POST GRADUATE PROGRAM
COURSE TITLE : MSc Phy
DURATION : 2 YEAR
MODE : SEMESTER
TOTAL DIPLOMA MARKS : 900
CLASSICAL MECHANICS SUBJECT CODE: MSCP/Y/110
Mechanics of a particle and system of particles, Constraints and generalized co-ordinates, D’Alembert’s principle, Principle of Virtual work, Lagrange’s equations of motion, Velocity dependent potential and dissipation function, Applications of Lagrange’s equation of motion for systems like single particle in space, Atwood’s machine, Bead sliding on rotating wire.
Hamilton’s principle, Derivation of Lagrange’s equations from Hamilton’s principle, Hamilton’s equation of motion, Cyclic co-ordinates and conservation theorems, Derivation of Hamilton’s equations from Variational principle and principle of least action.
The equations and examples of Canonical transformations, Harmonic oscillator, Poisson bracket, Poisson theorem, The angular momentum, Poisson bracket relation, Liouville’s Theorem.
Two Body Central Force Problems
Reduction to the equivalent one body problem, The equivalent one dimensional problem, Classification of orbits, Virial theorem, Differential equations for the orbit, Integral power law potential, Kepler’s problem, Motion and time in Kepler’s problem, Scattering in central force field, Transformation of scattering problem to laboratory co-ordinates.
MATHEMATICAL PHYSICS SUBJECT CODE: MSCP/Y/120
Bessel functions: Bessel function of first kind, Generating function, Recurrence relations, Jn(x) as solution of Bessel function , Expansion of Jn(x) when n is half an odd integer; ^ Generating functions for Pn(x), Recurrence relations and special properties, Pn(x) as solution of Legendre differential equation, Orthogonality of Pn(x).
Laplace and Inverse Laplace Transform
Conditions of existence, Laplace transformations of elementary functions, Basic theorem of Laplace transforms and its properties, Laplace transform of derivatives, Laplace transform of integrals.
Properties and related theorem for Inverse Laplace Transform, Inverse Laplace transforms of derivatives and integrals, Convolution theorem.
Gamma and Beta Functions: Definition of beta and gamma function in terms of Euler integrals, Evaluation of Γ(1/2), Recurrence relation for gamma functions, Various forms of beta functions, Relation between beta and gamma functions, Evaluation of integrals using gamma functions.
^ Fourier series, Dirichlet conditions, Expansion of periodic functions in Fourier series, Sine and Cosine transforms, Complex form of Fourier series, Fourier Integral theorem and Fourier Transform.
Fourier integrals, Physical applications of Fourier series analysis: Square waves (high frequencies), Full wave rectifier, Expansion of Riemann Zeta function.
NUCLEAR PHYSICS SUBJECT CODE: MSCP/Y/130
Survey of some nuclear properties, Nuclear radius, Nuclear masses and abundances, Binding energy, Electric and magnetic moments and nuclear shapes, Nuclear angular momentum and parity, Nuclear spin, Nuclear moments.
Nuclear stability and the forces between nucleons, Deutron problem, n-p scattering at low energies, Scattering length, Spin dependence of n-p scattering, Effective range in n-p scattering.
Liquid drop model, Semi-empirical mass formula, Magic numbers, Shell model, The collective model.
Types of nuclear reactions, Reaction cross-section, Conservation laws, Q-values and its significance, Breit-Winger formula, Compound nucleus, Optical model, Direct reactions.
Interaction of radiation with matter, G.M. counter: Basic principle, working, quenching and mechanism of pulse formation; Gamma Ray Spectrometer: Basic principle and working of NaI(TI) detector, Pulse formation mechanism, Basic idea of pulse processing unit, Concept of energy resolution and efficiency;
Semiconductor detectors: Basic principle, Construction and working of Si Surface barrier, Lithium drifted and high purity Germanium detectors.
SOLID STATE PHYSICS SUBJECT CODE: MSCP/Y/140
Basic Concepts, Crystal nomenclature, crystal structure, lattice planes and miller indices, Reciprocal lattice, Construction of reciprocal lattice, Relation between direct and reciprocal lattice vectors, Reciprocal lattice of simple cubic, bcc, fcc lattices. Origin of X-rays, Bragg’s law, Laue method, Powder method and Rotating crystal method,
Classical free electron theory, Drawbacks of Classical Theory, Relaxation time, Collision time and Mean free path, Quantum theory of free electrons, Fermi-Dirac Statistics and Distribution of Electrons in Solids, Effect of Temperature on F-D Distribution, Free Electron Gas in Three Dimension, Heat Capacity of Electron Gas, Electrical Conductivity and Ohm’s Law, Matthiessen’s Rule, Cyclotron Frequency, Hall Effect, Thermal Conductivity of Metals- Wiedemann-Franz Law.
Band Theory of Solids
Introduction, Classification of Solids on the Basis of Band Theory, Bloch theorem, Nearly free electron model, origin of energy gap, magnitude of energy gap, Bloch theorem, The Kroning-Penney Model, The motion of electrons in one dimension according to the band theory, effective mass, concept of holes.
Experimental Survey, Occurrence of Superconductivity, Destruction of Superconductivity by Magnetic Fields, Kondo Effect, Meissner Effect, Type I and Type II Superconductors, Thermal Properties of Superconductors, Magnetic Penetration Depth, Coherence Length., Ginzburg-Landau Coefficient, Isotope Effect, Thermodynamics of the superconducting transitions, London equation, Flux Quantization, Josephson Superconductor Tunneling, dc Josephson Effect, ac Josephson Effect, Applications of superconductors, High Temperature superconductors.
ELECTRONICS DEVICES AND CIRCUITS SUBJECT CODE: MSCP/Y/150
Bipolar Junction Transistor & its Biasing: Transistor Structure, Basic Transistor Operation, Transistor Characteristics and Parameters, Transistor as an Amplifier and as a Switch, DC Operating Point, Voltage Divider Bias.
^ Amplifier Operation, AC Equivalent Circuit, Common-Emitter Amplifier, Common-Collector Amplifier, Common-Base Amplifier.
Field Effect Transistor & its Biasing: JFET Structure, Basic Operation, JFET Characteristics and Parameters, JFET Biasing, MOSFET Structure & Operation, MOSFET Characteristics and Parameters.
^ FET Amplification, Common-Source Amplifier, Common-Drain Amplifier, Common-Gate Amplifier.
Two Terminal Devices: Schottky (Hot-Carrier) Barrier Diodes, Varactor (Varicap) Diodes, Power Diodes, Tunnel Diodes, Photodiodes, Thermistors.
^ Basic 4-layer device, Silicon controlled rectifier (SCR), SCR applications: on-off control of current, half wave power control, SCR crowbar, Difference between power FET and SCR, DIAC, TRIAC, TRIAC phase control application, Silicon controlled switch (SCS), Uni-junction transistor (UJT).
Operational Amplifiers: Introduction, Basic Information of Operational Amplifier, Ideal Operational Amplifier, Inverting and Non-Inverting Amplifier, Differential Amplifier, Common Mode Rejection Ratio (CMRR), Emitter Coupled Difference Amplifier.
^ Introduction, DC Characteristics, Input Bias Current, Input Offset Current, Input Offset Voltage, Total Output Offset Voltage, Thermal Drift, Slew Rate.
QUANTUM MECHANICS SUBJECT CODE: MSCP/Y/0160
Introduction to Quantum Mechanics
Inadequacy of classical mechanics, Operators and expectation values, Hermitian operator, Exchange operator and identical particles, Ehrenfest theorem, Postulates of quantum mechanics, Eigen values and eigenfunctions, Completeness of eigenfunctions, Uncertainty principle.
Hermitian and Unitary matrices, Matrix transformation and diagonalization, Construction of unitary matrix, Representation of operators, transformation of operators with unitary matrices, Hilbert’s space, Dirac’s bra and ket notation. Time development of quantum system: Schroedinger, Heisenberg and interaction pictures, One dimensional harmonic oscillator problem in matrix formulation.
Orbital angular momentum, Representation in cartesian and polar coordinates, Commutation relations, General angular momentum, Eigen values and eigenfunctions of L2 and Lz; J2 and Jz.
Matrix representation of angular momentum operators, Spin angular momentum and Pauli’s matrices, Addition of angular momenta, Clebsch-Gordon coefficients and its calculation for j1= j2= 1/2; j1=1, j2= 1/2, Properties of Clebsch-Gordon coefficients.
Time Independent Perturbation Theory
Time independent perturbation theory for non-degenerate system up to second order perturbation, Physical applications of non-degenerate perturbation theory, The Variation (Rayleigh -Ritz ) method with applications to ground state of helium, Zero point energy of one dimensional harmonic oscillator.
Time dependent perturbation theory, Transition probability: Fermi-Golden rule, Harmonic perturbation, Adiabatic approximation, Sudden approximation, Application of time dependent perturbation theory to transition probability for induced absorption and emission, Selection rules.
Quantum Theory of Scattering-I
The scattering amplitude and cross section, Green’s functions in scattering theory and expression for scattering amplitude, Born Approximation, Condition for validity of Born Approximation, Scattering by a screened Coulomb Potential, Rutherford’s scattering formula from Born Approximation.
Scattering by spherically symmetric potentials: Method of partial waves, phase shift, Scattering amplitude in terms of phase shift, Differential and total cross-sections, Optical theorem, Relation of phase shift with potential.
LAB. WORK SUBJECT CODE: MSCP/Y/170
LAB. WORK SUBJECT CODE: MSCP/Y/180