Nagarjuna university M.Sc physics first semister syllabus

M.Sc. Physics ( I Semester)
Paper I : MATHEMATICAL PHYSICS PHY 1.1

Unit-I
Special Functions: : Solution by series expansion: Legendre, Associated Legendre, Bessel, Hermite and Lagaurre equations: physical applications: Generating functions: orthogonality properties and recursion relations.

Unit-II
Integral Transforms, Laplace transform; first and second shifting theorems: Inverse LT by partial fractions; LT of derivative and integral of a function; Fourier series; Fourier series of arbitrary period; Half-wave expansions; Partial sums; Fourier n integral and transformations; FT of delta function.

Unit-III
Complex Variables: Complex, Algebra, Cauchy – Riemann Conditions, Analytic functions, Cauchy’s integral theorem, Cauchy’s integral formula, Taylor’s Series, Laurent’s expansion, Singularities, Calculus of Residues, Cauchy’s Residue theorem, Evaluation of Residues , Evaluation of contour integrals.

Unit-IV
Tensor Analysis: Introduction, Transformation of Co-ordinates, Contravariant, Covariant and Mixed tensors, Addition and multiplication of tensors, contraction and Quotient Law. The line element, fundamental tensors.

Text and reference books:

1. Mathematical Methods for Physics. By G.Arfken
2. Laplace and Fourier Transforms”-by Goyal and Gupta. Pragati Prakashan Meerut
3. Matrices and Tensors for Physicists by A W.Joshi
4. Mathematical Physics “ by B.D.Gupta. Vikas Publishing House, New Delhi
5. Complex Variables “ Schaum Series”
6. Vector and Tensor Analysis “Schaum Series”
7.

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 ( I Semester)
Paper II : CLASSICAL MECHANICS PHY 1.2

Unit-I
1. Mechanics of a particle. Mechanics of a system of particles, constraints, D’Alembert’s principle and Lagrange’s equations, Velocity Dependent potentials and the Dissipation function Simple applications of the Lagrangian Formulation

2. Hamilton’s principle, some techniques of the calculus of variations. .Derivation of Lagrange’s equations from Hamilton’s principle. Conservation theorems and symmetry properties, Energy function and the conservation of Energy

Unit-II
3. Reduction to the equivalent one body problem. The equation of motion and first Integrals, The equivalent One – Dimensional problem and classification of orbits, The differential equation for the orbit, and Integrable power –law potentials, Conditions for closed orbits (Bertrand’s theorem), The Kepler problem inverse square law of force , The motion in time in the Kepler problem, Scattering in a central force field..

4. Legendre transformations and Hamilton’s equations of motion. Cyclic Coordinates and conservation theorems, Derivation of Hamilton’s equation of motion from variational principle, Principle of Least Action.

Unit-III
5. Equations of canonical transformation, Examples of Canonical transformations, The harmonic Oscillator, Poisson brackets and other Canonical invariants, Equations of motion, Infinitesimal canonical transformations, and conservation theorems in the poisson bracket formulation, the angular momentum poisson bracket relations.

6. Hamilton – Jacobi equation of Hamilton’s principal function, The Harmonic oscillator problem as an example of the Hamilton – Jacobi Method, Hamilton –Jacobi equation for Hamilton’s characteristic function. Action – angle variables in systems of one degree of freedom.

Unit-IV
7. Independent coordinates of rigid body. , The Euler angles, Euler’s theorem on the Motion of a rigid body, Infinitesimal rotations, Rate of change of a vector, The Coriolis Effect.

8. The Inertia tensor and the moment of inertia, The Eigenvalues of the inertia tensor and the principal axis transformation, Solving rigid body problems and Euler equations of motion, Torque – free motion of a rigid body

9. The Eigenvalue equation and the principal axis transformation, Frequencies of free vibration, and normal coordinates, Free vibrations of a linear triatomic molecule

TEXT BOOKS :“ Classical Mechanics “ by H.Goldstein (Addison-Wleley, 1st & 2nd ed)

REFERENCE :“Classical Dynamics of Particles and Systems” by J.B.Marion.

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 ( I Semester)
Paper III : QUANTUM MECHANICS I PHY 1.3

Unit-I
Why QM? Revision; Inadequacy of classical mechanics; Schrodinger equation; continuity equation; Ehrenfest theorem; admissible wave functions; Stationary states. One-dimensional problems, wells and barriers. Harmonic oscillator by Schrodinger equation.

Linear Vector Spaces in Quantum Mechanics: Vectors and operators, change of basis, Dirac’s bra and ket notations. Eigen value problem for operators. The continuous spectrum. Application to wave mechanics in one dimension. Hermitian, unitary, projection operators. Positive operators. Change of orthonormal basis. Orthogonalization procedure.

Unit-II
Angular momentum: commutation relations for angular momentum operator. , Angular Momentum in spherical polar coordinates, Eigen value problem for Lz and Lz,L + and L_ operators Eigen values and eigen functions of Rigid rotator and Hydrogen atom

Unit III
Time-independent perturbation theory; Non-degenerate and degenerate cases; applications to a)normal helium atom b) Stark effect in Hydrogen atom. Variation method. Application to ground state of Helium atom. WKB method.

Unit IV
Time dependent perturbation : General perturbations, variation of constants, transition into closely spaced levels –Fermi’s Golden rule. Einstein transition probabilities, Interaction of an atom with the electro magnetic radiation. Sudden and adiabatic approximation.

TEXT AND REFERENCE 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

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 ( I Semester)
Paper IV : ELECTRONICS (General) PHY 1.4

UNIT I
Operational Amplifiers: Differential Amplifier –circuit configurations - dual input, balanced output differential amplifier – DC analysis – Ac analysis, inverting and non inverting inputs CMRR - constant current bias level translator .Block diagram of a typical Op-Amp-analysis. Open loop configuration inverting and non-inverting amplifiers. Op-amp with negative feedback- voltage series feedback – effect of feedback on closed loop gain input resistance output resistance bandwidth and output offset voltage- voltage follower.

UNIT-II
Practical Op-amps: Input offset voltage- input bias current-input offset current, total output offset voltage, CMRR frequency response.

DC and AC amplifier- summing, scaling and averaging amplifiers, instrumentation amplifier, integrator and differentiator.

Oscillators principles – oscillator types – frequency stability – response – The phase shift oscillator, Wein bridge oscillator – LC tunable oscillators – Multivibrators- Monostable and astable –comparators – square wave and triangular wave generators.

Voltage regulators – fixed regulators – adjustable voltage regulators switching regulators.

UNIT III
Communication Electronics: Amplitude modulation – Generation jof AM waves – Demodulation of AM waves – DSBSC modulation. Generation of DSBSC wages., coherent detection of DSBSC waves, SSB modulation, Generation and detection of SSB waves. Vestigial side band modulation, Frequency division multiplexing (FDM).

Digital Electronics: Combinational Logic- Decoder- encoders- Multiplexer(data selectors)-application of multiplexer - De multiplexer( data distributors) –Sequential Logic- Flip-Flops: A 1 bit memory – the R-S Flip – Flop, JK Flip-Flop – JK master slave Flip-Flops – T- Flip – Flop – D Flip – Flop – Shift registers – synchronous and asynchronous counters – cascade counters.

UNIT IV
Microprocessors:Introduction to microcomputers – memory – input/output –interfacing devices
8085 CPU -Architecture – BUS timings – Demultiplexing the address bus – generating control signals – instruction set – addressing modes – illustrative programmes – writing assembly language programmes –looping, counting and indexing – counters and timing delays – stack and subroutine.

Introduction to micro controllers-8051 micro controllers-architecture & pin description-Parallel I/O ports – memory organization.

Text and Reference Books

Electronic devices and circuit theory by Robert Boylested and Louis Nashlsky PHI 1991

Op-Amps & Linear integrated circuits by Ramakanth A.Gayakwad PHI 1991

Semi Conductor Electronics by A.K.Sharma New Age International Publishers.

Fundamentals of Digital Circuits by A.Ananda Kumar,PHI,New Delhi.

Digital principles and applications by A.P.Malvino and Donald P.Leech TMH 1993

Microprocessor Architecture, Programming and Applications with 8085/8086 by Ramesh S.Gaonkar, Wiely-Eastern 1987.

Micro Controllers: Theory and Applications by Ajay V. Deshmukh,Tata Mc Graw- Hill.New Delhi, 2005

Electronics-anlog and digital – Nagarath PHI

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.