Harmonic Perturbation-Transition
Probabilities-Selection Rules for Dipole Radiation-Collision-Adiabatic Approximation
Unit IV: Angular Momentum
Orbital Angular Momentum-Spin Angular Momentum-Total Angular Momentum
Operators-Commutation Relations of Total Angular Momentum with Components-
Ladder Operators-Commutation Relation of Jz with J+ and J- - Eigen Values of J2, Jz -
Matrix Representation of J2, Jz, J+ and J- - Addition of Angular Momenta- Clebsch
Gordon Coefficients-Properties.
Unit V: Relativistic Wave Equation:
Klein Gordon Equation-Plane Wave Equation-Charge and Current Density-Application
to the Study of Hydrogen Like Atom-Dirac Relativistic Equation for a Free Particle-
Dirac Matrices-Dirac Equation in Electromagnetic Field-Negative Energy States.
1. Young's modulus - Corn's method
2. Rydberg constant - hydrogen and solar spectrum
3. Photosensitive devices
4. Tracing of equipotential surfaces
5. Polarizability of liquids
6. Determination of charge of an electron
7. Arc spectra - copper - iron and brass
8. Michelson interferometer - l and d l
9. Compressibility of liquids
10. X-ray powder photograph
11. Hall effect in semiconductors
12. Determination of wavelength of - He-Ne laser/diode laser using reflection grating
and diffraction grating.
13. Refractive index of liquids - using-He-Ne laser/diode laser
14. Determination of optical absorption co-efficient of a material - using
He-Ne laser /diode laser
15. Measurement of laser parameters using He-Ne laser/diode laser
16. To determine the dielectric constant of liquids and solids
Unit - I
Bisection method - Convergence of Bisection method - False position method.
Convergence of False position method - Newton Raphson method - convergence of
Newton Raphson method - Secant method - Convergence of secant method - Method of
successive approximation (Iteration Method) - Convergence of iteration method - Basic
Gauss elimination method - Gauss elimination with partial pivoting - Gauss Jacobi
iteration method - Gauss Seidal iteration method - Inversion of a matrix using Gauss
elimination method.
Unit II
Power method to find dominant eigen value - Inverse power method to find all
eigen values - Jacobi method - (only 2x2 and 3x3 matrices ) Forward Backward and
central differences - Gregory Newton forward and backward interpolation formula for
equal intervals - Gauss forward and backward interpolation formula - Stirling's formula
- Divided differences - properties of divided differences - Newton's divided difference
formula - Lagrange's interpolation formula for unequal intervals - cubic spline
Unit - III
Method of least squares - straight line, parabola, y=axn, y=aebx, y=a+bxn type
curves - sum of squares of residuals for straight line and parabola fit - Newton's forward
and backward difference formula to get the derivatives (First and Second order) -
Divided difference table to calculate derivatives for unequal intervals Newton - cotes
formula - (Trapezoidal rule, Simpson's rule, Simpson's 3/8 rule, Boole`s rule) - Error
estimates in trapezoidal and Simpson's rule - Gaussian Quadrature method.
Unit - IV
Taylor series method for first order differential equation - Basic Euler method -
Improved Euler method - Modified Euler method - Runge Kulta fourth order method -RK4 method for simultaneous first order differential equation RK4 Method for second
order differential equation - Milne's Predictor - Corrector formulae - partial differential
equations - Difference -quotients - Graphical representations of partial quotients -
Classification of partial differential equation of the second order - standard and diagonal
five point formula for Laplace equations - solution of laplace`s equations (Liebmann`s
iterations process)
Unit V
Fortran programming - Flowcharts - Fortran constants Fortran variables -
subscripted variables - Input - Output statements - Control statements (Do, If, Goto
structures) subprograms - Function subprogram - subroutine subprograms simple
applications like, Ascending, descending order, matrix manipulation, character handling,
trapezoidal & Simpson's rule.
Unit I: Scattering Theory
Scattering Amplitude-Expression in terms of Green's Function-Born Approximation and
its Validity-Partial Wave Analysis-Phase Shifts-Scattering by Coulomb and Yukawa
Unit II: Application to Atomic Structure
Central Field Approximation-Thomas Fermi Model-Hartree's Self Consistent Model-
Hartree Fock Equation-Alkali Atoms-Doublet Separation-Intensities-Complex Atoms-
Coupling Schemes
Unit III: Application to Molecular Structure
Hydrogen Molecule Ion-Hydrogen Molecule-Heitler London Method-Covalent Bond-
Spin Orbit Interaction as Correction to Central Field Approximation- Hartree Fock Self
Consistent Field Method for Molecules-Hybridisation.
Unit IV: Theory of Radiation (Semi Classical Treatment)
Einstein's Coefficients-Spontaneous and Induced Emission of Radiation from Semi
Classical Theory-Radiation Field as an Assembly of Oscillators-Interaction with Atoms-
Emission and Absorption Rates-Density Matrix and its Applications
Unit V: Quantum Field Theory
Quantization of Wave Fields- Classical Lagrangian Equation-Classical Hamiltonian
Equation-Field Quantization of the Non-Relativistic Schroedinger Equation-Creation,
Destruction and Number Operators-Anti Commutation Relations-Quantization of
Electromagnetic Field Energy and Momentum.
Unit I:
Basics of crystal physics: Forces between atoms - Cohesive energy of ionic crystals - the
Born Haber cycle - the atomic packing theory - the Laue and Bragg's X-ray diffraction
theory - Ewald construction - the reciprocal lattice and its important properties -
diffraction intensity - the powder, Laue and rotation/oscillation methods of x - ray
Unit II:
Defects in solids and diffusion theory : Point and line defects in solids - surface
imperfections - Fick's law of diffusion - solution to Fick's second law - different
diffusion mechanism - application of diffusion -diffusion in alkali Halides and their ionic
Unit III:
Free electron theory of metals : Drude model of electrical conduction - Lorentz
modification of Drude model - the density of states - Fermi Dirac statistics - effect of
temperature of Fermi Dirac distribution - the electron heat capacity - the Sommerfield
theory of electrical conduction - resistivity in metals - thermionic emission - Hall effect
and its importance
Unit IV:
Phonon theory and thermal conductivity : Lattice vibration of one dimensional mono
atomic and diatomic chains - their dispersion relations - Quantization of lattice vibrations
- inelastic neutron scattering to measure dispersion - classical and quantum theory of
lattice heat capacity (Debye and Einstein theory) - Anharmonic effect.
Unit V:
Band theory and Fermi surfaces : Band theory: Bloch theorem - the Kronig Penney
model - the nearly free electron model - the tight binding model - construction of one,
two and three dimensional Brillouin zones - extended, reduced and periodic zone
schemes - the effective mass of electrons;
Fermi surfaces: Fermi surface in metals - effect of electric and magnetic fields on Fermi
surface - quantization of electron orbit - Anomalous skin effect - the cyclotron
resonance - de Hass von Alphen effect
1. Zener diode Characteristics
2. Regulated power supply - using IC 7809 & 7805
3. IC Regulated dual power supply - using IC 7809 & 7805
4. JFET characteristics
5. JFET amplifier -frequency response
6. Operational amplifier - characteristics
7. Operational amplifier - applications - frequency response
8. UJT Relaxation oscillator
9. A stable multivibrator - using Op. amp and transistor
10. IC 555-Timer - Study of waveforms
11. Logic circuits - using ICs, AND, OR, NOT, NAND & NOR
12. Study of flip - flops - using ICs
13. Decoder and display circuits - LED & Seven segment display
14. D/A and A/D converter
15. Microprocessor Programming
16. Computer Programming
Quantum states of one electron atoms-Atomic orbitals-Hydrogen spectrum-
Pauli's principle-Spectra of alkali elements-Spin orbit interaction and fine structure in
alkali Spectra-Equivalent and non-equivalent electrons.
Normal and anomalous Zeeman effect - Paschen Back effect- Stark effect-Two
electron systems-interaction energy in LS and JJ Coupling-Hyperfine structure
(qualitative)- Line broadening mechanisms (general ideas).
Types of molecules-Diatomic linear symmetric top, asymmetric top and spherical
top molecules-Rotational spectra of diatomic molecules as a rigid rotor-Energy levels and
spectra of non rigid rotor-intensity of rotational lines.
IR Spectroscopy: Practical Aspects-Theory of IR Rotation Vibration Spectra of Gaseous
Diatomic Molecules-Applications-Basic Principles of FTIR Spectroscopy.
Raman Spectroscopy: Classical and Quantum Theory of Raman Effect-Rotation
Vibration Raman Spectra of Diatomic and Polyatomic Molecules-Applications-Laser
Raman Spectroscopy.
NMR Spectroscopy: Quantum Mechanical and Classical Description-Bloch Equation-
Relaxation Processes-Experimental Technique-Principle and Working of High
Resolution NMR Spectrometer-Chemical Shift
ESR Spectroscopy: Basic Principles-Experiments-ESR Spectrometer-Reflection Cavity
and Microwave Bridge-ESR Spectrum-Hyperfine Structure
Unit - I
Theory of semiconductors and dielectrics: Theory of semiconductors:
Classification of semiconductors - direct and indirect semiconductors - intrinsic carrier
densities - population of donor and acceptor levels at thermal equilibrium - extrinsic
semiconductors - temperature dependence on electrical conductivity; Theory of
dielectrics: definition of dielectric constant - sources of dielectric constant
Unit - II
Theory of magnetism in solids: Langevin theory of dia and para magnetism -
Paulis theory of Para magnetism - magnetic resonance - Weis theory of Ferromagnetism -
Ferromagnetic domains - Neel model of antiferro and ferri magnetisms- spin wave theory
Unit- III
Theory of superconductivity: Critical temperature - persistent current - Meissner
effect - London equation - type I and type II superconductors - Energy gaps in
superconductor - BCS theory - theory of Josephson tunneling - elementary knowledge
on high temperature superconductors.
Unit- IV
Growth of thin solid films
Theories of thin film nucleation: the capillary and atomistic model - structural
consequences of thin film nucleation - the four stages of nucleation - thickness
determination by optical interference method - sources of resistivity in metallic thin films
Unit -V
Electrical conduction through thin solid films : Ohmic, Neutral and blocking
contacts of metal insulator interface contacts - effect of surface states on the interface -
tunnel effect through thin film insulators - electrode limited conduction process, Pool-
Frenkel effect - Space charge limited currents in insulator - Negative Resistance effect
and Memory effect - Principles of Hot-Electron thin film devices
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 diode, transfer electron devices (Gunn diode).
Avalanche Transit time devices, Impact diodes, and parametric devices.
Photonic Devices : Radiative and non-radiative transitions. Optical Absorption,
Bulk and Thin film Photoconductive devices (LDR), diode photodetector, 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), diode lasers
(conditions for population inversion, in active region, light confinement factor. Optical
gain and threshold current for lasing,Fabry-Perrot cavity Length for lasing and the
Memory Devices: Static and dynamic random access memories SRAM and
DRAM, CMOS and NMOS, non-volatile - NMOS, magnetic, optical and ferroelectric
memories, charge couple devices (CCD).
Other Electronic Devices: Electro-Optic, Magneto-Optic and Acousto-Optic
Effects. Material Properties related to get these effects. Important Ferro electric, Liquid
Crystal and Polymeric materials for these devices. Piezoelectric, Electrostrictive and
magnetostrictive 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
1. Thin film evaporation
2. Thickness measurement
3. Measurement of capacitance and dielectric loss of thin films and calculation of
dielectric constant
4. Breakdown potential of gases
5. Conductivity of fast ionic conductors
6. Frequency dependence - fast Ionic conductors
7. Construction of a wave function for Schrödinger equation
8. Solution of Schrödinger equation by Fourier Grid Hamiltonian
9. Thickness distribution
10. Fabrication of a thin film capacitor
11. Calculation of band gap energy of semi conducting thin films
12. Measurement of resistance by four probe method
13. Collision cross - section for electrons in the discharge tube
14. Average energy of electrons in the discharge tube
15. Dielectric study of fast ionic conductors
16. Thermo luminescence study of fast ionic conductors
17. Radiation dose measurements
18. Determination of Lennard Jone's potential
19. Determination of equilibrium distance by using the potential function.
Unit I: Electrostatics
Coulomb's law- Gauss law-differential and integral representation- Electric field-
Electric potential- energy density-Method of images-Multipole expansions.
Unit II: Electrostatics in macroscopic media
Potential and Field due to an Electric Dipole-Dielectric Polarization-External Field of a
Dielectric Medium-Guass' Theorem in a Dielectric-Electric Displacement Vector DLinear
Dielectrics-Relations connecting Electric Susceptibility Χe, Polarization P,
Displacement D and Dielectric Constant-Boundary Conditions of Field Vectors-
Molecular Field-Clausius Mosotti Relation for Non-Polar Molecules- Electrostatic
Energy and Energy Density
Unit III: Magnetostatics
Biot-Savart Law- Statement-Lorentz Force Law and Definition of B-General Proof of
Ampere's Circuital Law-Divergence and Curl of B-Magnetic Scalar Potential (derivatives)
of expression only)-Equivalence of Small Current Loop and Magnetic Dipole-Magnetic
Vector Potential (derivation of expression only).
Unit IV: Electromagnetics
Equation of Continuity-Displacement Current-Derivation of Maxwell's Equations-
Physical Significance-Poynting Vector-Momentum in EM Field-Electro Magnetic
Potentials-Maxwell's Equations in terms of EM Potentials-Lorentz Gauge-Coulomb
Gauge- Boundary Conditions at Interfaces-Reflection and Refraction-Fresnel's Laws-
Brewster's Law & Degree of Polarization-Total Internal Reflection and Critical Angle-
Reflection from a Metal Surface-Wave Guides-Rectangular Wave Guide
Unit V
Fluid equations for plasma, equilibrium and stability: Relation of plasma physics
to ordinary electromagnetics, the fluid equations for plasma, fluid drifts perpendicular
and parallel to B, the plasma approximation. Hydromagnetic equilibrium, the concept of
Β, diffusion of magnetic field into a plasma, Classification of instabilities, two stream and
gravitational instabilities.
Unit - I
Properties of nuclear force - Deutron ground state properties - square well
solution for the deuteron - Neutron proton scattering at low energies - scattering length -
phase shift - Proton proton scattering at low energies - Exchange forces - non-central
forces - meson theory of nuclear forceUnit - II
Binding energies of nuclei - Liquid drop model (Weizacker's semi empirical
mass formula) - Bohr-Wheeler theory of fission - Evidences for shell effects (Magic
numbers) - Spin orbit coupling of an electron bound in an atom - spin orbit coupling in
nuclei - single particle shell model - parabolic and square well potential - Predictions of
shell model (stability, spin and parities of ground state, magnetic moments, nuclear
Unit - III
Alpha spectrum and fine structure - alpha decay paradox (barrier penetration) -
Beta decay spectrum - Pauli's neutrino hypothesis - Fermi's theory of beta decay -
selection rules for beta decay - parity non conservation in beta decay - gamma ray
emission - selection rules - multipole radiation - internal conversion - nuclear isomerism
Unit - IV
Kinds of nuclear reactions - conservation laws - nuclear cross section - partial
wave analysis of reaction cross section - compound nucleus - reciprocity theorem -
resonance scattering and reaction cross sections - Breit Wigner dispersion formula
Unit - V
Classification of elementary particles - Fundamental interactions - Quantum
number of individual particles (orbital, spin, isospin, strangeness) - Parity - Charge
conjugation - law of conservation of leptons - law of conservation of baryons -
symmetries and conservation laws - (CPT Theorem) - SU(3) multiplets of Hadrons -
Gellmann Okubo mass formula for SU(3) multiplets
Unit I: Basics of Nanotechnology I
Background to Nanotechnology - scientific revolutions - types of
nanotechnology and nanomachines - atomic structure molecules & phases - molecular
and atomic size - surfaces and dimensional space - top down and bottom up Nanoscale
Unit II: Forces between atoms and molecules
Strong intermolecular forces - covalent and coulomb interactions - interactions
involving polar molecules and polarization - weak intermolecular forces and total
intermolecular pair potentials - Van der Waals forces - repulsive forces; special
interactions such as hydrogen -bonding, hydrophobic and hydrophilic interactions
Unit III: Nanostructures and their properties
Definition of nano systems - dimensionality and size dependent phenomena in
Quantum dots, and Quantum wires - size dependent variation in magnetic, electronic
transport properties
Unit IV: High vacuum technology
Evaporation theory - different sources for evaporation - working principles of
rotary and diffusion pumps - cryogenic pumps - cryo sorption and getter pumps -
vacuum materials
Unit I: Sol-gel processing
Fundamentals of sol-gel process - sol-gel synthetic methods for oxides - other
inorganics and nano composites - the Pecheni method - silica gel - Zirconia and Yttrium
gel - aluminosilicate gel - polymer nano composites
Unit II: Film deposition methods
Introduction - fundamentals of film deposition - thermal evaporation - molecular
beam epitaxy - pulsed laser deposition - sputter deposition - chemical vapour deposition
- layer by layer growth and ultra thin films - chemical solution deposition - Langmuir
Blodgelt films.
Unit III: Synthesis of nanostructures
Surface Chemistry and its role to prepare quantum dots - Polymer as quantum dot
size stabilizer - One-dimensional (1D) by Spontaneous Growth - 1D structure by VLS
and SLS Growth - Template Assisted Growth - Electrochemical growth of 1D structures
Unit IV: New forms of carbon
Types of nanotubes - formation of nanotubes - methods and reactants - arcing in
the presence of cobalt - laser methods - ball milling - chemical vapour deposition
methods - properties of nano tubes - plasma arcing - electro deposition - pyrolytic
synthesis - Zeolites and templated powders layered silicates.
Unit I: Nano characterizing tool 1
Working of Atomic Force Microscopy - Mode of operations (qualitative) and its
application - X-Ray diffraction basics and its application to Size Analysis of
nanomaterials - NMR Basics and application to Nanomaterials
Unit II: Nano characterizing tool 2
Scanning Electron Microscope: Theory- Instrumental setup and its application -
Low KV SEM and its application - Low temperature SEM and its application - working
of electron probe micro analysis and its application in elemental analysis - EDX spectra
Important material systems - optical process in semiconductors - optical process
in quantum wells - semiconducting optoelectronic devices - organic optoelectronic
devices (qualitative)
Unit III: Applications of nanomaterials
Quantum dot IR photo detectors- Quantum dot lasers - Synthesis of Zinc oxide
nanomaterials and its application - Synthesis of group three nitride nanostructures and
their applications - SK growth of germanium dots on silicon and its application.
Unit IV: Cell Biology (quantitatively)
Amino acids, Protein structure: Primary, Secondary, teritary, structure of Nucleic
acids - Nucleosides and Nucleotides - physical properties of nucleosides & nucleotides -
base pair - mismatch base pair - stacking - Backbone of Nucleic acids
Antibodies and their use in nano based drug delivery and imaging - Tumor
targeted drum delivery.
1. Preparation of nano particles by chemical method.
2. Preparation of nano materials by vacuum coating unit.
3. Preparation of nano particles by ball milling method.
4. Processing of particles by plasma torch
5. Characterization of size of nano particles.
6. Characterization of nano particles by using LCR bridge.
7. Construction of virtual bio nanobulas.
8. Interactions of water molecules with bio nanotubes.
9. Polymer nanocomposite

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