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DR. BHIM RAO AMBEDKAR UNIVERSITY, AGRA . Course Structure for M.Sc. (Physics) under Semester System to come into force from Academic Session 2013-14. M.Sc. (PHYSICS) SEMESTER SYSTEM PAGE 1 DR. BHIM RAO AMBEDKAR UNIVERSITY, AGRA . MASTER OF SCIENCE (PHYSICS) SEMESTER COURSE STRUCTURE This is a two years (4 semesters) course. There will be four theory papers and one practical with maximum marks 400 in each semester. The details are given below: FIRST SEMESTER 400 Marks Paper-101 Mathematical Physics I 075 Marks Paper-102 Classical mechanics 075 Marks Paper-103 Statistical Mechanics 075 Marks Paper-104 Electromagnetic Theory 075 Marks Paper-105 Practical:- 100 Marks (a) Practical 60 Marks (b) Record 20 Marks (c) Viva-Voce 20 Marks First Semester Total ========== 400 Marks PAGE 2 DR. BHIM RAO AMBEDKAR UNIVERSITY, AGRA . MASTER OF SCIENCE (PHYSICS) SEMESTER COURSE STRUCTURE SECOND SEMESTER 400 Marks Paper-201 Mathematical Physics II 075 Marks Paper-202 Quantum Mechanics I 075 Marks Paper-203 Atomic and Molecular spectra 075 Marks Paper-204 Electrodynamics and plasma Physics 075 Marks Paper-205 Practical:- 100 Marks (a) Practical 60 Marks (b) Record 20 Marks (c) Viva-Voce 20 Marks Second Semester Total ========== 400 Marks PAGE 3 DR. BHIM RAO AMBEDKAR UNIVERSITY, AGRA . MASTER OF SCIENCE (PHYSICS) SEMESTER COURSE STRUCTURE THIRD SEMESTER 400 Marks Paper-301 Quantum Mechanics II 075 Marks Paper-302 Nuclear Physics I 075 Marks Paper-303 Solid State Physics 075 Marks Paper-304 Basic Electronics and devices 075 Marks Paper-305 Practical:- 100 Marks (a) Practical 60 Marks (b) Record 20 Marks (c) Viva-Voce 20 Marks Third Semester Total ========== 400 Marks PAGE 4 DR. BHIM RAO AMBEDKAR UNIVERSITY, AGRA . MASTER OF SCIENCE (PHYSICS) SEMESTER COURSE STRUCTURE FOURTH SEMESTER 400 Marks Paper-401 Numerical Methods in Physics 075 Marks Paper-402 Nuclear Physics II 075 Marks Paper-403 (Optional Group A-i) Condensed Matter Physics I Paper-404 (Optional Group A-ii) Condensed Matter Physics II } 075 Marks 075 Marks OR Paper-403 (Optional Group B-i) Electronics I } 075 Marks Paper-404 (Optional Group B-ii) Electronics II 075 Marks Paper-405 Practical:- 100 Marks (a) Practical 60 Marks (b) Record 20 Marks (c) Viva-Voce 20 Marks Fourth Semester Total GRAND TOTAL ( I+II+III+IV SEMESTER) ========== 400 Marks 1600 Marks PAGE 5 DR. BHIM RAO AMBEDKAR UNIVERSITY, AGRA . *Note: Courses PH-403(A-i) and PH-404(A-ii) are for specialization in Condensed matter Physics Courses PH-405(B-i) and 406(B-ii) are for specialization in Electronics PAGE 6 DR. BHIM RAO AMBEDKAR UNIVERSITY, AGRA . M.SC. (PHYSICS) RULES & REGULATION • Each practical performance will be of 100 marks. • Passing marks in individual theory as well as practicals be 40%, overall the Total aggregate of the candidate should be 45% in each semester. • The entire course of M.Sc. (Physics) will be of 1600 marks. So every semester will be of 400 marks. • Each theory paper will be of 075 Marks. • Practical Paper will be of 100 Marks. PAGE 7 DR. BHIM RAO AMBEDKAR UNIVERSITY, AGRA . MASTER OF SCIENCE (PHYSICS) FIRST SEMESTER PAPER-101 Mathematical Physics I MAX. MARKS: 075 Unit – I Fundamental laws of Algebra on complex numbers, polar form of complex numbers, Regions in the complex plane, Analytic (regular) functions, The Cauchy-Riemann equations, Harmonic functions. Unit – II Line integral in complex plane, Cauchy’s theorem, Cauchy’s integral formula, Taylor’s and Laurent’s expansions, singularities, Zeroes and poles, Residue theorem and countour integration of simple functions. Unit – III Power series, solution of second order differential equations, ordinary point and singularities of a linear differential equation, Solutions of Hyper- geometric, Bessel, Legendre, Laguerre and Hermite equations. Unit – IV Bessel and Legendre functions and polynomials, Rodrigue’s formula for Legendre polynomial Orthonrmality and other properties of Legendre, Associated Legendre, Hermit, Laguerre and Associated Lagurre polynomials. PAGE 8 DR. BHIM RAO AMBEDKAR UNIVERSITY, AGRA . Books Recommended 1. Matrices and tensors for physicists by A.W. Joshi , Wiley Eastern. 2. Advanced Engineering Mathematics by E. Kreyszig 3. Introduction methods of numerical analysis by Sastry 4. Mathematical Physics: PC Chattopadhyay, Wiley Eastern PAGE 9 DR. BHIM RAO AMBEDKAR UNIVERSITY, AGRA . MASTER OF SCIENCE (PHYSICS) FIRST SEMESTER PAPER -102 Classical Mechanics MAX. MARKS: 075 UNIT I Mechanics of a system of particles, Constraints, Generalized coordinates D’Alembert’s principle, Lagrangian formulation and equations of motion, velocity dependent potential, dissipative systems, symmetry, invariance and conservation laws. UNIT II Two body central force problem, stability of orbits, two body collisions, scattering in laboratory and centre of mass frame; Rigid body dynamics, moment of inertia tensor, Euler angles, Non inertial frames and pseudo forces, Coriolis force and applications. UNIT III Calculus of variations and its applications, Hamilton’s principle and Principle of least action, Hamilton’s equations of motion; Canonical transformations, Poisson brackets, Infinite canonical transformations in Poisson bracket notation. UNIT IV Hamilton Jacobi equations, action angle variables; Periodic motion, Theory of small oscillations and normal modes. PAGE 10 DR. BHIM RAO AMBEDKAR UNIVERSITY, AGRA . Books Recommended 1. Classical Mechanics: H. Goldstein, Narosa Publishing Home, New Delhi 2. Classical Mechanics: N.C. Rana and P.S. Joag, Tata Mc Graw Hill, New Delhi. 3. Classical Mechanics: J.C. Upadhyay, Himalaya Publishing House, Mumbai. 4. Classical Mechanics: R.G. Takawale and PS Puranik, Tata Mc Graw Hill, New Delhi. PAGE 11 DR. BHIM RAO AMBEDKAR UNIVERSITY, AGRA . MASTER OF SCIENCE (PHYSICS) FIRST SEMESTER -103 PAPER PAPER-103 Statistical Mechanics MAX. MARKS: 075 UNIT I Specification of the state of a system, macroscopic and microscopic states, phase space, statistical ensemble, postulate of equal a priori probability, density of states, Liouville’s theorem, Distribution of energy between systems in equilibrium, Boltzman equation, equilibrium between interacting systems. UNIT II Micro canonical ensemble, ideal mono atomic gas, entropy of mixing, Gibb’s paradox, canonical ensemble, applications, partition function, calculation of mean value and fluctuations in canonical ensembles, connection with thermodynamics, Grand canonical ensemble, Chemical potential in equilibrium state, Mean value and fluctuations in grand canonical ensemble.: UNIT III Quantum Statistics of ideal gases, Symmetry of wave functions, Quantum distribution functions, Boltzmann limit of Boson and Fermion gases, evaluation of partition function, Bose Einstein statistics, Photon gas, Black body radiation, Planck’s law, Ideal Bose system, B.E. condensation. Ideal Fermi systems, Fermi energy, Fermi energy as a function of temperature, electronic specific heat of solids. PAGE 12 DR. BHIM RAO AMBEDKAR UNIVERSITY, AGRA . UNIT IV Random walk and Brownian motion, Introduction to non equilibrium processes, Diffusion equation; First and second order phase transitions, para and ferromagnetism, Ising model. Books Recommended 1. Fundamentals of statistical and thermal Physics: F.Reif, Mc. Graw Hill. 2. Statistical Mechanics: R.K. Patharia , Befferworgh Heinemann. 3. Statistical Mechanics: K. Huang, John Wiley & sons. 4. Statistical Mechanics: Satya Prakash, RamNath Publications. 5. Statistical Mechanics by R.K. Kubo PAGE 13 DR. BHIM RAO AMBEDKAR UNIVERSITY, AGRA . MASTER OF SCIENCE (PHYSICS) FIRST SEMESTER PAPER-104 Electromagnetic Theory MAX. MARKS: 075 UNIT I Maxwell’s equations in vacuum and dielectrics, Maxwell’s correction to Ampere’s law, displacement current, Boundary conditions, Poynting theorem, Poynting vector, Conservation of energy and momentum for a system of charged particles and electromagnetic field. UNIT II Scalar and vector potentials, Maxwell’s equations in terms of scalar and vector potentials, Electromagnetic wave equation, non uniqueness of electromagnetic potentials, concept of Gauge and gauge transformations, Coulomb and Lorentz gauge, Transformation properties of e.m. fields under rotation, spatial reflections and time reversal. UNIT III Plane waves in vacuum, non conducting medium, conducting medium and Plasma, Reflection, refraction and polarization of electromagnetic waves, Stoke’s parameter, Frequency dispersion characteristics of dielectrics and conductors, Normal and anomalous dispersion, spreading of pulse in a dispersive media, Kramer- Kronig relation. UNIT IV Propagation of electromagnetic waves in rectangular wave guides, TE and TM modes, cut off frequency, Energy flow and attenuation, Modal analysis of guided waves in a cylindrical wave PAGE 14 DR. BHIM RAO AMBEDKAR UNIVERSITY, AGRA . guide, field and radiation due to moving charges and oscillating dipole, magnetic dipole and electric quadrupole fields. Books Recommended 1. Classical electrodynamics, JD Jackson, 3rd Ed. , John Wiley 2. Classical Electricity and Magnetism, Panofsky and Phillips, Addison Wesley 3. Electrodynamics, DJ Griffith 3rd Ed., Prentice Hall of India, New Delhi 4. Introduction to Electrodynamics, AZ Capri and PV Panat, Narosa Publishing House. PAGE 15 DR. BHIM RAO AMBEDKAR UNIVERSITY, AGRA . MASTER OF SCIENCE (PHYSICS) FIRST SEMESTER PAPER-105 PRACTICAL MAX. MARKS: 100 (a) Practical 60 Marks (b) Record 20 Marks (c) Viva-Voce 20 Marks 1. Viscosity of fluid by rotation viscometer. 2. Velocity of Ultrasonic waves in a liquid. 3. Thickness of mica sheet by Biprism. 4. Verification of Fresnel’s laws. 5. B.H. curve and hysteresis loss by Ballistic Galvanometer 6. λ by Michelson interferometer 7. LCR oscillation at high frequency. 8. Study of active filter (L section Π section) 9. Use of universal gates to make AND, OR, NOT gates. 10. Verification of Chauchy’s relation PAGE 16 DR. BHIM RAO AMBEDKAR UNIVERSITY, AGRA . MASTER OF SCIENCE (PHYSICS) SECOND SEMESTER PAPER-201 Mathematical Physics-II MAX. MARKS: 075 Unit – I Partial differential equations, Lagrange’s linear equation, Method of multipliers, Solutions of Laplace, Poisson, Diffusion and wave equations. Unit – II Inhomogeneous equations, Green’s function for a free particle, Fourier series, Fourier integral, Fourier sine, cosine and complex transforms, Applications to boundary value problems, Fundamental properties of Beta and Gamma functions. Unit – III Binary operation, Definitions of Group, Semi-Group and Abelian group, Multiplicationtable, Equivalence class, Conjugate elements and classes, Invariant subgroups, Permutation group, Cyclic group, Cosets of a subgroup, finite and infinite group, Period of the group. Unit – IV Similarity transformations, Representation Character of Trace of the group, Schur’s Lemma and the Orthgonality theorem, Examples of C2v, Regular representation, Symmetriesed basis functions for irreducible representation, Direct product of representation. Applications to simple vibrational problems. PAGE 17 DR. BHIM RAO AMBEDKAR UNIVERSITY, AGRA . Books Recommended 1. Elements of Group Theory for Phycisicists : AW Joshi,Wiley eastern 2.Group Theory and Quantum Mechanics: M Tinkham : TMH 3. Special Functions by WW Bell 4. Mathematics for Physicists : Mary L Boas 5. Mathematical Methods for Physics : G Arfken PAGE 18 DR. BHIM RAO AMBEDKAR UNIVERSITY, AGRA . MASTER OF SCIENCE (PHYSICS) SECOND SEMESTER PAPER-202 Quantum Mechanics-I MAX. MARKS: 075 Unit I Linear operators, Null operator, Identity operator, Singular and Non singular operator, Eigen functions and Eigen values, orthogonal Eigen functions, The operator formalism in quantum mechanics, Momentum operator, Hamiltonian operator, communication in operators, Hermition operator, properties of Hermittion operator, Parity operator. Unit II Postulates of quantum mechanics coordinate and momentum representation, superposition of Eigen states, continuous spectra, equation of motion, Ehrenfest’s theorem, simultaneous measurements and communiting operator, Schwartz inequality. Unit III Heisenberg uncertainty relation derived from operator, commutator algebra, Angular momentum operator, Commutation relation for Lx, Ly and Lz, Ladder operators. Completeness of Eigen functions, Dirac delta function, bra and ket notation, Matrix representation of operator, unitary transformation. The Schrödinger equation for spherically symmetric potentials, Degeneracy, Hydrogen atom, radial equation, Eigen value, Radial probability. Unit IV Stationary perturbation theory, Non-degenerate case, First order perturbation, second order perturbation, perturbation of an oscillator, helium atom, Degenerate case, Removal of PAGE 19 DR. BHIM RAO AMBEDKAR UNIVERSITY, AGRA . degeneracy in first and second order, First order Stark effect in hydrogen, weak field Zeeman effect. The variatonal method, expectation value of the energy, Ground state of Helium, Exchange degeneracy, Heitler-London theory of hydrogen molecule. WKB method and its application. Books Recommended 1. Quantum Mechanics : LI Schiff , McGraw Hill 2.Quantum Mechanics: Mathews and Venkatesan 3. Quantum Mechanics , Ghatak and Loknathan 4. Quantum Mechanics, Merzbacker 5. Quantum Mechanics AP Messiah PAGE 20 DR. BHIM RAO AMBEDKAR UNIVERSITY, AGRA . MASTER OF SCIENCE (PHYSICS) SECOND SEMESTER PAPER-203 Atomic and Molecular Spectra MAX. MARKS: 075 Unit I Quantum states of an electron in atom, Electron spin, spectrum of Hydrogen and helium atom, Relativistic corrections for energy levels for hydrogen, spectra of alkali elements, spin orbit interaction and fine structure in alkali spectra, magnetic moment of an atom, lande g factor, L-S and J-J coupling, spectra of alkaline earth, penetrating and non-penetrating orbits. Unit II Normal and anomalous Zeeman Effect, Paschan Back effect, stark effect, Hyperfine structure and isotropic shift, electron spin resonance, nuclear magnetic resonance. Unit III Rotational spectra of diatomic molecules as a rigid and non rigid rotator, vibrational spectra, explanation considering molecule as harmonic and anharmonic oscillator, Rotationalvibrational spectra. Unit IV Raman spectra, experimental arrangement, Quantum theory of Raman Effect, Pure rotational raman spectra of diatomic molecules , stokes and antistokes lines, X-ray spectra, Mosely Law, Fine structure in X-ray emission spectra PAGE 21 DR. BHIM RAO AMBEDKAR UNIVERSITY, AGRA . Books Recommended 1. Introduction to atomic spectra H. E. white 2. Fundamentals of molecular spectroscopy C. B. Banwell(T) 3. Spectroscopy Vol . I.II & III- Walker and Straughen 4. Introduction of molecular spectroscopy G.h. Barrow 5. Spectra of diatomic molacules :Herzberg 6. Modern spectroscopy J. M. Holias PAGE 22 DR. BHIM RAO AMBEDKAR UNIVERSITY, AGRA . MASTER OF SCIENCE (PHYSICS) SECOND SEMESTER PAPER-204 Electrodynamics and Plasma Physics MAX. MARKS: 075 Unit I Relativistic Electrodynamics: Structure of space and time, Four vectors, proper time and velocity, relativistic dynamics, Minkowski force, Lorentz transformation of electromagnetic field, e.m. field tensor, electrodynamics in tensor notation, potential formulation of relativistic electrodynamics. Unit II Retarded and advanced potentials, Lienard- Wiechart potentials for moving charge, fields produced by a charge in uniform and accelerated motion, Radiated power, angular distribution of radiation due to accelerated charge, Brehmstrahlung, synchrotron radiation. Unit III Multipole expansion of electromagnetic fields, properties of multipole fields, energy and angular momentum of multipole radiation, radiation damping, radiative reaction force and its derivation, scattering by free and bound electrons, Rayleigh scattering. Unit IV Definition of plasma, concept of temperature, Debye shielding, criteria for plasma, single particle motion in E and B fields, magnetic mirrors and plasma confinement, plasma as a fluid, the fluid equation of motion, Plasma frequency ωp, electron plasma waves, ion waves, electron and ion oscillations, cutoffs and resonance. PAGE 23 DR. BHIM RAO AMBEDKAR UNIVERSITY, AGRA . Books Recommended 1. Electrdynamics, JD Jackson, John Wiley 2. Electrodynamics, DJ Griffith, Prentice Hall of India 3. Introduction to Plasma Physics: Francis F. Chen 4. Plasma Physics,: S.N. Sen PAGE 24 DR. BHIM RAO AMBEDKAR UNIVERSITY, AGRA . MASTER OF SCIENCE (PHYSICS) SECOND SEMESTER PAPER-205 PRACTICAL MAX. MARKS: 100 (a) Practical 60 Marks (b) Record 20 Marks (c) Viva-Voce 20 Marks 1. e/m by Zeeman Effect. 2. Analysis of elliptically polarized light by Babinet Compensator. 3. Absorption spectra by constant deviation spectrometer 4. Hall constants 5. Study of regulated power supply. 6. Study of multivibrators. 7. Study of filters (Low pass, high pass, band pass, band rejection) 8. Verification of Hartmann’s relation 9. Stefan’s constant 10. Magnetic susceptibility measurement PAGE 25 DR. BHIM RAO AMBEDKAR UNIVERSITY, AGRA . MASTER OF SCIENCE (PHYSICS) THIRD SEMESTER PAPER- 301 Quantum Mechanics-II MAX. MARKS: 075 Unit I Scattering theory and time dependent perturbation, scattering cross-section, relation between angles, energies etc. in laboratory and center of mass system of coordinates, Normalization of incoming wave, Differential scattering cross section. Partial wave and phase shifts, optical theorem, Born approximation and its validity condition, study of scattering from a square well potential and a rigid sphere. Unit II Transition probability, Density of continuous states. Golden rule, harmonic perturbation, second order perturbation, Identical particles, Physical meaning of identity, Distinguishability of identical particles, Symmetric and Antisymmetric wave function, Construction from unsymmetrised function, Connection of spin and statistics, collision of identical particles with spin, Pauli spin matrices. Unit III Schrödinger relativistic equation for free particles (Klein-Gorden equation), Dirac relativistic equation, Free particle equation, Properties of Dirac matrices, Free particles solutions, Electron spin, Magnetic moment, Dirac equation of central field of force, Spin-orbital coupling, solution for hydrogen atom, Negative energy states. Unit IV PAGE 26 DR. BHIM RAO AMBEDKAR UNIVERSITY, AGRA . Quantum theory of radiation, Formulation in terms of transition probability, Matrix elements of the perturbation, Transition probability for absorption, Transition probability for emission, Einstein coefficients. Angular momentum, Integral and Half integral angular momentum spin eigen functions, Conservation rules, Coupling of two angular momenta, Clebsch-Gordon coefficients. Books Recommended 1. Quantum Mechanics : LI Schiff, McGraw Hill 2. Modern Quantum Mechanics, JJ Sakurai,Addison Wesley 3. Quantum Mechanics, DJ Griffith, Pearson Education 4. Quantum Mechanics Vol I and II, Cohen Tannoudji, John Wiley. PAGE 27 DR. BHIM RAO AMBEDKAR UNIVERSITY, AGRA . MASTER OF SCIENCE (PHYSICS) THIRD SEMESTER PAPER -302 Nuclear Physics – I MAX. MARKS: 075 Unit – I Basic facts about nuclei, Mass and binding energy, Semi-empirical mass formula, Nuclear size determination using mu-mesic X-rays and scattering of fast electrons, Nuclear spin and magnetic moment of nuclei, Molecular beam resonance method, Nuclear resonance absorption and induction method, Electric quadruple moment Unit – II Alpha decay, Experimental results on alpha decay-Alpha spectra and Geiger- Nutall relation, Theory of alpha decay. Beta-spectra, Fermi’s theory of beta decay, Sergeant’s law, Kurie Plot, Allowed and forbidden transitions, Parity violation in beta-decay, Detection of neutrino. Unit III Gamma emission, Multipolarity of gamma rays, Selection rules, Theoretical prediction of decay constants, Estimation of Transition probabilities, Internal conversion, Angular correlation, Nuclear isomerism, Mossbauer Effect. PAGE 28 DR. BHIM RAO AMBEDKAR UNIVERSITY, AGRA . Unit IV Nuclear models, Evidence of shell structure, magic numbers and spin-orbit coupling, extreme single particle model. Predictions of spin, parity and electromagnetic moments, Collective model-Vibrational and rotational spectra. Books Recommended 1. Nuclear Physics , Kenneth S Krane, John Wiley 2. Nuclear Physics , BL Cohen, TMH 3. Nuclear Physics, HS Hans, New Age International 4. Introductory Nuclear Physics, SM Wong, Prentice Hall of India PAGE 29 DR. BHIM RAO AMBEDKAR UNIVERSITY, AGRA . MASTER OF SCIENCE (PHYSICS) THIRD SEMESTER PAPER-303 Solid State Physics MAX. MARKS: 075 Unit I Crystalline solids, Unit cell and direct lattice, Two and three dimensional Bravais lattices, Close packed structure, Interaction of X rays with matter, elastic scattering from perfect lattice, Reciprocal lattice and its application to diffraction, Laue, powder and rotating crystal method, crystal structure factor and intensity of diffraction maxima. Unit II Point defects , line defects and planer stacking faults, dislocations, role of dislocations in plastic deformations and crystal growth, Observation of imperfections in crystals , X-ray and electron microscopic techniques. Unit III Electrons in periodic lattices, Kronig Penny model, energy bands, Bloch theorem, effective mass, Tight binding, Cellular and pseudo potential method of energy band calculation, Fermi surface, De-Hass Van Alfen effect, cyclotron resonance, magneto resistance , quantum hall effect. PAGE 30 DR. BHIM RAO AMBEDKAR UNIVERSITY, AGRA . Unit IV Superconductivity, critical temperature, persistence currents, isotope effect, Meissner effect, London equations. Weiss theory of ferromagnetism, Heisenberg model and molecular field theory, spin waves and magnons, Curie Weiss law for susceptibility, Ferri and antiferro order, domains and Bloch wall energy. Books Recommended 1. Crystallography and solid state Physics, Verma and Srivastava 2. Introduction to solid state Physics, C. Kittel 3. Solid State Physics, Aschrofft and Mermin 4. Solid State Physics, M. Ali Omar 5. Solid State Physics, JP Srivastava 6. Introduction to solid state theory, Madlung 7. Quantum Theory of solid state, Callaway 8. Theoretical Solid State Physics, Huang PAGE 31 DR. BHIM RAO AMBEDKAR UNIVERSITY, AGRA . MASTER OF SCIENCE (PHYSICS) THIRD SEMESTER PAPER-304 Basic Electronics and Devices MAX. MARKS: 075 UNIT-I Working, Characteristics and Applications of PN junction diode, Zener diode, Tunnel diode, LED, Photo Cell, Solar Cell, PIN diode, SCR, TRIAC, DIAC, Backward Diode. UNIT-II Various current components in junction transistor, Emitter efficiency, the transistor Alpha analytical for transistor Characteristics, analysis of cut off and saturation region, maximum voltage rating, the physical model of C-B transistor. UNIT-III Single stage CB, CE & CC amplifiers and their comparisons, Emitter follower, cascade amplifier. Classification of amplifiers, Load line, Analysis of R C coupled amplifier and T C amplifier using hybrid equivalent circuits. Working characteristics and applications of UJT, PUT, FET, JFET, and MOSFET. UNIT-IV Feedback in amplifiers, Principle, its effect on amplifier characteristics, Classification of oscillators, principle of feedback oscillators, Barkhausen criterion, Analysis of tuned collector, tuned base, Hartley, Colpitt, R C phase shift and Wien bridge Oscillators and Crystal Oscillators. PAGE 32 DR. BHIM RAO AMBEDKAR UNIVERSITY, AGRA . Books Recommended 1. Electronics fundamentals and applications, J.D. Ryder, PHI 2. Electronic devices, circuits and applications, W.D. Stanley, PHI 3. Introduction to electronics, V. K. Mehta PAGE 33 DR. BHIM RAO AMBEDKAR UNIVERSITY, AGRA . MASTER OF SCIENCE (PHYSICS) THIRD SEMESTER PAPER-305 PRACTICAL MAX. MARKS: 100 (a) Practical 60 Marks (b) Record 20 Marks (c) Viva-Voce 20 Marks 1. ESR 2. Millican ‘s method for electronic charge(e). 3. Ionization potential of mercury. 4. e/m by magnetron method. 5. e/m by Thomsan’s method. 6. G. M. counters. 7. Leacher wire (transmission line). 8. Four probe method for conductivity. 9. Operational amplifier (adder/subtractor, differentiation/integration) 10. Characteristics of SCR. PAGE 34 DR. BHIM RAO AMBEDKAR UNIVERSITY, AGRA . MASTER OF SCIENCE (PHYSICS) FOURTH SEMESTER 401 PAPERPAPER-401 NUMERICAL METHODS IN PHYSICS MAX. MARKS: 075 Unit I Interpolation and Curve fitting- Errors in polynomial interpolation, Finite differences (forward, backward and central differences), Interpolation with equally spaced and unevenly spaced points (Newton and Lagrange interpolation formulae), Curve fitting, Polynomial, least squares and cubic spline fitting. Unit II Numerical differentiation and integration - Numerical differentiation – Errors in Numerical differentiation - Trapezoidal rule-Simpson’s 1/3 rule - Simpson’s 3/8 rule - Romberg Integration-Gaussian Integration – Monte Carlo evaluation of integrals - Double Integration Newton-cotes integration formulae. Unit III Solution of linear systems of equations -Matrix inversion method - Gauss elimination method - Gauss-Jordan Method – Modification of Gauss method to compute the inverse of a matrix, Solution of linear systems-Iterative methods - The eigen value problem-Power and Jacobi’s method to solve eignvalue problems. Numerical solution of ordinary differential equations Euler’s and Runge-Kutta methods, Predictor-Corrector methods. PAGE 35 DR. BHIM RAO AMBEDKAR UNIVERSITY, AGRA . Unit IV Numerical Solutions of partial differential equations - Finite difference approximations to derivatives - Laplace equation-Jacobi’s method – Gauss Seidal method, Iterative methods for the solution of equations. Books Recommended 1. Mathematical Methods, G. Sanker Rao, K. Keshava Reddy, I.K.International Publishing House, Pvt. Ltd. 2. Introductory Methods of Numerical Analysis, S.S. Sastry, PHI Pvt. Ltd. 3. An Introduction to Computational Physics, Tao Pang, CUP 4. Computer Oriented Numerical Methods, V. Rajaraman, PHI, 2004. 5. Numerical Methods, Balaguruswami, Tata McGraw Hill, 2009. PAGE 36 DR. BHIM RAO AMBEDKAR UNIVERSITY, AGRA . MASTER OF SCIENCE (PHYSICS) FOURTH SEMESTER 402 Nuclear Physics – II PAPERPAPER-402 MAX. MARKS: 075 Unit I Nuclear two-body problem, Simple theory of deuteron, Spin dependence and non-central feature of nuclear forces, Partial wave analysis, Low energy n-p scattering, Scattering length and effective range theory, Low energy p-p scattering, Charge symmetry and charge independence of nuclear forces, Meson theory of nuclear forces. Unit – II Nuclear reactions, Conservation laws, The Q-equation and deduction of nuclear energy levels, Compound nucleus, Bohr hypothesis, Resonance phenomena, Breit- Wigner one level formula, Optical model, Simple discussion of direct reactions, Nuclear fission, Bohr-Wheeler theory of nuclear fission, Controlled chain reaction, Nuclear reactors, Nuclear Fusion. Unit III Classification of fundamental forces, elementary particles and their quantum numbers (charge, spin parity, isospin, strangeness etc.), conservation laws, associated production and strangeness, TAU – Theta puzzle, parity, time reversal and charge conjugation, CP violation, CPT Theorem. PAGE 37 DR. BHIM RAO AMBEDKAR UNIVERSITY, AGRA . Unit IV Special Unitary groups, SU(2) and SU(3), Quark, Quark Structure of hadrons, Gellman Okubo mass Formula, Hyperons, Hyper-nuclei. Books Recommended 1. Introduction to Nuclear Physics, HA Enge, Addison Wesley 2. Concepts of Nuclear Physics, BL Cohen, TMH 3. Physics of Nuclei and particles, marmier and Sheldon Vol I and II , Academic Press 4. Introductory Nuclear Physics, SM Wong, Prentice Hall of India PAGE 38 DR. BHIM RAO AMBEDKAR UNIVERSITY, AGRA . MASTER OF SCIENCE (PHYSICS) FOURTH SEMESTER PAPER-403 (OPTIONAL GROUP A – i) Condensed Matter Physics I MAX. MARKS: 075 Unit I Interatomic forces, vibrations of mono and diatomic linear chain of atoms, lattice dynamics of simple metals, ionic and covalent solids, optical phonons and dielectric constants, Inelastic neutron scattering, Mossbauer effect, Debye Waller factor, Anhamonicity and thermal expansion. Unit II Interaction of electrons and phonons with photons, Direct and indirect transitions absorption in insulators, polaritons, one phonon absorption, optical properties of metals, skin effect and anomalous skin effect. Unit III Interaction of electrons with acoustic and optical phonons, polarons, superconductivity, manifestation of energy gap, Electrodynamics and thermodynamics of superconductors. Unit IV Electron –electron interaction via phonons, Cooper pairs, BCS theory of superconductivity, Ginzberg Landau theory, d.c. and ac Josephson effect, macroscopic quantum interference, vortices and type II superconductors, High temperature superconductors. PAGE 39 DR. BHIM RAO AMBEDKAR UNIVERSITY, AGRA . Books Recommended 1. Integrated electronics, Millman and Halkias 2. Opamp and linear integrated circuit, R. A. Gayakwad 3. Linear integrated circuit, Choudhary and Jain 4. Digital principle and applications, A P Malvino and D P Leach, McGrawHill 5. Digital circuit and design, S. Salivahanan and S. Arivazhagan 6. Modern digital electronics, R.P. Jain 7. Microwave communication system, Kennedy 8. Introduction to radar system, Skolnik 9. Electronics communication system, Symon Hykins 10.Opto Electronics, Wilson and Halks 11.Principle of communication system, Taub and Schilling 12.Microelectronics, Millman and Grabel PAGE 40 DR. BHIM RAO AMBEDKAR UNIVERSITY, AGRA . MASTER OF SCIENCE (PHYSICS) FOURTH SEMESTER PAPER-404 (OPTIONAL GROUP A – ii) Condensed Matter Physics II MAX. MARKS: 075 Unit I Electrons in solids: Interacting electron gas, Hartree and Hartree Fock approximations, correlation energy, screening, plasma oscillations, dielectric function of an electron gas in random phase approximation, Limiting cases and Friedal oscillations, Strongly interacting Fermi systems, Landau theory of Fermi liquids Unit II Structure and symmetry of liquids, liquid crystals and amorphous solids, types and properties of liquid crystals, applications, aperiodic solids and quasicrystals, Fibonacci sequence, Penrose lattices and their extension to three dimensions. Unit III Special carbon solids, Fullerines and carbon nano tubes, single wall and multi wall nanotubes, mechanical and electronic properties of tubules, carbon nanotube based electronic devices, methods of synthesis of nano structured materials, Quantum size effects: quantum wells, wires and quantum dots. Unit IV PAGE 41 DR. BHIM RAO AMBEDKAR UNIVERSITY, AGRA . Films and surfaces: Study of surface topography by multiple beam interferometry, conditions of accurate determination of step height and film thickness, electrical conductivity of thin films. Elementary concepts of surface crystallography, scanning, tunneling and atomic force microscopy. Books Recommended 1. Integrated electronics, Millman and Halkias 2. Opamp and linear integrated circuit, R. A. Gayakwad 3. Linear integrated circuit, Choudhary and Jain 4. Digital principle and applications, A P Malvino and D P Leach, McGrawHill 5. Digital circuit and design, S. Salivahanan and S. Arivazhagan 6. Modern digital electronics, R.P. Jain 7. Microwave communication system, Kennedy 8. Introduction to radar system, Skolnik 9. Electronics communication system, Symon Hykins 10.Opto Electronics, Wilson and Halks 11.Principle of communication system, Taub and Schilling 12.Microelectronics, Millman and Grabel PAGE 42 DR. BHIM RAO AMBEDKAR UNIVERSITY, AGRA . MASTER OF SCIENCE (PHYSICS) FOURTH SEMESTER PAPER-403 (OPTIONAL GROUP B – i) Electronics-I MAX. MARKS: 075 Unit I Operational Amplifier, Applicability of OP-Amp in analog computation, OP-Amp as voltage follower, Adder substractor , Integrator, Differentiator, Log Amplifier, Antilog amplifier, Analog multimeter, Divider circuit, RMS circuit, function fitting and time function generator. Unit II Active Filter, Comparator, Multivibrator, Schmitt Trigger, Triangular wave generator, voltage controlled oscillator, phase locked loop, voltage to frequency and frequency to voltage convertor, A/D and D/A convertor circuit, 555 timer. Unit III Number system, codes (Grey code, ASCII code and BCD code), Basic circuit, logic gates, DTL, RTL and TTL and ECL logic circuit, Karnaough (K) map, pairs, Quads and octaves. Unit IV Half adder, full adder, half substracter and full substracter, data processing circuit, Multiplexers, Demultiplexers, Encoder and Decoder, Flip-Flop, Synchronous and asynchronous counters, Serial and parallel shift registers. PAGE 43 DR. BHIM RAO AMBEDKAR UNIVERSITY, AGRA . Books Recommended 1. Verma and Srivastava: Crystallography and solid state Physics 2. C. Kittel: Introduction to solid state Physics 3. Aschrofft and Mermin: Solid State Physics 4. M. Ali Omar: Solid State Physics 5. JP Srivastava: Solid State Physics 6. Madlung: Introduction to solid state theory 7. C.Kittel: Quantum Theory of Solids 8. Huang: Theoretical Solid State Physics 9. . Nano Technology , C Poole 10. SO Pillai, Solid State Physics, New Age Publishers 11. Callaway: Quantum Theory of solid state 12. Heavens: Thin Films 13. Tolansky ; Multiple Beam Interferometry PAGE 44 DR. BHIM RAO AMBEDKAR UNIVERSITY, AGRA . MASTER OF SCIENCE (PHYSICS) FOURTH SEMESTER PAPER-404 (OPTIONAL GROUP B – ii) Electronics-II MAX. MARKS: 075 Unit I Amplitude Modulation, Modulation and Demodulation Techniques, Frequency Modulation, Phase modulation, Equivalence between AM, FM and PM modulation, Digital modulation, sampling and quantization, pulse code modulation, ASK, FSK, PSK and DPSK. Unit II Generation of microwave by Klystron Osculated, reflex Klystron, magnetron, TWT and semiconductor gun diode, wave guide, cavity resonator, Microwave antenna, microwave detector, VSWR, power and dielectric measurement. Unit III Basic of satellite communication, link factors affecting satellite communication, transponders, basic radar system, types of radar, Modern radar, T.V. transmitter and receiver, colour Television, Antenna system, Yagi Antena. Unit IV Wave propagation in an isotropic media, Transmission and fiber losses in fiber, Dispersion, optical wave guide, optical fiber source and detector, Coupler, Modern telephone optic mux, basic ideas of CDMA, GSM mobiles, GPS & GPRS Technology. PAGE 45 DR. BHIM RAO AMBEDKAR UNIVERSITY, AGRA . Books Recommended 1. Verma and Srivastava: Crystallography and solid state Physics 2. C. Kittel: Introduction to solid state Physics 3. Aschrofft and Mermin: Solid State Physics 4. M. Ali Omar: Solid State Physics 5. JP Srivastava: Solid State Physics 6. Madlung: Introduction to solid state theory 7. C.Kittel: Quantum Theory of Solids 8. Huang: Theoretical Solid State Physics 9. . Nano Technology , C Poole 10.SO Pillai, Solid State Physics, New Age Publishers 11.Callaway: Quantum Theory of solid state 12.Heavens: Thin Films 13.Tolansky ; Multiple Beam Interferometry PAGE 46 DR. BHIM RAO AMBEDKAR UNIVERSITY, AGRA . MASTER OF SCIENCE (PHYSICS) FOURTH SEMESTER PAPER-405 PRACTICAL MAX. MARKS: 100 (a) Practical 60 Marks (b) Record 20 Marks (c) Viva-Voce 20 Marks Paper 405 (A) Electronics 1. Solution of second order differential equations using operational amplifier. 2. Amplitude modulation 3. Frequency modulation 4. Pulse amplitude modulation. 5. Hybrid (h) parameters 6. Hartley oscillator 7. Colpitt oscillator 8. Power amplifier 9. UJT 10. J K and R S flip flop PAGE 47 DR. BHIM RAO AMBEDKAR UNIVERSITY, AGRA . 11. Phase shift resistors and counters 12. A/D and D/A convertors 13. Sattellite Communication 14. Emitter follower Paper 405 (B) Condensed Matter Physics 1. Hall Effect 2. Ge conductivity 3. Modulus of rigidity 4. Conductivity of Ge by fouir probe method 5. Magneto resistance 6. Fluorescence 7. ESR 8. Lattice dynamics 9. Solar cell and photo diode 10. Hystresis 11. Study of ferromagnetic material PAGE 48