PHYSICS, Paper - II
(English Version)
Time: 3 Hours Max. Marks: 60
SECTION-A
Note: i) Answer all questions. [2 x 10 = 20M]
ii) Each question carries two marks.
iii) All are very short answer type questions.
1. What are the Fraunhofer lines? State any two of their significances.
2. Mention any applications of diffraction?
3. Two magnetic poles of strength 40Am and 10Am are separated by a distance of 20cm in air. Find the force between them.
4. The potential of the earth is taken as zero. Explain.
5. On what factors does the resistance of a conductor depend?
6. What is a thermocouple? Write one of its uses.
7. How do you convert a moving coil galvanometer into a voltmeter?
8. What type of transformer is used in a bed lamp?
9. Define Modulation. Why is it necessary?
10. Draw the circuit symbols for p-n-p and n-p-n transistors.
SECTION-B
Note: i) Answer any six of the following questions. [6 x 4 = 24M]
ii) Each question carries four marks.
iii) All are short answer type questions.
11. Explain the construction and working of a Ramaden's eyepiece with a neat diagram.
12. State and explain the "Tangent Law" in magnetism.
13. Define intensity of electric field E and potential difference V. Derive the relationship between them.
14. Derive the balancing condition of a Wheatstone bridge.
15. Write short notes on the working principle of a thermopile?
16. Define the terms, work function and threshold frequency.
17. Write a short note on the discovery of a neutron.
18. What are n-type and p-type semiconductors? How is a semiconductor junction formed?
SECTION-C
Note: i) Answer any two of the following questions. [8 x 2 = 16M]
ii) Each question carries eight marks.
iii) All are long answer type questions.
19. State the laws of transverse vibrations in stretched strings. Describe and explain the experimental verification of the laws using a sonometer.
Problem:A wire length of 1m and mass 20kg is stretched with a force of 800N. Find its fundamental frequency.
20. Describe a tangent galvanometer with its necessary theory. Compare it with a moving coil galvanometer.
21. Explain the principle and working of a nuclear reactor with the help of a labeled diagram.
Problem:How much ²³5U is consumed in a day in an atomic power house operating at 400MW, provided that whole of the mass of the ²³5U is converted into energy?
Maxwell’s equations –General wave equation-Propagation of light in isotropic dielectric medium – dispersion –Propagation of light in conducting medium –Skin depth –Reflection and refraction at the boundary of a dielectric interface-Fresenel’s equations-Propagation of light in crystals – double refraction.
Electromagnetic Radiation –Retarded Potentials –Radiation from an Oscillating dipole –Linear Antenna –Lienard-Wiechert Potentials.
UNIT-II Lasers
Lasers: Introduction – directionality- brightness- monochromacity- coherence – relation between the coherence of the field and the size of the source – absorption and emission processes - the Einstein coefficients - amplification in a medium- laser pumping Boltzman’s principle and the population of energy levels – attainment of population inversion - two level – three level and four level pumping . Optical feedback: the optical resonator laser power and threshold condition confinement of beam within the resonator – stability condition.
Laser output: Absorption and emission - shape and width of broadening lines – line broadening mechanisms – natural, collision and Doppler broadening.
Types of Lasers: Ruby laser, He-Ne Laser, CO2 laser, Semiconductor GaAs laser, applications of lasers.
UNIT –III Non linear Optics and Holography
Basic Principles- Harmonic generation – Second harmonic generation- Phase matching –Third Harmonic generation-Optical mixing –Parametric generation of light –Parametric light oscillator-Frequency up conversion-Self focusing of light.
Introduction to Holography-Basic theory of Holography-Recording and reconstruction of Hologram-Diffuse object illumination-Speckle pattern –Fourier transform Holography-Applications of Holography.
UNIT-IV Fiber Optics
Fiber Optics : Introduction – total internal refraction –optical fiber modes and configurations- fiber types – rays and modes- Step index fiber structures – ray optics representation – wave representation – Mode theory for circular wave guides- wave guide equations – wave equations for step indexed fibers – modal equation – modes in step indexed fibers – power flow in step indexed fibers . Graded indexed fiber structure : Structure – Numerical aperture and modes in graded index fibers- Signal degradation in optical fibers – attenuation – losses – absorptive scattering – and radiative – core cladding – Signal distortion in optical wave guides – Information capacity determination – Group delay – Material dispersion – wave guide dispersion – inter modal dispersion – pulse broadening . Preparation of different techniques of optical fibers
Reference Books:
1.Introduction to Electrodynamics , D.J.Griffiths, Prentice-Hall, India
2.Electromagnetics, B.B.Laud, Wiley –Eastern, New Delhi.
3.Modern Optics, Fowels
4.Laser and their applications, M.J.Beesly, Taylor and Francis, 1976.
5.Laser and Non-Linear Optics, B.B.Laud, Wiley Eastern Ltd.,1983.
6.Optics , E.Hecht, Addison Wiley, 1974.
7.Optical fibers communications, Gerel Keiser, McGraw Hill Book, 2000.
NOTE : Question paper contains 5 questions. FOUR questions with internal choice have to be set from each unit. The 5thquestion has 4 short answers question covering units I to IV and any two be answered.
M.Sc (IV Semester)
Paper-II Molecular and Solid State Spectroscopy
UNIT -I
Molecular States :Molecular Quantum numbers and classification of electronic states. Hund’s coupling cases ‘a’ and ‘b’. Symmetry adapted linear combination (SALC) of atomic orbitals of individual atoms and the resulting molecular orbitals, electronic configuration and ground states of linear molecules H2 , C2 , N2 ,O2 and CO2 and non-linear molecules H2CO and H2O . Symmetry properties of electronic and rotational levels. ( Ch. 6.2, 6.3 )
ROTATIONAL SPECTROSCOPY: Microwave spectrum of a diatomic molecule. Rigid
rotator and non-rigid rotator approximations. The effect of isotopic substitution. Vibrational satellites . Moment of Inertia and bond lengths of diatomic and linear triatomic molecule. Quantum theory and mechanism of Raman scattering. Rotational Raman spectra. Symmetry properties of rotational levels of 1S states. Influence of nuclear spin and statistical weights on pure rotational Raman spectra of CO2 , O2 , H2, D2 .(Ch. 1.3, 4.2, 4.4, 4.8)
UNIT-II
VIBRATIONAL SPECTROSCOPY: The vibrating-rotating diatomic molecule. Harmonic and anharmonic oscillator energy levels. Evaluation of rotational constants from Infrared spectra .Evaluation of rotational constants from Raman vibration–rotation spectra. Vibrational modes of CO2 and the influence of nuclear spin on Infrared and Raman vibration-rotation spectrum of CO2. (Ch. 5.1, 5.2.4)
MOLECULAR VIBRATIONS: C2v and C3v Character tables from the properties of irreducible representations. Relationship between reducible and irreducible representations. C2V character table: Symmetry types of translational, rotational and binary products. Reducible representation, vibrational modes and their activity (allowed and forbidden fundamentals, overtones and combination bands in IR and Raman) of H2O, NH3, and formaldehyde molecules.
ELECTRONIC SPECTROSCOPY OF DIATOMIC MOLECULES:
Vibrational analysis of an electronic band system of a diatomic molecule. Progressions and sequences. Deslandres table and vibrational constants. Isotope effect in vibrational spectra and its applications.
Rotational analysis: Selection rules and rotational fine structure of vibronic transistions. The fortrat diagram and the band head. Combination relations and evaluation of rotational constants for bands (1S - 1S ) having only P and R branches. Ch. 6.2.
UNIT-III
NMR Theory, Basic Principles, Nuclear spin and Magnetic moment, Relaxation mechanism, spin lattice and spin-spin relaxation(12) times by pulse methods, Bloch’s equations and solutions of Bloch’s equations – Experimental methods, CW NMR Spectrometer.
Electron Spin Resonance – The ESR spectrometer, experimental methods, thermal equilibrium and Relaxation methods, characteristics of g and A values, Unpaired electron, fine structure and Hyperfine structure
UNIT IV
Nuclear quadrupole resonance (NQR) spectroscopy, The fundamental requirements of NQR spectroscopy, General principles, Integral spins and Half Integral Spin., experimental detection of NQR frequencies, block diagram of NQR spectrometer, Experimental methods of SR oscillator, CW oscillator, pulse methods.
Mossbauer spectroscopy: The Mossbauer Effect, Recoil less Emission and Absorption, The Mossbauer spectrometer, Experimental Methods, Chemical shift, Magnetic Hyperfine interactions.
Photo Electron Spectroscopy, its theory, instrumentation and Applications.
Books:
High resolution Spectroscopy (Butterworths) J.M.Hollas.
Molecular spectra and Molecular Structure (van Nostrand) – G.Herzberg
Introduction to atomic spectra – H.E. White(T)
Fundamentals of molecular spectroscopy – C.B.Banwell (T)
Nuclear Magnetic Resonance By E R Andrew, Cambridge University Press 1955
Spectroscopy by B.P. Stranghon and S.Walker Volume 1 John Wiley and Sons Inc.,
New York, 1976
Pulse and Fourier transform NMR by TC farrar and ED Becker, Academic Press 1971
Mossbauer Spectroscopy – M.B. Bhide.
NOTE : Question paper contains 5 questions. FOUR questions with internal choice have to be set from each unit. The 5thquestion has 4 short answers question covering units I to IV and any two be answered.
M.Sc,.(IV Semester)
Paper-III Condensed Matter Physics-III
Unit-I
Classification of Materials: Types of materials, Metals, Ceramics (Sand glasses) polymers, composites, semiconductors.
Metals and alloys: Phase diagrams of single component, binary and ternary systems, diffusion, nucleation and growth. Diffusional and diffusionless transformations. Mechanical properties. Metallic glasses. Preparation, structure and properties like electrical, magnetic, thermal and mechanical, applications.
Unit-II
Glasses : The glass transition - theories for the glass transition, Factors that determine the glass-transition temperature. Glass forming systems and ease of glass formation, preparation of glass materials.
Applications of Glasses: Introduction: Electronic applications, Electrochemical applications, optical applications, Magnetic applications.
Unit-III
Biomaterials - Implant materials: Stainless steels and its alloys, Ti and Ti based alloys, Ceramic implant materials; Hydroxyapatite glass ceramics, Carbon Implant materials, Polymeric Implant materials, Soft tissue replacement implants, Sutures, Surgical tapes and adhesives, heart valve implants, Artificial organs, Hard Tissue replacement Implants, Internal Fracture Fixation Devices, Wires, Pins, and Screws, Fracture Plates.
Unit-IV
Liquid Crystals: Mesomorphism of anisotropic systems, Different liquid crystalline phases and phase transitions, Few applications of liquid crystals.
Nanomaterials
Different types of nano crystalline materials: nano crystalline metals, nano crystalline ceramics, Mesoporous materials, Carbon nanotubes, nano-coatings, zeolites, quantum dot lasers, nano structured magnetic materials; Synthesis of nanomaterials: Vacuum synthesis, sputtering, laser ablation, liquid metal ion sources, Gas-Phase synthesis, condensed-phase synthesis Characterization methods: XRD and TEM, Properties of Nanostructure materials, Electrical and mechanical properties Optical properties by IR and Raman spectroscopy. Applications of nanomaterials
Text books
1 Inorganic solids D. M. Adams (John-Wiley)
2 Physics of Amorphous Materials by S.R.Elliott.
3 Phase transformation in metal and alloys, D. A. Porter and K. E. Easterling
4 Fundamental of thermotropic liquid crystals deJen and Vertogen
5 Nanocrystalline materials- H. Gleiter
6 . Biomaterials Science and Engg. J.B. Park
7. Materials Science and Engg. – C. M. Srivastava
NOTE : Question paper contains 5 questions. FOUR questions with internal choice have to be set from each unit. The 5thquestion has 4 short answers question covering units I to IV and any two be answered.
M.Sc. Physics (IV Semester)
Paper IV : Condensed Matter-IV
UNIT I
Lattice Dynamics and Optical properties of Solids
Inter atomic forces and lattice dynamics of simple metals, ionic and covalent crystals. Optical phonons and dielectric constants. Inelastic neutron scattering. Anhormonicity, thermal expansion and thermal conductivity. Interaction of electrons and phonons with photons., Direct and indirect transitions.
UNIT II
Crystal growth techniques: Bridgeman-Czochralski-liquid encapsulated czochralski (LEC) growth technique-zone refining and floating zone growth-chemical vapour deposition (CVD)-Molecular beam epitaxy(MOVPE)-vapour phase epitaxy-hydrothermal groth-Growth from melt solutions-Flame fusion method.
UNIT III
Absorption in insulators, Polaritons, One – phonon absorption, optical properties of metals, skin effect and anomalous skin effect. Interaction of electrons with acoustic and optical phonons, polarons.
UNIT IV
Superconductivity: The Meissner effect –- Isotope effect- specific heat-thermal conductivity and manifestation of energy gap. Quantum tunnelling-Cooper pairing due to phonons, BCS theory of superconductivity, Ginzsburg-Landau theory and application to Josephson effect: d-c Josephson effect, a-c Josephson effect, macroscopic quantum interference. Vortices and type I and type II superconductors, applications of superconductivity-high temperature superconductivity (elementary).
Text and Reference Books
Madelung : Introduction to Solid State Theory.
Callaway : Quantum theory of Solid State.
Huang : Theoretical Solid State Physics
Kittel : Quantum theory of Solids
Solid state Physics by Guptha Kumar and Sarma
Solid State Physics S.O.Pillai New Age International
NOTE : Question paper contains 5 questions. FOUR questions with internal choice have to be set from each unit. The 5thquestion has 4 short answers question covering units I to IV and any two be answered.
Objective of studying Nuclear Physics, Nomenclature, nuclear radius, mass & Binding energy, angular momentum, magnetic dipole moment, Electric quadrupole moment, parity and symmetry, domains of instability, Energy levels, mirror nuclei.
2. NUCLEAR FORCES :
Characteristics of Nuclear Forces- Ground state of deuteron, scattering cross-sections, qualitative discussion of neutron-proton and proton- proton scattering at low energies- charge independence, spin dependence and charge symmetry of nuclear forces - exchange forces and tensor forces- Meson theory of nuclear forces( Yukawa’s Potential).
UNIT-II
3.NUCLEAR MODELS:
Weisazacker’s semi-empirical mass formula- mass parabolas- Liquid drop model -Bohr –Wheeler theory of nuclear fission - Nuclear shell model : magic numbers, spin orbit interaction, prediction of angular momenta and parities for ground states, Collective model., More-realistic models
4 NUCLEAR DECAY:
Alpha decay process, Energy release in Beta-decay, Fermi’s theory of
b - decay, selection rules, parity violation in b -decay, Detection and properties of neutrino, energetics of gamma decay, selection rules, angular correlation, Mossbauer effect.
UNIT-III
5. NUCLEAR REACTIONS :
Types of reactions and conservation laws, Nuclear kinematics - the Q – equation, threshold energy- Nuclear cross section
6. NUCLEAR ENERGY
Nuclear fission- energy release in fission- Stability limit against spontaneous fission, Characteristics of fission, delayed neutrons, Nuclear fusion, prospects of continued fusion energy. Four factor formula for controlled fission (nuclear chain reaction)-nuclear reactor- types of reactors.
UNIT-IV
7. ELEMENTARY PARTICLE PHYSICS:
Classification - Particle interactions and families, symmetries and conservation laws ( energy and momentum, angular momentum, parity, Baryon number, Lepton number, isospin, strangeness quantum number)
Discovery of K-mesons and hyperons ( Gellmann and Nishijima formula) and charm, Elementary ideas of CP and CPT invariance, SU(2), SU(3) multiplets, Quark model.
8.ACCELERATORS:
Electrostatic accelerators, cyclotron accelerators, synchrotrons, linear
accelerators, colliding beam accelerators.
9. APPLICATIONS OF NUCLEAR PHYSICS:
Trace Element Analysis, Rutherford Back-scattering, Mass spectrometry with accelerators, Diagnostic Nuclear Medicine, Therapeutic Nuclear Medicine.
TEXT BOOKS :
Nuclear Physics by D.C.Tayal, Himalaya publishing Co.,
Introductory Nuclear Physics Kenneth S. Krane
Reference Books:
1. Introduction to Nuclear Physics by Harald A.Enge
2. Concepts of Nuclear Physics by Bernard L.Cohen.
3. Introduction to High Energy physics by D.H. Perkins
4. Introduction to Elementary Particles by D. Griffiths
5. Nuclear Physics by S.B.Patel, Wiley Eastern Ltd.,
6.Fundamentals of Nuclear Physics by B.B. Srivastava , Rastogi Pub,. Meerut.
NOTE : Question paper contains 5 questions. FOUR questions with internal choice have to be set from each unit. The 5thquestion has 4 short answers question covering units I to IV and any two be answered.
M.Sc., Physics(III Semester)
Paper-II Advanced Quantum Mechanics
Relativistic quantum mechanics:
Unit - I
Klien –Gordan equation –continuity equation (probability and Current density) - Klien –Gordan equation in presence of electromagnetic field – Dirac equation (for a free particle) - probability and Current density – constants of motion - Dirac equation in presence of electromagnetic fields
Unit - II
Hydrogen atom – Covariant notation – Covariance of Dirac equation - Invariance of Dirac equation under Lorenz transformation – Pure rotation and Lorenz transformation. Charge conjugation – Hole theory and Charge conjugation – projection Operators for energy and spin - bilinear covariant – Dirac equation for Zero mass and spin ½ particles.
Filed Quantization:
Unit - III
Introduction for quantization of fields – Concept of field Hamiltonian formulation of classical field – real scalar field Schrodinger field – Dirac field – Maxwell’s field – Quantum equation of the field – quantization of real scalar field and second quantization – Quantization of complex scalar field – Quantization of schrodinger field - quantization of Dirac field.
Unit - III
The Hamiltonian in the radiation field – The interaction term in the semi classical theory of radiation – quantization of radiation field .
Covariant perturbation theory, S-matrix expansion in the interaction picture, Feynman diagrams and Feynman rules for Q.E.D. Thompson scattering, Compton scattering and Miller scattering. A brief introduction to charge and mass renormalization, Bethe’s treatment of Lamb shift.
Books
1.Advanced Quantum Mechanics J. Sakurai
2. Relativistic Quantum Fields. Vols. I & II Bjorken and Drell
3. Quantum Field Theory Mandl
4. Particles and Fields Lurie
5. Quantum Theory of Fields. Vols. I & II Weinberg
NOTE : Question paper contains 5 questions. FOUR questions with internal choice have to be set from each unit. The 5thquestion has 4 short answers question covering units I to IV and any two be answered.
M.Sc. Physics (III Semester)
Paper III: Condensed Matter Physics -1
UNIT I
1 Defects: Properties of metallic lattices and simple alloys: The structure of metals –classification of lattice defects. Configurational -entropy –The number of vacancies and interstitial as function of temperature –The formation of lattice defects in metals . Lattice defect in ionic crystals and estimation of concentration of defects in ionic crystals. Edge and screw dislocation The Frank read mechanism of dislocation multiplication.
UNIT-II
Optical Properties:
Optical and thermal electronic excitation in ionic crystals, The ultraviolet spectrum of the alkali halides; excitons, Illustration of electron-hole interaction in single ions, Qualitative discussion of the influence of lattice defects on the electronic levels, Non stoichiometric crystals containing excess metal, The transformation of F centers into F1 centers and viceversa, Photoconductivity in crystals containing excess metal, The photoelectric effect in alkali halides, Coagulation of F centers and colloids, Color centers resulting from excess halogen, Color centers produced by irradiation with X-rays.
Luminescence General remarks, Excitation and emission , Decay mechanisms, Thallium-activated alkali halids, The sulfide phosphors, Electroluminescence.
UNIT-III
Lattice Vibrations and Thermal Properties
Elastic waves in one dimensional array of identical atoms. Vibrational modes of a diatomic linear lattice and dispersion relations. Acoustic and optical modes. Infrared absorption in ionic crystals. Phonons and verification of dispersion relation in crystal lattices.
Lattice heat capacity – Einstein and Debye theories. Lattice thermal conductivity- Phonon mean free path . Origin of thermal expansion and Gruneisen relation.
UNIT IV: Magnetic Properties of Solids
Quantum theory of Para magnetism, Crystal Field Splitting, Quenching of the orbital Angular Momentum Ferromagnetism Curie point and the Exchange integral, Saturation Magnetization at Absolute Zero, Magnons, Bloch’s T3/2 law. Ferromagnetic Domains. Antiferromagnetism The two-sublattice model, Superexchage interaction Ferrimagnetism The structure of ferrites, The saturation magnetization, Elements of Neel’s theory.
(Solid State Physics by C.Kittel Chapters 14 and 15)
Text and Reference Books
1. Madelng : Introduction to Solid State theory
2. Callaway: Quantum theory of solid state
3.A.J.Dekker: Solid state physics
4. C.Kittel :Solid State Physics
5. Solid State Physics S.O.Pillai New Age International
NOTE : Question paper contains 5 questions. FOUR questions with internal choice have to be set from each unit. The 5thquestion has 4 short answers question covering units I to IV and any two be answered.
M.Sc. Physics (III Semester)
Paper IV: Condensed Matter Physics -II
UNIT- I Elements of group theory
Introduction to crystallographic point groups, the five platonic solids, procedure for symmetry classification of molecules, class , matrix notation for geometrical transformations, matrix representation of point groups , reducible and irreducible representations, great orthoganality theorem and its consequences, Character tables for C2V and C3V point groups, Mullikan symbolism, Symmetry species.
Unit II: Elements of Ligand field theory Electronic spectra
Concept of ligand field and crystal field. Free ion configurations- terms and states. Derivation of free ion terms for d1 and d2 configuration. Energy ordering of terms- Hund’s rules. Strength of crystal fields, Crystal field potentials for Oh and Td fields. Meaning of Dq. Construction of ligand field energy level diagrams- effect of weak crystal fields on terms. Splitting due to lower symmetries Electronic spectra of d1 and d9 systems.T-S Diagrams
Electrical Properties of Solids
Unit-III Dielectrics
Macroscopic description of the static dielectric constant , The static electronic and ionic polarizabilities of molecules , Orientational Polarization, The static dielectric constant of gases. The internal field according to Lorentz, The static dielectric constant of solids, Clasius -Mosetti equation The complex dielectric constant and dielectric losses, Dielectric losses and relaxation time, Cole-Cole diagrams.The classical theory of electronic polarization and optical absorbtion.
Unit IV Ferroelectrics
General properties of ferroelectric materials. Classification and properties of representative ferroelectrics, the dipole theory of ferroelectricity, objections against the dipole theory, Ionic displacements and the behaviour of BaTiO3 above the curie temperature, the theory of spontaneous polarization of BaTiO3 . Thermodynamics of ferroelectric transitions, Ferroelectric domains.
Text Books:
1.Chemical applications of group theory – F.A. Cotton
2.Spectroscopy of molecules - Veera Reddy
3.Solid State Physics by A.J.Dekker (Macmillan)
4.Solid State Physics by C.Kittel
NOTE : Question paper contains 5 questions. FOUR questions with internal choice have to be set from each unit. The 5thquestion has 4 short answers question covering units I to IV and any two be answered.
Total angular momentum J. Explicit matrices for J2,Jx,Jy & Jz.Combination of two angular moment and tensor operator: Clebsch-Gordon coefficients for j1=1/2 , j2 =1/2 and j1=1 , j2 =1/2 Wigner-Eckart theorem.
UNIT-II
Quantum Dynamics and identical particles
Equation of motion in Schrödinger’s picture and Heisenberg’s picture, correspondence between the two. Correspondence with classical mechanics. Application of Heisenberg’s picture to Harmonic oscillator. The indistinguishability of identical particles – The state vector space for a system of identical particles – Creation and annihilation operators- continuous one particle system- Dynamical variables – the Quantum dynamics of identical particle systems
UNIT-III
Scattering Theory
Introduction of scattering – notion of cross section – scattering of a wave packet- scattering in continuous stream model – Green’s function in scattering theory – Born’s approximation – first order approximation – criteria for the validity of Born’s approximation . Form factor- scattering from a square well potential – partial wave analysis – Expansion of a plane wave – optimal theorem – calculation of phase shifts – low energy limit – energy dependence of be - scattering from a square well potential.
UNIT-IV
Molecular Quantum Mechanics
The Born-Openheimer Approximation – The hydrogen molecule ion the Hydrogen molecule – The valance bond method – The molecular orbital method- Comparison of the methods – Heitler-London method.( Ref : Atkins, Chapter-9, 279-294).
Text books
Merzbecher, Quantum Mechanics
L I Schiff, Quantum Mechanics (Mc Graw-Hill)
B Craseman and J D Powell, Quantum Mechanics (Addison Wesley)
A P Messiah, Quantum Mechanics
J J Sakural, Modem Quantum Mechanics
Mathews and Venkatesan Quantum Mechanics
Quantum Mechanics” by R.D. Ratna Raju
Quantum mechanics by Kakani and Chandalia
NOTE : Question paper contains 5 questions. FOUR questions with internal choice have to be set from each unit. The 5thquestion has 4 short answers question covering units I to IV and any two be answered.
M.Sc. Physics ( II Semester)
Paper II : Statistical Mechanics PHY 2.2
Classical Statistical Mechanics
UNIT I
Foundations of statistical mechanics; specification of states of a system,
contact between statistics and thermodynamics, Postulate of classical stastical mechanics- phase space, trajectories - Ensembles-micro canonical,canonical and grand canonical - Density of states - Liouville’s theorem -equi-partition theorem- Classical ideal gas: entropy of ideal gas in micro canonical ensemble- Gibb’s paradox.
UNIT-II
2.Canonical ensemble - ensemble density- partition function - Energy fluctuations in canonical ensemble -Grand canonical ensemble- Density fluctuations in the Grand canonical ensemble- Equivalence between the canonical ensemble and Grand canonical ensemble.
Quantum statistical mechanics
UNIT III
3. Postulates of quantum statistical mechanics-Density matrix- Ensembles in quantum statistics- statistics of indistinguishable particles, Maxwell-Boltzmann, Bose-Einstein and Fermi- Dirac statistics - Thermodynamic properties of ideal gases on the basis of micro canonical and grand canonical ensemble. The Partition function: Derivation of canonical ensemble using Darwin and Fowler method.
UNIT IV
4.Ideal Fermi gas : Equation of state of an ideal Fermi gas, theory of
White dwarf stars, Landau diamagnetism.
Ideal Bose gas : Photons – Phonons - Bose Einstein condensation- Random walk- Brownian motion
Text and Reference Books:
Statistical and Thermal Physics by S. Lokanadham and R.S.Gambhir ( PHI).
Statistical Mechanics by K. Huang ( Wiley Eastern )
Statistical Mechanics: Theory and applications by S.K. Sinha
Fundamentals of Statistical and Thermal Physics by F. Reif
Statistical Mechanics by Gupta and Kumar, Pragathi Prakashan Pub. Meerut.
NOTE : Question paper contains 5 questions. FOUR questions with internal choice have to be set from each unit. The 5thquestion has 4 short answers question covering units I to IV and any two be answered.
M.Sc. Physics ( II Semester)
Paper-III:COMPUTATIONAL METHODS AND PROGRAMMING PHY 2.3
UNIT-I
a)Fundamentals of C Language:
C character set-Identifiers and Keywords-Constants-Variables-Data types-Declarations of variables –Declaration of storage class-Defining symbolic constants –Assignment statement.
Arithmetic expressions –Precedence of arithmetic operators-Type converters in expressions –Mathematical (Library ) functions –Data input and output-The getchar and putchar functions –Scanf – Printf-Simple programs.
UNIT –II
a)Control statements and arrays:
If-Else statements –Switch statements-The operators –GO TO –While, Do-While, FOR statements-BREAK and CONTINUE statements.
b)Arrays
One dimensional and two dimensional arrays –Initialization –Type declaration-Inputting and outputting of data for arrays –Programs of matrices addition, subtraction and multiplication
c)User Define functions
The form of C functions –Return values and their types –Calling a function – Category of functions. Nesting of functions. Recursion. ANSI C functions-Function declaration. Scope and life time of variables in functions.
UNIT-III
Linear and Non –linear equations:
Solution of Algebra and transcendental equations-Bisection, Falsi position and Newton-Rhapson methods-Basic principles-Formulae-algorithms
(b) Simultaneous equations:
Solutions of simultaneous linear equations-Guass elimination and Gauss
Concept of linear interpolation-Finite differences-Newton’s and Lagrange’s interpolation formulae-principles and Algorithms
(b) Numerical differentiation and integration:
Numerical differentiation-algorithm for evaluation of first order derivatives using formulae based on Taylor’s series-Numerical integration-Trapezoidal and Simpson’s 1/3 rule-Formulae-Algorithms
Reference: 1.Programming with ‘C’ – Byron Gottfried. Tata McGraw Hill
2.Programming In ‘C’ – Balaguruswamy, Tata McGraw Hill
3.Numerical Methods, E. Balaguruswamy, Tata McGraw Hill
4.Computer oriented numerical methods-Rajaraman
NOTE : Question paper contains 5 questions. FOUR questions with internal choice have to be set from each unit. The 5thquestion has 4 short answers question covering units I to IV and any two be answered.
M.Sc. Physics ( II Semester)
Paper-IV SOLID STATE PHYSICS (General) PHY 2.4
UNIT I
CRYSTAL STRUCTURE:
Periodic array of atoms—Lattice translation vectors and lattices, symmetry operations, The Basis and the Crystal Structure, Primitive Lattice cell, Fundamental types of lattices—Two Dimensional lattice types, three Dimensional lattice types, Index system for crystal planes, simple crystal structures-- sodium chloride, cesium chloride and diamond structures.
UNIT II
CRYSTAL DIFFRACTION AND RECIPROCAL LATTICE:
Bragg’s law, Experimental diffraction methods-- Laue method and powder method, Derivation of scattered wave amplitude, indexing pattern of cubic crystals and non-cubic crystals (analytical methods). Geometrical StructureFactor, Determination of number of atoms in a cell and position of atoms. Reciprocal lattice, Brillouin Zone, Reciprocal lattice to bcc and fcc Lattices.
UNIT III
FREE ELECTRON FERMI GAS:
Energy levels and density of orbitals in one dimension, Free electron gas in 3 dimensions, Heat capacity of the electron gas, Experimental heat capacity of metals, Motion in Magnetic Fields- Hall effect, Ratio of thermal to electrical conductivity.
FERMI SURFACES OF METALS:
Reduced zone scheme, Periodic Zone schemes, Construction of Fermi surfaces, Electron orbits, hole orbits and open orbits, Experimental methods in Fermi surface studies-- Quantization of orbits in a magnetic field, De-Hass-van Alphen Effect, extremal orbits, Fermi surface of Copper.
UNIT IV
THE BAND THEORY OF SOLIDS:
Nearly free electron model, Origin of the energy gap, The Block Theorem, Kronig-Penny Model, wave equation of electron in a periodic potential, Crystal momentum of an electron-Approximate solution near a zone boundary, Number of orbitals in a band--metals and isolators. The distinction between metals, insulators and semiconductors
TEXT BOOKS:
1.Introdcution to Solid State Physics, C.Kittel, 5th edition,
2.Solid State Physics, A.J.DEKKER.
NOTE : Question paper contains 5 questions. FOUR questions with internal choice have to be set from each unit. The 5thquestion has 4 short answers question covering units I to IV and any two be answered.
