Semester II
Quantum Mechanics - II
Course No: PHY-C201
Duration of Examination: 2.30 hrs.
Max. Marks: 100
(a) External Examination: 80
(b) Internal Assessment: 20
(Valid for sessions 2011, 2012 & 2013)
UNIT I
Time-independent perturbation theory; Non-degenerate & degenerate cases,
Applications such as linear harmonic oscillator, Zeeman effect, Stark effect;
Variational method and its applications, WKB approximation, Solution of bound state
problems, Time – dependent perturbation theory, Harmonic perturbation; Fermi’s
golden rule; Adiabatic and sudden approximation
UNIT II
Collision in 3-D and scattering; Laboratory and CM reference frames; Scattering
amplitude; differential scattering cross and total scattering cross; Scattering by
spherically symmetric potentials; Partial waves and phase shifts; Scattering by a
perfectly rigid sphere and by square well potential; Complex potential and absorption.
UNIT III
Identical particles; Symmetric and antisymmetric wave functions; Spin and Statistics,
The Exclusion Principle, Distinguishability of Identical Particles, Collision of
identical particles; Spin angular momentum; Spin functions for a many-electron
system;
Semi classical theory of radiation; Transition probability for absorption and induced
emission; Electric dipole and forbidden transitions; Selection rules.
UNIT IV
Relativistic QM: The Klein – Gordon equation, Free particle solutions, probability
density & probability current density, interpretation of negative energy solutions of
the K-G equation. The Dirac equation, Free particle solutions, Probability density and
probability density current for the free particle Dirac equation, Spin of an electron,
Interpretation of negative energy states.
Text and Reference Books
L l Schiff, Quantum Mechanics (McGraw-Hill)
Cohen, Diu and Laloe Quantum Mechanics
A P Messiah, Quantum Mechanics
J J Sakurai, Modern Quantum Mechanics
Mathews and Venkatesan, Quantum Mechanics
Bjorken & Drell, Relativistic Quantum Mechanics
J.R. Aitchson, Relativistic Quantum Mechanics
W.Greiner, Relativistic Quantum Mechanics
Semester II
Statistical Mechanics
Course No: PHY-C202
Duration of Examination: 2.30 hrs.
Max. Marks: 100
(a) External Examination: 80
(b) Internal Assessment: 20
(Valid for sessions 2011, 2012 & 2013)
UNIT I
Statistical Distributions; Statistical independence. Liouvilles theorem, Significance of
energy. Statistical Matrix, Statistical Distributions in quantum Statistics. Entropy;
Law of increase of Entropy. Microcanonical, Canonical and Grand Canonical
ensmble. Partition Function, Calculation of Statistical Quantities, Energy and Density
Fluctuations.
Unit II
Gibbs distribution, Maxwellian distribution. Probability distribution for an Oscillator.
Free energy in the Gibbs distribution. Thermodynamics Perturbation theory,
Expansion in powers of ħ. Gibbs distribution for rotating bodies and for a variable
number of particles. Derivation of thermodynamics relations from the Gibbs
distribution.
Unit III
Fermi distribution, Bose distribution. Fermi and Bose gases of elementary particles.
Degenerate electron gas, Specific heat of degenerate electron gas. Magnetism of an
electron gas. Weak fields, Strong fields. Relativistic degenerate electron gas.
Degenerate Bose gas. Black body Radiation.
Deviation of gases from the ideal state, Expansion in powers of density. Relationship
of the virial coefficient and the scattering amplitude.
Unit IV
Conditions for phase equilibrium; the Clapeyron-Clausius formula, Critical point.
Law of Corresponding states. Phase transitions of the second kind. Discontinuity of
Specific heat. Effect of an external field on a phase transition. Change in symmetry in
a phase transition of the second kind. Fluctuations of the order parameter. The
effective Hamiltonian. Critical indices, scale invariance. Isolated and Critical points
of Continous transition. Phase transition of the second kind in a two dimensional
lattice.
Text book and reference books
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Statistical Physics, Landau and Lifshitz.
Statistical Mechanics, by K Huang.
Statistical and Thermal Physics, by F. Reif.
Statistical Mechanics by Pateria
Fundamentals of Statistical Mechanics by B.B. Laud
Statistical Mechanics by R.K.Srivastava & j.Ashok
Thermodynamics and Statistical Mechanics by Greiner, Neise and Stocker
Semester II
Electrodynamics and Plasma Physics
Course No: PHY-203
Duration of Examination: 2.30 hrs.
Max. Marks: 100
(a) External Examination: 80
(b) Internal Assessment: 20
(Valid for sessions 2011, 2012 & 2013)
UNIT I
Four Vectors and Tensors, Covariant and Contravariant tensors and their properties,
Lorentz transformation, Four potential, Equations of motion of a charge in
electromagnetic field, Gauge invariance, Constant electric and magnetic fields and
constant electromagnetic field.
UNIT II
Electromagnetic field tensor, Invariants of the field, Maxwell’s equations in covariant
form, Four dimensional current vector and continuity equation, Electromagnetic
energy-momentum field tensor, Electric and magnetic dipole and quadropole
moments.
UNIT III
Field due to moving charges, Retarded potential, Leinard – Wiechert potential, Field
of a system of charges at large distance, Dipole radiation during collision,
Quadrupole and magnetic dipole radiation, Synchrotron radiation, radiation damping.
UNIT IV
Elementary concepts: Plasma oscillation, Debye shielding, Plasma parameters,
Plasma confinement, Hydrodynamical description of plasma, Wave phenomena in
Magneto plasma, Polarization, Phase velocity, Group velocity, Cutoffs, Resonance for
Electromagnetic wave, Propagation parallel & perpendicular to the Magnetic field,
Propagation of E.M.Wave through ionosphere and Magnetosphere, Helican, Whistler,
Faraday rotation.
Text Books and Reference books:
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Landau and Lifshitz, Classical Theory of Fields.
Chen, Plasma Physics
Semester II
Atomic and Molecular Physics
Course No: PHY-C204
Duration of Examination: 2.30 hrs.
Max. Marks: 100
(a) External Examination: 80
(b) Internal Assessment: 20
(Valid for sessions 2011, 2012 & 2013 )
UNIT I
One-electron atoms: Fine structure of hydrogenic atoms;energy shifts. The Lamb
shift, Hyperfine structure; magnetic dipole hyperfine structure. Zeeman effect; weak
and strong fields-Paschen-Back effect. Stark effect (linear and quadratic).
Two-electron atoms: The Schrodinger equation for two-electron atoms. Spin wave
functions and the role of the Pauli exclusion principle. The independent particle
model: The ground state of two-electron atoms.
UNIT II
Many-electron atoms: The central field approximation, Spin-orbitals and Slater
determinants The Thomas-Fermi model of the atom. The Thomas-Fermi Theory of
multielectron atoms. Introduction to Hartree-Fock method and Density functional
theory
Correlation effects; L-S coupling and j-j coupling: Possible terms of a multi-electron
configuration in L-S coupling. Fine structure of terms in L-S coupling, Lande interval
rule.
UNIT III
Interaction of atom with an electromagnetic field: Transition rates for absorption,
stimulated emission and spontaneous emission; dipole approximation. The Einstein’s
coefficients. Selection rules of one electron atoms. Selection rules for many-electron
atoms; electric dipole and electric quadrupole transitions. Line shapes and widths:
Pressure Broadening and Doppler Broadening.
UNIT IV
Molecular structure: The Born-Oppenheimer separation for diatomic molecules.
The rotation and vibration of diatomic molecules. Rotational spectra of diatomic
molecules: Vibrational and vibrational-rotational spectra of diatomic molecules.
Raman Effect: quantum mechanical theory of Raman Effect. Rotational and
Vibrational-Rotation Raman Spectroscopy.
Text Books and reference books
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Physics of atoms and molecules by B.H. Brandsen and C.J. Joachain ,2 nd Ed.
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Spectra of Atoms and Molecules by Peter F. Bernath (Oxford University Press)
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Atoms and Molecules by Mitchel Weissbluth.
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Introduction to Atomic Spectra - H E White (T)
Fundamentals of molecular spectroscopy – C B Banwell (T)
Spectroscopy Vol I, II & III – Walker & Straughen
Introduction to Molecular Spectroscopy – G M Barrow
Spectra of diatomic molecules – Herzberg
Molecular spectroscopy – Jeanne L McHale
Molecular spectroscopy – J M Brown
Spectra of atoms and molecules – P F Bermath
Modem Spectroscopy – J M Holias
Semester II
Laboratory and Practical Course
Course No: P - II
Duration of Examination: 6 hrs.
Max. Marks: 100
(a) External Examination: 80
(b) Internal Assessment: 20
(Valid for sessions 2011, 2012 & 2013 )
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Experiment on FET and MOSFET characterization and application as an
amplifier
Experiment on Uni-junction Transistor and its application
Digital I: Basic Logic Gates, TTL, NAND and NOR
Digital II: Combinational Logic
Flip Flops
Operational Amplifier (741)
Differential Amplifier
Measurement of resistivity of a semiconductor by Four probe method at
different temperatures and determination of band gap
Determination of Lande’s factor of DPPH using Electron-Spin resonance
(E.S.R) spectrometer
Measurement of Hall coefficient of given semiconductor: Identification of type of
semiconductor and estimation of charge carrier concentration
To study the fluorescence spectrum of DCM dye and to determine the quantum
yield of fluorescence maxima and full width at half maxima for this dye using
monochromator
To study Faraday effect using He-Ne Laser
Tutorial:
Laboratory/Practical Course
1. Effect of capacitance and load resistance on output of an amplifier
2. Integrated circuit timer familiarization
3. Op-amp differentiator
4. Multiplexers and Demultiplexers
5. Resistors and counters
6. Radiation level and activity measurement
7. Shielding, mass absorption coefficient
8. Coincidence circuits, counters, timers
9. Coherence and it’s relevance in diffraction
10. Identification of charge type by Hall voltage measurement
11. How do four probe methods solve the problem of contact resistance?