Sunday, January 17, 2010

PG model papers for physics

Approved in P.G.B.O.S. meeting held on 08-08-2008
Acharya Nagarjuna University M.Sc Physics I Semester
Model paper

Answer the following Questions.
All Questions carry equal marks
Time : 3 hours Max. Marks 80

1 a). State and prove Ehrenfest’s theorem? Write the significance of the result.
b). Obtain the Eigenvalue of a particle in a finite Potential-well?
c). Describe “Dirac” notations for state vectors, Eigen values, Orthogonality and
normalization, in quantum mechanics
d). Solve for eigen values and eigen functions of one Dimensional Harmonic oscillator by
operator method
2 a) Discuss the eigen value problem of L2 and Lz
b) Discuss the eigen values and eigen functions of rigid rotator

3. a) Outline the time-independent Non-degenerate perturbation theory for obtaining the
energy levels of a stationary system and apply it to find the energy of the ground state of
. OR
b) Derive the expressions for eigen values and eigen functions for a degenerate perturbation
c) Explain linear Stark effect on hydrogen-atom?

4 . a) State and prove variation theorem.
b) Evaluate the ground state energy of helieum atom using varation method.
c) Derive the expression for the transition probability using time dependent perturbation
d) Derive Fermi – Golden rule for the transition into continuum.

5 Write notes on any two of the following.
a) Hermitian-operator and it’s eigen values
b) Angular momentum in Quantum-mechanics
c) Adibatic approximation.
d) Einstein transition probabilities

M.Sc.Physics ( I SEMESTER )

Time 3 hours Max Marks 80

Answer ALL Questions. All questions carry equal marks

1 a) Explain about the important electrical parameters of OP.AMP.
b) Explain the type of feedback used with amplifiers.
c)With suitable diagrams explain how Op. Amp can be used to perform Summing, integration,
differentiation operations.

2. a) Draw the circuit diagram of a R-C phase shift oscillator and explain its working.
b) Give the reasons for instability in oscillator circuits.
c) Draw the circuit diagram of adjustable IC regulated power supply and explain its working.
d) Explain the principle of working of switching regulator

3. a) Draw the circuit diagram to produce DSBSC modulation.
b) Explain the method of detecting DSBSC.
c).What do you mean by decoder and encoder?
d) With truth tables explain the working of T-flip flop, D- flip flop JK flip flop and RS clocked

4 a) Explain with functional block diagram the architecture of 8085.
b) Write an assembly language program to create time delay of 200 microseconds if the clock
frequency of 8085 processor is 1MHz.
c) What do you mean by stack and subroutine?
d) Explain the architecture of microcontroller 8051.

5. Write notes on any TWO of the following
a) Differential amplifier and CMRR
b) Effect of negative feedback on gain and band width
c) Frequency division multiplexing
d) Memory organization

Approved in P.G.B.O.S. meeting held on 08-08-2008
Acharya Nagarjuna University M.Sc Physics II Semester
Model paper PHY 2.1
Paper 1 : Quantum Mechanics -II
Time: 3 hrs Max.Marks:80
Answer all questions

1. (a)What are C-G coefficients? Describe their properties
(b) Derive C-G coefficients for
( c) Derive Pauli’s spin matrices
(d). Prove any three properties of Pauli’s spin matrices.

2. (a) What do you understand by a picture in quantum dynamics? What is the difference
between different pictures.
(b) Obtain the equation of motion in Heisenberg picture and explain constant of motion .
(c) Establish the correspondence of quantum mechanical pictures with classical mechanics
with specific examples.
(d) Apply the Heisenberg picture to a harmonic oscillator and explain its significance.
3. (a) Discuss Born- approximation in scattering calculations.
(b) Calculate the differential cross-section for the square well potential.
(c) Define the scattering cross-section according to classical mechanics and quantum theory.
(d) Discuss the significance of Green’s function in scattering theory.

4 (a) Explain L.C.A.O. Method.
(b) Solve the Schrödinger equation for the hydrogen molecule ion using L.C.A.O. Method.
(c) Explain the essential principles of the Valence bond method and apply it for the problem of
hydrogen molecule.

5. Write notes on any TWO of the following .
(a) Wigner-Eckart theorem
(b) Creation and annihilation operators
(c) Optimal theorem
(d) Born –Openheimer approximation


Time :3hrs. Max.marks.80

Answer any five questions. All questions carry equal marks

1. a) State and prove equipartition theorem.
b) What is Gibb’s Paradox ? How was it resolved?
c) Explain the concept of phase space and ensemble.Distinguish between three ensembles,
namely, Microcanonical, canonical and Grand canonical ensemble.
d) State and prove Liouvilles theorem .

2. a) Obtain expression for ensemble density in the canonical ensemble
b) Discuss energy fluctuations in canonical ensemble.
c) Discuss the density fluctuations in the grand canonical ensemble and prove the equivalence
between canonical and Grand canonical ensembles.

3. a) Obtain the Sackur Tetrode equation for ideal Boltzmann gas on the basis of microcanonical
b) Employing the method of Darwin and Fowler, derive the energy distribution for a canonical

4. a) Derive the equation of State of an ideal Fermi gas and discuss the Fermi energy and
pressure for ideal Fermi gas at low temperature and high densities.
b). What is Bose -Einstein condensation? Explain the phenomenon using Grand partition
function. Explain the role of super fluidity and conductivity.

5. Write short notes on any TWO of the following
a) Entropy of classical ideal gas
b) Density matrix
c) Landau diamagnetism
d) Brownian motion

Paper- IV Solid State Physics (General) PHY 2.4

Time:3hrs. Max. marks.80

Answer ALL questions .All questions carry equal marks

1. a) What do you mean by periodic array of atoms ?
b) What do you mean by primitive lattice cell
c) What are the various types of lattices?.
d)Describe the crystal structure of Diamond.

2.a) Derive Laue conditions for X-ray diffraction.
b) Compare the relative advantages and disadvantages of Laue’s powder and Rotating crystal
method of determining Crystal structures.
c) Explain neutron diffraction method .
d) Explain why neutron diffraction is complementary to X-ray diffraction in the determination
of crystal structure.

3. a)What is free electron Fermi Gas
b)Obtain an equation for number of orbitals for unit energy in three dimensions.
c) Explain the electrical conductivity process in a metal. Obtain an equation for electrical
d) Discuss the quantization of orbits in magnetic field.

4.a) Describe the behaviour of the electrons in a periodic potential using Kronig-Penny model.
b) What are its important conclusions.
c) Explain the crystal momentum of an electron
d) Describe the classification of band theory of solids.

5. Write short note on any TWO of the following.
a) Sodium chloride crystal structure
b) Reciprocal lattice to bcc lattice
c) De-Hass-van Alphen effect
d) Bloch theorem

Model paper
M.Sc Physics (III Semester)
Time: 3 hrs Max.Marks:80
Answer ALL questions All questions carry equal marks

1 a) Explain the features of binding energy per nucleon (B/A)versus mass number(A) curve
b)Obtain an expression for electric quadrupole moment of nucleus. What would be the value of
classical quadrupole moment for a single proton located at the nuclear equator?
c) Obtain an expression for wave function for ground state of deuteron on the basis of central
force assumption
d) Describe the basic ideas in Yukawa’s meson exchange theory of the nuclear force and show
how the pion was postulated.

2. a) Explain how magic numbers are predicted based on the shell model of nucleus.
b) Determine the ground state spin and parity of the following nuclei 1) 6C13 2) 7N16 3)
28Ni61 4)33As75
c)Explain the Gamow’s theory of alpha decay and hence derive the Geiger-Nuttal Law.
d) Explain the Mossbauer effect.

3. a) What is the Q-equation of nuclear reaction? How the nuclear reactions are classified based
on the Q- value?
b) Explain about the direct and compound nuclear reaction mechanisms. Give some examples.
c) Explain the terms nuclear fission and nuclear fusion. Give some examples. discuss about the
energy release in nuclear fission.
d) Briefly describe various types of reactors.

4 a) How do you classify the electrostatic accelerators?
b) Explain the working principle of cyclotron.
c) Explain the Rutherford back scattering
d) How nuclear medicine can be used for diagnostic purpose?

5. Write notes on any two of the following
a) Spin dependence of nuclear forces
b)Weizsacker’s semi empirical mass formula
c)Classification of elementary particles
d) SU(2) and SU (3) multiplet

Approved in P.G.B.O.S. meeting held on 08-08-2008
Acharya Nagarjuna University M.Sc Physics III Semester
Model paper
Time: 3 hrs Max.Marks:80

Answer the following questions. All questions carry equal marks

1 (a) Derive the Klein – Gordon relativistic wave equation for a free particle.
(b) What are the short comings of the Klein – Gordon equation? Explain how they are
removed by Dirac’s equation.
(c) Develop Dirac’s relativistic theory of an electron.
(d) Show that the spin of electron is directly explained by Dirac’s theory .

2. (a) show that the Dirac equation is invariant under Lorentz transformations.
(b) Explain charge conjugation from Dirac’s theory.
(c ) Obtain the free particle solutions (Dirac spinors) for a Dirac particle . Explain their
physical significance.
(d). Explain the Dirac equation for zero mass

3. (a) Explain the method of second quantization .
(b) Discuss the quantization procedure applied to Maxwell field
(c) Discuss the difficulties of the relativistic unquantized Dirac equation
(d) Discuss the quantization of Dirac field.

4. (a) Give the Classical field theory of Real scalar field and obtain for the Lagrangian.
(b) Explain the quantization of real scalar field .
(c) Write down the Hamiltonian for an atom in the presence of radiation field. Solve the Wave
equation to obtain the formula for transition probability.
(d) Discuss the transition probabilities for emission and absorption in radiation field.
5. Write any TWO of The Following :
(a) Dirac matrices and their properties.
(b) Negative energy solutions.
(c) Creation, annihilation and number operators and their physical significance.
(d) Hamiltonian formulation of a classical field.

Approved in P.G.B.O.S.meeting held on 08-08-2008
Acharya Nagarjuna University M.Sc Physics IV Semester
Model paper PHY 4.1
Time: 3 hrs Max.Marks:80
Answer all questions

1. a) State the boundary conditions that are to be satisfied by the electric and magnetic fields at
the surface of separation of two dielectric media.
b) Deduce the expressions for the intensity of the reflected and transmitted wave is incident
at such an interface.
c) What is double refraction and discuss the propagation of light in double refracting media.

2. .a) Explain the working of ruby laser .
b) Discuss the line broadening mechanism.
c) What are the central features of semi conductor lasers.
d) Derive the expression for the laser action in semiconductor laser.

3. a) Give the basic principles of holography and explain its importance and uses.
b) Write in detail about Fourier transform holography

4 a) Discuss in detail the mode theory of circular wave guides.
b) Discuss various types of dispersions in optical fibers.
c) Explain the structure and advantages of a step index optical fiber
d) Explain the signal degradation in optical fibers.

5 Write notes on any two of the following
a) Retarded Potentials
b) Population Inversion
c) Speckle pattern
d) Attenuation in optical fibers

Nagarjuna university M.Sc physics 4th semister syllabus(2010)

M.Sc, (IV Semeter)

UNIT-I Electromagnetic Theory
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 PHY 4.2

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 1 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)
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.
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 (1 - 1 ) having only P and R branches. Ch. 6.2.
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

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.

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 PHY 4.3A

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.
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.
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.
Liquid Crystals: Mesomorphism of anisotropic systems, Different liquid crystalline phases and phase transitions, Few applications of liquid crystals.
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 PHY 4.4A

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.
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.
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.
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.

Nagarjuna university M.Sc physics third semister syllabus(2010)

M.Sc. PHYSICS (III rd semester )
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.
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).
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
Alpha decay process, Energy release in Beta-decay, Fermi’s theory of
 - decay, selection rules, parity violation in  -decay, Detection and properties of neutrino, energetics of gamma decay, selection rules, angular correlation, Mossbauer effect.
Types of reactions and conservation laws, Nuclear kinematics - the Q – equation, threshold energy- Nuclear cross section
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.
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.
Electrostatic accelerators, cyclotron accelerators, synchrotrons, linear
accelerators, colliding beam accelerators.
Trace Element Analysis, Rutherford Back-scattering, Mass spectrometry with accelerators, Diagnostic Nuclear Medicine, Therapeutic Nuclear Medicine.
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 PHY 3.2

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.

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 PHY3.3
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.
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.
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 PHY3.4

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.

Nagarjuna university M.Sc physics second semister syllabus(2010)

M.Sc. Physics ( II Semester) PHY 2.1



Spin and Total angular momentum;

Spin angular momentum and Paulis spin matrices

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.


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


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.


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


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.


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


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.


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) PHY 2.3



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.

Operators: Arithmetic operators-Relational Operators-Logic Operators-Assignment operators- Increment and decrement operators –Conditional operators.

b) Expressions and I/O Statements:

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.


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.


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

Seidel iterative methods-Basic principles- Formulae-Algorithms


(a) Interpolations:

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) PHY 2.4




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.



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.



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.


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.



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


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.