Govt College for Women (Auto)

GOVT COLLEGE FOR WOMEN (AUTO)

KUMBAKONAM

DEPARTMENT OF PHYSICS

PG CBCS 2008-09

I

II

Total Hours-120

Credit-90

Marks-1900

M.Sc., Physics-Syllabus

CCI-CLASSICAL DYNAMICS AND RELATIVITY

UNIT-I :

Fundamental Principles and Lagrangian Formulation:

Mechanics of a particle and system of particles –Conservation laws-Constraints-Generalized coordinates –D’Alember’s principle and Lagrange’s equation-Hamiltonian Principle –Lagrange’s equation of motion

UNIT-II :

Lagrangian formulation : Applications

a.)Rigid body dynamics

Euler angles-Moments and products of inertia-Euler’s equations-Symmetrical top.

b.)Oscillatory Motion

Theory of small oscillations-Normal modes and frequencies-Two coupled harmonic oscillators

Wave motion-Wave equation-Phase velocity-group velocity-Dispersion

UNIT III:

Hamilton’s Formulation

Hamilton’s canonical equations of motion-Hamilton’s equations from variational principle-Principle of least action-Canonical transformations-Poisson brackets-Hamilton-Jacobi method.

UNIT-IV :

Nonlinear Dynamics

Dynamical systems- mathematical implications of nonlinearity- definition and defects of non linearity- regular and chaotic motion-linear and nonlinear oscillators, phase trajectories- fixed points and limit cycles-period doubling bifurcation and onset of chaos in logistic map-solitons-experiments of Kruskal and Zabusky on Kdv equation-block diagram of IST and description.

UNIT V:

Relativity

Review of basic ideas of special theory of relativity- energy momentum four vector- Minkowski’s four dimensional space-four and energy equations in relativistic mechanics-Lagrangian formulation in relativistic mechanics-Invariance of Maxwell’s equations under Lorentz transformation.

BOOKS FOR STUDY

1. Classical Dynamics-Gupta Kumar

1. Classical Dynamics-Sathya Prakash
2. Non linear dynamics-M.Lakshmanan

BOOKS FOR REFERENCE

Relevant chapters in

1. H.GOLDSTEIN, Classical mechanics, Narosa Book distributors, New Delhi(1980)
2. N.C. RANA and P.S.JOAG, Classical mechanics, Tata Mc Graw Hill, New Delhi

CCII – MATHEMATICAL PHYSICS-I

UNIT I: Vector Fields

Gauss theorem, green’s theorem, Stoke’s theorem and applications- Orthogonal Curvilinear coordinates-Expression for Gradient, Divergence, Curl and Laplacian in cylindrical and spherical coordinates.

UNIT II: Vector spaces

Definitions-Linear independence and linear dependence of vectors-Schmitt Orthogonalisation process-Schwartz inequality.

Tensors

Transformation of coordinates – Summation convention - Contravariant, Covariant, mixed tensors and Invariant tensors- Rank of a tensor - Symmetric and antisymmetric tensor – contraction of tensor – Metric tensor.

UNIT III : Matrix theory:

Solution of linear algebraic equations – Rank of a matrix – Characteristics equation of a matrix – Eigen values and Eigen vectors – Cayley – Hamilton theorem – Reduction of a matrix to diagonal form – Hermitian and unitary matrices – Direct sum and products of matrices – Sylvester’s theorem – Function of matrices.

UNIT IV : Ordinary Differential Equations

Linear ordinary differential equations – Elementary methods – Linear second order differential equations with variable coefficients – Frobenius method – Variation of parameters Sturm – Liouville differential equation.

UNIT V: Partial Differential Equations

Method of forming partial differential equations – Solutions by direct integration – Method of separation of Variables – Special types of differential equations arising in Physics – Diffusion equation – Wave equation.

BOOKS FOR STUDY :

1. Mathematical Physics-B.D. Guptha
2. Mathematical Physics- Sathya Prakash
3. Mathematical Physics- P.K. Chattpadhay
4. Mathematical Physics- A.K. Ghattak.T.C.Goyal&S.J.Chua
5. Matrices & Tensors in Physics – A.w.Joshi.

Books for reference

Relevant chapters in

1. G.ARFKEN and H.J. WEBER, Mathematical Methods for Pyhsicists 4th ed prism Books, Bangalore(1995)
2. M.D. GREENBERG,Advanced engineering mathematics, 2nd edition International ed Prentice- Hall international,NJ(1998)
3. E.Kreyszig, Advanced Engineering Mathematics, 8th ed.Wiley,NY,(1999).

CCIII STATISTICAL MECHANICS

UNIT I: Thermodynamics

Energy and First law of thermodynamics – heat content and heat capacity – Specific heat – entropy and the second law of thermodynamics – thermodynamic potentials and the reciprocity relations – Maxwell’s relation – Properties of thermodynamic relations – Gibb’s Helmholtz relation – thermodynamic equilibrium – Nernst Heat theorem.

UNIT II : Kinetic theory

Distribution function and its evolution – Boltzmann ‘stransport equation and its validity – Boltzmann’s H – theorem – Maxwell – Boltzmann ‘s distribution – Transport phenomena – Mean free path.

UNIT III : Classical Statistical Mechanics

Introduction – Phase space and ensembles – Density function – Liouville’s theorem – Maxwell – Boltzmann distribution law – Micro canonical ensemble – Ideal gas – Entropy – Partition function – Principle of equipartition of energy – Canonical and grand canonical ensemble.

UNIT IV : Quantum Statistical Mechanics

Basic Concepts – Bose – Einstein and Fermi – Dirac Statistics – Distribution laws – Equations of state – Bose – Einstein condensation.

UNIT V: Applications of Q.S.M.

Ideal Bose gas: Photons – Black body and planck radiation – Photons – Specific heat of solids – Liquid Helium.

Ideal Fermi gas : Properties – Degeneracy – Electron gas – Pauli paramagnetism

Books for study Relevant Chapters in

1. Fundamental of Statistical and thermal Physics – FREDERIC REIF.
2. Statistical Mechanics – Guptha Kumar & Sharma
3. Statistical Mechanics – Sathya Prakash & Agarwal.

Books for reference:

1. Statistical Mechanics (Wiley Eastern Limited, New Delhi,1963) – K.HUANG
2. Statistical Mechanics (Wiley Eastern Limited, New Delhi,1994) – B.K.AGARWAL and M.EISNER.
3. Thermodynamics (Narosa, New Delhi,1989)- N. SEARS and L.SALINGER
4. Thermodynamics and Statistical Mechanics (Springer, New York, 1995)-

W. GREINER, L. NEISE and H. STOCKER.

CCIV GENERAL EXPERIMENTS

ANY 12 EXPERIMENTS

1. Determination of q,, - Elliptical Fringes.
2. Determination of q,, - Hyperbolic Fringes.
3. Determination of Stefan’s Constant.
4. Hartmann’s Formula – Wavelength calculation.
5. Lecher wire – Dielectric constant determination.
6. e/m – Magnetron method
7. e/m – Thomson method.
8. Plank’s constant – Photoelectric effect.
9. Biprism – Wavelength determination – scale and Telescope method.
10. Spectrometer – Hydrogen Spectrum – Rydberg’s Constant.
11. Spectrometer – Polarisability of liquids.
12. Spectrometer – Charge of an electron.
13. Biprism – Determination of Refractive index.
14. Polarimeter – Determination of Specific rotatory power of a liquid.
15. Four probe method – Determination of resistivities of the given samples.
16. Forbe’s method – Determination of thermal conductivity.
17. Michelson’s interferometer – Determination of Wavelength of monochromatic source.
18. B-H loop – Energy loss of the magnetic material – Anchor ring using BG.
19. Determination of L of a coil using Anderson’s method.

ECI-ELECTRONICS

UNIT I: IC Fabrication and Operational amplifier

Basic monolithic Ics- epitaxial growth- masking- etching-impurity diffusion- Fabricating monolithic resistors ,diodes, Transistors, inductors and capacitors – circuit layout – contacts and interconnections. Op- amp characteristics – Inverting and non inverting amplifier – voltage follower – summing and Difference amplifier – integrating and differential circuits – log and antilog amplifiers – Op – amp as Comparator – active filters – low pass, high pass, band pass and band Rejection filters – solving simultaneous and differential equations.

UNIT II: Op – amp Applications (Oscillators and Convertors)

Wien bridge, Phase shift Oscillators and twin-T oscillators – triangular, Saw – tooth and square wave generators – Schmitt’s trigger – Sample and Hold circuits – voltage control oscillator – phase locked loops – basic D to A conversion: weighted resister DAC – binary R-2R ladder DAC – basic A to D Conversion: counter type ADC – successive approximation converter – dual slope ADC.

UNIT III: Microprocessor architecture and software programs

8085 Microprocessor architecture – various registers – central processing unit of micro computers – timing and control unit – instruction and data flow – system timings – examples – Instruction set – Data transfer group – logical group – branch group – stack and I/O control instructions – addressing modes.

BCD arithmetic programs – searching and array of a given number – choosing the biggest and smallest numbers from a list – ascending and descending orders – square root of a Microprocessor number – Time delay – square wave generator.

UNIT IV: Interfacing memory and I/O devices

Interfacing memory and devices – I/O and memory mapped I/O – Type of Interfacing devices – Data transfer schemes – Programmed and DMA data transfer schemes – programmable peripheral interface(8255A) – 8253 Timer Interface –DMA controller – Programmable Interrupt controller(8259) –Programmable communication Interface(8251).

UNIT V: Microwaves and Colour Television

Microwave generation and applications

Klystron – Magnetron – Microwave propagation through wave guides – Crystal detection – measurement of SWR – Transmitters and receivers.

Colour Television

Introduction – Perception – Three colour theory – luminescence – TV camera – Image Orthicon – Vidicon – LCD Colour Television.

BOOKS FOR STUDY

Relevant chapters in

1. J.MILMAN and C.C. HALKIAS, Integrated Electronics, Mc Graw Hill (1972).
2. R.P. JAIN,Integrated Electronics, Mc Graw Hill.
3. B. RAM, Fundamentals of Microprocessors and Micro computers(Dhanapet Rai and sons, New Delhi, 1995).
4. R. R. GULATI, Monochrome and Colour Television(Wiley Eastern, New Delhi, 1995).

Books for reference

1. R.A. GAYAKWAD,OpAmps and linear integrated circuits, printice Hall India pvt Ltd(1999).
2. G. KENNEDY, Electronic communication system, Tata Mc Graw Hill Ltd, New Delhi(1995).
3. R. GOANKAR, Microprocessor architecture, programming and applications (Wiley Eastern, New Delhi, 1985).

CCV – MATHEMATICAL PHYSICS – II

UNIT I: Complex Analysis

Functions of complex variables – Differentiability – Cauchy Riemann conditions – Complex integration – Cauchy’s integral theorem and integral formula – Taylor’s and Laurent’s Series – Residues and Singularities – Cauchy’s residue theorem – Evaluation of definite integrals.

UNIT II: Integral Transforms

Fourier series – Drichlet’s conditions – Determination of Fourier Coefficients – Fourier integrals – Fourier transforms – Faltung theorem – Application to heat and wave equations – Laplace transform – Convolution theorem – solution of ordinary differential equations.

UNIT III: Green’s Function Techniques and Integral Equations

Green’s Function – Properties – Methods of solutions in one dimension – Applications – Linear integral equations – Fredholm and Volterra type – Neumann series – Eigen function expansion – Applications.

UNIT IV: Special Functions

Gamma and Beta functions – Sturm Liouville problem – Legendre, associated Legendre, Bessel, Laugerre and Hermite Differential equations: Series solutions – Rodriguez formula – generating functing – Orthogonality relations – important recurrence relations.

UNIT V: Group Theory

Basic definitions – Multiplication table – sub groups, cosets and classes – direct product groups – point groups – space groups – representation theory – Homomorphism and isomorphism – reducible and irreducible representations – Schur ‘s Lemma – the great

Orthogonality theorem – character table – C3v and D3h as examples – elementary ideas of rotation groups.

BOOKS FOR STUDY

1. Mathematical methods for Physicists & Engineers – Joshi
2. Mathematical Physics – Sathya Prakash
3. Mathematical Physics – B.D. Gupta
4. A.W. JOSHI, Elements for Group Theory of Physicists (Wiley Eastern, New Delhi,1971)

Relevant chapters in

Books for reference:

1. L.A. PIPES and L.R. HARVILL, Applied Mathematics for Engineers and Physicists(Mc Graw Hill, Singapore,1970)
2. E. KREYSZIG, Advanced Engineering Mathematics(Wiley Eastern, New Delhi,1983)
3. G. ARFKEN and H.J. WEBER, Mathematical Methods for Physicists (Prism Books, Bangalore
4. A.K. GHATAK, I.C. GOYAL and A.J.CHUA, Mathematical Physics (McMillan, New Delhi,1995)
5. P.K. CHATTTOPADHYAY,Mathematical Physics(Wiley Eastern, New Delhi, 1990)
6. W.W. BELL, Special functions for Scientists and Engineers (Van Nostrand, New York, 1968)

CCVI – QUATUM MECHANICS

UNIT I: Schroedinger Equation and General Formulation

Schroedinger Equation – Physical meaning and conditions on the wave function – Expectation values and Ehrenfest’s theorem – Hermitian operators and their properties – Commutatos relations – Uncertainty relation – Bra and Ket vectors – Hilbert space –Schrodinger, Heisenberg and interaction pictures.

UNIT II: Exactly Solvable Systems

Linear harmonic oscillator – Solving the one dimensional Schrodinger equation – Abstract operator method – Particle in a box – Square well potential – Rectangular barrier potential – Rigid rotator – Hydrogen atom.

UNIT III: Approximation Methods

Time independent perturbation theory: Non-degenerate perturbation and to tunneling problem and quantization rules.

Time dependent perturbation theory: Harmonic perturbation – transition probability.

UNIT IV: Scattering theory and Angular momentum

Scattering theory: Scattering cross section – green’s function approach – Born approximation – Partial wave analysis.

Angular momentum: Matrix representation of J – Spin angular momentum – Eigen values – addition of angular momenta – Clebsch – Gordan coefficients (basic ideas only).

UNIT V: Relativistic Quantum Mechanics

Klein – Gordon equation for a free particle and in an electromagnetic field – partial wave solutions – Dirac equation for a free particle – charge and current densities – Dirac matrices – plane wave solutions – Negative energy states – spin angular momentum – spin – orbit coupling

BOOKS FOR STUDY

1. P.M. MATHEWS and K. VENKATESAN, A text book of Quantum mechanics, (Tata Mc Graw Hill, New Delhi,1987).
2. Quantum mechanics – Gupta Kumar
3. Quantum mechanics – Sathya Prakash
4. Theory & Problems of Quantum mechanics – Schaum outline series.

Books for reference

1. L. SCHIFF, Quantum mechanics (Tata Mc Graw Hill, New Delhi,1968).
2. V. K. THANKAPPAN,Quantum mechanics(Wiley – Eastern, New Delhi,1985)
3. J. SINGH, Quantum mechanics: Fundamentals and applications to technology(John –Wiley, New York, 1997)
4. A. GOSWAMI, Quantum mechanics (W.C. Brown, Dubuque, 1992).

CCVII – ELECTRONICS EXPERIMENTS

ANY 12 EXPERIMENTS

1. Construction of Power Supply – Bridge rectifier.
2. Feed – back Amplifier.
3. Darlington Pair Amplifier.
4. Phase – shift oscillator.
5. Characteristics of UJT.
6. Common Source FET Amplifier.
7. Relaxation Oscillator – UJT.
8. Operational Amplifier – Parameters (Input impedance, Output impedance, Offset voltage).
9. Operational Amplifier – Parameters (Inverting, Non inverting, Unit gain and closed loop gain)
10. Operational Amplifier – Summing and Difference Amplifiers.
11. Operational Amplifier – Differentiating and integrating circuits.
12. Dual Power supply – Construction.
13. Bistable Multivibrator.
14. Common Drain FET amplifier.
15. Wein’s bridge oscillator.
16. SCR characteristics.
17. Operational amplifier filters.
18. DIAC, TRIAC Characteristics.

ELECTIVE COURSE II – PROGRAMMING IN C++

UNIT I

Principles of object oriented programme (OOP) – software evolution – object oriented programming paradigm – Basic concepts of oop’s – Benefits fo oop’s. Introduction to C++ - tokens – keyword’s – identifiers – variables – operators – Manipulators Expressions.

UNIT II

Control structures in C++ - functions in C++ - Main function – Function prototyping – Call by Reference – Return by reference – Function Overloading – Friend and virtual functions.

UNIT III

Classes and objects : Species – passing object as Function arguments – Friend functions – Constant Member functions – special member functions Constructors

- Destructors – Operator Overloading – Rules for Overloading operator – type conversions

UNIT IV

Inheritance: Single Inheritance – multilevel Inheritance – Multiple Inheritance – Hierarchical Inheritance.

Pointers – Virtual functions and polymorphism – Managing console I/O operators.

Working with Files: Classes for file stream operators – Opening and closing a file – End – of – file, deduction – file pointers updation a file Handling during file operations – Command line arguments.

UNIT V: Programs

1. Arranging words in alphabetical order.
2. Picking Largest and smallest of a set of numbers
3. Solving Quadratic equation
4. Multiplication of two square matric
5. Least square curve fitting
6. Integration – Simpson’s rule
7. To find the determinant of a matric
8. To find the inverse of a matric
9. Solution of differential equation by runge Kutta 11th order method
10. To solve simultaneous equations by Gauss Elimation method

Books for study and reference:

1. Object oriented programming in C++ E. Balagurusamy

Non Major Elective Course -LASER AND APPLICATIONS

UNIT I:

Lasers- Characteristic properties – Directionality – intensity – Monochromaticity – Coherence – Principles of lasers – Absorption – Spontaneous emission – Stimulated emission – Einstein’s theory of stimulated emission – Population inversion – Methods of achieving population inversion – Schawlow and Townes Threshold condition.

UNIT II:

Types of lasers – Solid state lasers – Ruby laser – Construction and working – Semiconductor – GaAs Laser – Advantages – Gas lasers – He –Ne laser – Working principle – Energy level diagram – Argon ion laser – Helium cadmium laser – Molecular gas laser – CO2 laser – Principle – Construction and working.

UNIT III:

Continuous wave and pulsed lasers – Nd – YAG laser – Tunable laser – Q switching – Mode locking – Frequency doubling – Laser materials – Preparation and testing.

UNIT IV:

Application of lasers – Interferometry – Testing of optical systems – Holography – Lasers in communication – In computers – Weapons –Medical applications – Industrial applications.

Books for study and reference:

1. Lasers and their applications Beesley, Taylor and Francis, London

2. Lasers principles and applications J.Wilson, J.F.B.Hawkers, Prentice Hall, 1987

Non Major Elective Course– ASTROPHYSICS

UNIT – I:

Structure of the solar system – Data on planets and orbits – Planetary cosmology – Laplace hypothesis – Jean’s hypothesis – Schmidt’s theory – First and second stage of evolution – Origin of proto- Planetary cloud – Composition of planets.

UNIT – II:

Eclipses – Solar – Lunar – Asteroids, Meteoroids and Comets – Structure of comets – Internal constitution of the earth – Age of the earth.

UNIT III:

Cosmology: Galactic structure and Kinenatics – Galary –Elements of cosmology – Cosmology from general relativity – Red shift – Hubble constant and age crisis – Steady stat universe.

Books for study and reference:

1. Astronomy and Astro physics with V.B.Bhatia, Narosa publishing house, 2001

Elements of cosmology

1. A different approach to cosmology F.Hoyle, G.Burbidge & J.V. Narlikar,

Cambridge University

CCVIII – ATOMIC AND MOLECULAR PHYSICS

UNIT- I : Atomic Spectra

Quantum states of electron in atoms – Hydrogen atom spectrum – Electron spin – Stern – Gerlach experiment – Spin orbit interaction – Two electron systems – LS – JJ coupling schemes – Fine structure – Spectroscopic terms and selection rules – Hyperfine structure – Exchange symmetry of wave functions – Pauli’s exclusion principle – Periodic table – Alkali type spectra – Equivalent electrons – Hund’s rule.

UNIT –II: Atoms in external fields and Quantum Chemistry

Quantum chemistry of molecules: Covalent, ionic and Waals instructions – Born Oppenheimer approximation – Heitler – London and molecular orbital theories of H2 – Bonding and anti bonding – MOS Hartee fock equation self consistent field – Huckel’s molecules approximation – Application to Butadiene and Benzene.