M.Sc. Physics ( II Semester)
Paper-I QUANTUM MECHANICS-II PHY 2.1
UNIT-I
Spin and Total angular momentum;
Total angular momentum J. Explicit matrices for J2,Jx,Jy & Jz.Combination of two angular moment and tensor operator: Clebsch-Gordon coefficients for j1=1/2 , j2 =1/2 and j1=1 , j2 =1/2 Wigner-Eckart theorem.
UNIT-II
Quantum Dynamics and identical particles
Equation of motion in Schrödinger’s picture and Heisenberg’s picture, correspondence between the two. Correspondence with classical mechanics. Application of Heisenberg’s picture to Harmonic oscillator. The indistinguishability of identical particles – The state vector space for a system of identical particles – Creation and annihilation operators- continuous one particle system- Dynamical variables – the Quantum dynamics of identical particle systems
UNIT-III
Scattering Theory
Introduction of scattering – notion of cross section – scattering of a wave packet- scattering in continuous stream model – Green’s function in scattering theory – Born’s approximation – first order approximation – criteria for the validity of Born’s approximation . Form factor- scattering from a square well potential – partial wave analysis – Expansion of a plane wave – optimal theorem – calculation of phase shifts – low energy limit – energy dependence of be - scattering from a square well potential.
UNIT-IV
Molecular Quantum Mechanics
The Born-Openheimer Approximation – The hydrogen molecule ion the Hydrogen molecule – The valance bond method – The molecular orbital method- Comparison of the methods – Heitler-London method.( Ref : Atkins, Chapter-9, 279-294).
Text books
Merzbecher, Quantum Mechanics
L I Schiff, Quantum Mechanics (Mc Graw-Hill)
B Craseman and J D Powell, Quantum Mechanics (Addison Wesley)
A P Messiah, Quantum Mechanics
J J Sakural, Modem Quantum Mechanics
Mathews and Venkatesan Quantum Mechanics
Quantum Mechanics” by R.D. Ratna Raju
Quantum mechanics by Kakani and Chandalia
NOTE : Question paper contains 5 questions. FOUR questions with internal choice have to be set from each unit. The 5thquestion has 4 short answers question covering units I to IV and any two be answered.
M.Sc. Physics ( II Semester)
Paper II : Statistical Mechanics PHY 2.2
Classical Statistical Mechanics
UNIT I
Foundations of statistical mechanics; specification of states of a system,
contact between statistics and thermodynamics, Postulate of classical stastical mechanics- phase space, trajectories - Ensembles-micro canonical,canonical and grand canonical - Density of states - Liouville’s theorem -equi-partition theorem- Classical ideal gas: entropy of ideal gas in micro canonical ensemble- Gibb’s paradox.
UNIT-II
2.Canonical ensemble - ensemble density- partition function - Energy fluctuations in canonical ensemble -Grand canonical ensemble- Density fluctuations in the Grand canonical ensemble- Equivalence between the canonical ensemble and Grand canonical ensemble.
Quantum statistical mechanics
UNIT III
3. Postulates of quantum statistical mechanics-Density matrix- Ensembles in quantum statistics- statistics of indistinguishable particles, Maxwell-Boltzmann, Bose-Einstein and Fermi- Dirac statistics - Thermodynamic properties of ideal gases on the basis of micro canonical and grand canonical ensemble. The Partition function: Derivation of canonical ensemble using Darwin and Fowler method.
UNIT IV
4.Ideal Fermi gas : Equation of state of an ideal Fermi gas, theory of
White dwarf stars, Landau diamagnetism.
Ideal Bose gas : Photons – Phonons - Bose Einstein condensation- Random walk- Brownian motion
Text and Reference Books:
Statistical and Thermal Physics by S. Lokanadham and R.S.Gambhir ( PHI).
Statistical Mechanics by K. Huang ( Wiley Eastern )
Statistical Mechanics: Theory and applications by S.K. Sinha
Fundamentals of Statistical and Thermal Physics by F. Reif
Statistical Mechanics by Gupta and Kumar, Pragathi Prakashan Pub. Meerut.
NOTE : Question paper contains 5 questions. FOUR questions with internal choice have to be set from each unit. The 5thquestion has 4 short answers question covering units I to IV and any two be answered.
M.Sc. Physics ( II Semester)
Paper-III:COMPUTATIONAL METHODS AND PROGRAMMING PHY 2.3
UNIT-I
a) Fundamentals of C Language:
C character set-Identifiers and Keywords-Constants-Variables-Data types-Declarations of variables –Declaration of storage class-Defining symbolic constants –Assignment statement.
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.
UNIT –II
a) Control statements and arrays:
If-Else statements –Switch statements-The operators –GO TO –While, Do-While, FOR statements-BREAK and CONTINUE statements.
b) Arrays
One dimensional and two dimensional arrays –Initialization –Type declaration-Inputting and outputting of data for arrays –Programs of matrices addition, subtraction and multiplication
c)User Define functions
The form of C functions –Return values and their types –Calling a function – Category of functions. Nesting of functions. Recursion. ANSI C functions-Function declaration. Scope and life time of variables in functions.
UNIT-III
Linear and Non –linear equations:
Solution of Algebra and transcendental equations-Bisection, Falsi position and Newton-Rhapson methods-Basic principles-Formulae-algorithms
(b) Simultaneous equations:
Solutions of simultaneous linear equations-Guass elimination and Gauss
Seidel iterative methods-Basic principles- Formulae-Algorithms
UNIT-IV
(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)
Paper-IV SOLID STATE PHYSICS (General) PHY 2.4
UNIT I
CRYSTAL STRUCTURE:
Periodic array of atoms—Lattice translation vectors and lattices, symmetry operations, The Basis and the Crystal Structure, Primitive Lattice cell, Fundamental types of lattices—Two Dimensional lattice types, three Dimensional lattice types, Index system for crystal planes, simple crystal structures-- sodium chloride, cesium chloride and diamond structures.
UNIT II
CRYSTAL DIFFRACTION AND RECIPROCAL LATTICE:
Bragg’s law, Experimental diffraction methods-- Laue method and powder method, Derivation of scattered wave amplitude, indexing pattern of cubic crystals and non-cubic crystals (analytical methods). Geometrical StructureFactor, Determination of number of atoms in a cell and position of atoms. Reciprocal lattice, Brillouin Zone, Reciprocal lattice to bcc and fcc Lattices.
UNIT III
FREE ELECTRON FERMI GAS:
Energy levels and density of orbitals in one dimension, Free electron gas in 3 dimensions, Heat capacity of the electron gas, Experimental heat capacity of metals, Motion in Magnetic Fields- Hall effect, Ratio of thermal to electrical conductivity.
FERMI SURFACES OF METALS:
Reduced zone scheme, Periodic Zone schemes, Construction of Fermi surfaces, Electron orbits, hole orbits and open orbits, Experimental methods in Fermi surface studies-- Quantization of orbits in a magnetic field, De-Hass-van Alphen Effect, extremal orbits, Fermi surface of Copper.
UNIT IV
THE BAND THEORY OF SOLIDS:
Nearly free electron model, Origin of the energy gap, The Block Theorem, Kronig-Penny Model, wave equation of electron in a periodic potential, Crystal momentum of an electron-Approximate solution near a zone boundary, Number of orbitals in a band--metals and isolators. The distinction between metals, insulators and semiconductors
TEXT BOOKS:
1.Introdcution to Solid State Physics, C.Kittel, 5th edition,
2.Solid State Physics, A.J.DEKKER.
NOTE : Question paper contains 5 questions. FOUR questions with internal choice have to be set from each unit. The 5thquestion has 4 short answers question covering units I to IV and any two be answered.
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