Download Program Scheme - Manipal University Jaipur

PROGRAM STRUCTURE
MSc: (Physics) by - Research
SEMESTER- I
Course
Code
PY2314
PY 2312
PY 2214
PY 2353
PY 2232
PY 2331
Exam Duration
(Hrs)
Course Name
L
T
P
C
Theory
Atomic, Molecular
& Laser Physics
Nuclear Physics
Solid State Physics
Program Elective-I:
NanoScience and
NanoTechnology- I
Spectroscopy Lab
Solid State Physics Lab
Total Credits
2
1
0
3
3
3
3
3
1
1
1
0
0
0
4
4
4
3
3
3
-
10
10
10
-
0
0
11
0
0
4
6
6
12
3
3
21
-
4
4
-
60
60
SEMESTER- II
Course
Code
PY 2113
PY 2212
PY 2411
PY 2454
PY2180
PY 2132
PY 2431
Practical
Relative Weightage (%)
CWS
10
Exam Duration
(Hrs)
PRS MTE
T
40
40
40
40
ETE
PRE
50
50
50
50
-
-
40
40
Relative Weightage (%)
Course Name
L
T
P
C
Theory
Practical
CWS
PRS
T
-
Electronics
Quantum Mechanics
Nuclear and Radiation
physics
PE-II : Nanoscience
and Nanotechnology-II
Seminar
Electronics Lab
Nuclear Physics Lab
Total Credits
3
3
3
1
1
1
0
0
0
4
4
4
3
3
3
-
10
10
10
3
1
0
4
3
-
10
-
0
0
0
12
0
0
0
4
4
6
6
16
2
3
3
24
-
1
4
4
-
60
60
60
MTE
ETE
PRE
40
40
40
50
50
50
-
40
50
-
-
40
40
40
-
SEMESTER- III
Course
Code
PY 2381
PY 2111
PY 2380
Exam Duration
(Hrs)
Course Name
L
T
P
C
Theory
Practical
CWS
Project I
Mathematical Physics*
Seminar
3
0
1
0
0
2
20
4
1
3
2
1
10
-
Total Credits
*Self Study course
25
SEMESTER- IV
Course
Code
PY 2481
PY 2211
PY 2480
Relative Weightage (%)
Course Name
Project II
Classical
Electrodynamics*
Seminar
Total Credits
*Self Study course
Total Credit: 100
ETE
PRE
50
-
40
40
-
Exam Duration
(Hrs)
Relative Weightage (%)
L
T
P
C
Theory
Practical
CWS
3
1
0
24
4
3
2
-
10
0
0
4
2
1
-
30
PRS MTE
T
60
40
60
-
-
PRS MTE
T
60
40
60
-
ETE
PRE
50
40
-
-
40
L = Number of Lectures hrs/week
T= Number of Tutorials hrs/week
P = Number of practical hours/week
C= Number of Credits.
CWS: Class Work Sessionals
PRS: Practical Sessionals
MTE: Mid-Term Exam
ETE: End Term Exam
PRE: End Term Practical Exam
* Presentations Only
First Semester
PY2314
Atomic, Molecular and Laser Physics
[3 1 0 4]
Spectra of single & Multi electron atoms: H-atom, relativity and spin Correction, Central
Field Approximation (CFA), L-S and J-J coupling approximation, spectral terms :(i) atoms
with two or more non-equivalent optical electrons, Lande`s interval Rule, Normal and
inverted multiplets, order of terms and fine structure levels, selection rules for multi
electron atoms in LS coupling and J-J coupling.
Spectra of alkali elements: Fine structure and intensity ratio for doublets, spectra of
alkaline earth elements, interaction energies in L-S and J-J coupling, comparison of terms,
spectra of elements with “P” configuration, spectra of elements with unfilled d & f – shells.
Molecular spectra: Rotational & vibrational spectra for diatomic molecules, Electronic
spectra of diatomic molecules, vibrational coarse structure, Frank–Condon principle,
Dissociation energy & products, Rotational fine structure of electronic vibration transitions,
Electronic angular momentum in diatomic molecules, Raman Spectroscopy.
Atoms in external fields (Electric & Magnetic) : The normal Zeeman effect, Weak fields,
Russel–Saunder`s terms and general case, Intensity of lines in Weak fields and Quadrupole
lines, Paschen back effect, Stark effect, Linear stark effect, illustration for H-atom & series
limit, theory for nonhydrogenic atoms- He & Alkali metals.
Spectrographs: Working principle of spectroscopic instruments for UV- Vis- IR region
and applications.
Laser Physics:
Basic elements of Laser, Threshold condition, 4-level Laser system, CW operation of
Laser, critical pumping rate, population inversion & photon number in the cavity around
threshold, output coupling of Laser power. Optical resonators, cavity modes, mode
selection, pulsed operation of Laser, Q- switching and mode locking; Experimental
technique of Q- switching & mode locking.
Laser systems: Ruby, Co2, Dye & Semiconductor diode Laser.
Holography: Basics, recording and reconstruction of reflection hologram, simple
applications.
Text/Reference Books:
1. Sobel`man : introduction to the theory of atomic spectra, Wiely, (2008).
2. E.V. condon & G.H. Shortley: Theory of Atomic Spectra, Cambridge University Press (1935)
3. G. Hertzberg : Atomic spectra & atomic structure power publication, Dover Publications, Inc., New York,
1944)
4. G. Aruldas, Molecular structure & spectroscopy PHI, New Delhi(2001)
5. Colin N. Banwell & Elaine M. Mccash: Fundamentals of Molecular spectroscopy, TMH publishing co.
Ltd. IV edn. (2002)
6. Barrow G. M. , Introduction to Molecular Spectroscopy, Tata McGraw Hill (1962).
7. Molecular spectra & Molecular structure G: Hertzberg, di Lauro, Carlo, Elsevier (2013)
8. Laser Theory & its application: Ghatak & Thyagarajan (Mcmillan), Plenum Publishing Corporation, New
York , (1981).
9. Laud B.B. ,Laser & Nonlinear optics, Wiley Eastern, II edition,(1991) .
10. White, H. E., Atomic Spectra, TMH (1934).
PY 2312
NUCLEAR
PHYSICS
[3 1 0 4]
Properties of Nuclei & Nuclear Forces
Nuclear Mass, Nuclear Binding Energy Nuclear radius, Spin and magnetic moments
of
Nuclei, Parity, Angular Moment, Electric Um Quardrupole moments, Concept of meson
theory of Nuclear forces, Exchange Force andTensor Force. Charge independence and
Charge symmetry of nuclear forces. Isospin formalism.
Nuclear Interaction
Bound State of two nucleons, Theory of Ground State of two nucleons. Nucleon- nucleon
scatterings (n-p & p-p) at Low energies (<10MeV). Scattering Length.
Effective range
theory in n-p and p-p scattering, Spin dependence of nuclear forces.
Scattering
of
Neutrons by ortho and para hydrogen molecule
Nuclear Reactions
Classification of nuclear reactions – Direct and Compound nuclear reaction mechanisms.
Scattering and reactor cross sections by partial wave analysis, Bohr’s theory of compound
nucleus. Resonance reaction and Briet-Winger one level formula. Bohr-Wheeler theory of
fission& Nuclear Reactors.
Nuclear Models
Shell model - Experimental evidence for shell effects and magic numbers, Shell
model
spin orbit coupling. Schmidts lines and prediction of angular momentum and parity of
nuclear ground states. Collective model of Bohr and Mottelson – rotational States and
Vibrational levels, Nilsson Model.
Elementary Particles and their classifications.
Elementary Particles and their classifications, conservation laws, parity conservation and
violation, conservation of isotopic spin, Gell Mann Nishigima scheme,Charge conjugation
and time reversal, CP violation and CPT theorem. Strong, Weak and electromagnetic
interactions : coupling constants,
decay life times and cross sections.
Text and Reference Books:
1. Roy R.R. and Nigam B.P., Nuclear Physics, New age International, (1996)
2. Halliday D., Nuclear Physics. Wiley, 5th ed, (2001)
3. Enge H.A., Introduction to Nuclear Physics, Addison Wesley, 1 st ed, (1996)
4. Fermi E., Nuclear Physics, University of Chicago press, (1974)
5. Kaplan I Nuclear Physics, Addison Wesley, 2 nd ed, (1962)
6. Cohen B.L., Concepts of Nuclear Physics, Tata Mc- Graw Hill, 1st ed., 1971
7. Brown G.E. and Jackson A.D., Nuclein-Nucleon interactions, North Holland Publication, (1976)
8. Benedetti Side, Nuclear Interactio, John Wiley & Sons, 2 nd ed, (1966).
9. Bohr and B.R. Mottelson, Nuclear Structure, Vol.1 and Vol.2 , WA Benjamin, (1975).
10. Evans R.D. Atomic Nucleus, Krieger Pub. Company, (1982).
PY 2214
SOLID STATE PHYSICS
[3 1 0 4]
Crystal Physics and X-ray Crystallography: Crystal solids, unit cells and direct lattice,
two- and three-dimensional Bravais lattices, crystal systems, crystal planes and Miller
indices, close packed structures, symmetry elements in crystals.Reciprocal Lattice and
Experimental X-ray diffraction Techniques: Reciprocal lattices Bragg`s Law of
diffraction, X-ray single crystal diffractometer Ewald Sphere, powder X-ray diffraction
technique, structure factor.
Semiconductors: law of mass action, calculation of impurity conductivity, ellipsoidal
energy surfaces in Si and Ge, Hall effect, recombination mechanism.
Lattice Vibrations and Thermal Properties: Interrelations between elastic constants
,vibrations of linear mono and diatomic lattices, Determination of phonon dispersion by
inelastic scattering of neutrons.
Electronic Properties of Solids: Electrons in periodic lattice: Bloch theorem, NFE model
the Kronnig Penny model, classification of solids on the basis of band theory, effective
mass, Fermi surface and Fermi gas, Hall Effect, Superconductivity
Magnetic Properties of Solids: Classification and general properties of magnetic
materials, Weiss theory of
ferromagnetism, temperature dependence of spontaneous
magnetization, Heisenberg’s model and molecular field theory, curie-Weiss law for
susceptibility.
Superconductivity: Experimental results: Meissner effect, nuclear spin relaxation, Giver
and AC and DC, Josephson tunnelings.
Text and Reference Books:
1. Azaroff, Introduction to Solids, Mc Graw hill, (1984)
2. Verma and Srivastava, Crystallography for Solid State Physics, New age publication, 1991
3. Kittle, Solid State Physics, Wiley, 8th ed., (2004)
4. Wahab M.A., Solid State Physics, Alpha Science international Ltd, 1 st ed, (2011)
7. Chaikin and Lubensky, Principals of Condensed Mater Physics, Cambridge University Press, (2000)
PY 2353 NANO SCIENCE AND NANOTECHNOLOGY-I
[3 1 0 4]
Emergence of Nanotechnology
Nanotechnology Timeline and Milestones, Overview of different nanomaterials available,
Schrodinger equation, Electron confinement, Tunnelling of a particle through potential
barrier, Density of states (0D, 1D, 2D, 3D)
Synthesis of Nanomaterials
Introduction, mechanical method, method based on evaporation, sputter deposition, CVD
electric arc deposition, Ion beam techniques, Novel physical chemistry related to
nanoparticles such as colloids and clusters, Exploitation of self-assembly and selforganization to design functional structures in 1D, 2D or 3D structures. Examples to
emphasize on self-assembled monolayers, Role of polymers in lithography resists,
Nanomaterials (Nanoparticles, nanoclusters, quantum dots synthesis): Preparation and
Characterization: “Top-Down” and “Bottom-Up” approaches of nanomaterial
(nanoparticles, nanoclusters and quantum dots) synthesis: Top-down techniques:
photolithography, optical lithography Bottom-up techniques: self-assembly, self-assembled
monolayers, Combination of Top-Down and Bottom-up techniques: current state-of-the-art.
L-B methods, Sol-Gel method.
Introduction of Nanoelectronics
Metals and insulators, Semiconductors: classification, electrons and holes, transport
properties, size and dimensionality effects, Quantum size effects in semiconductor quantum
dots and nanowires, Introduction to single electron transistors (SETs): quantum dots, single
electron effects, Coulomb blockade.
Text and References Books:
1. Introduction to Nanotechnolology – Charles P. Poole Jr. et.al John Wiley & Sons, (Asia) Pte. Ltd, (2010)
2. Nanotechnology: Principles and Practices – Sulabha K. Kulkarni, Delhi, (2007)
3. Nanostructures and Nanomaterials: Synthesis, Properties and Application, Guozhong Cao, Imperial
College Press, UK., (2004)
4. Nanostructured Materials and nanotechnology, Editor Hari Singh Nalwa, (Concise Edition) Academic
Press. (2001)
PY 2232
Spectroscopy lab
[0 0 8 4]
[Minimum 10 experiments to be performed]
1. Hydrogen spectra - determination of Rydberg constant
2. Absorption spectrum of iodine- determination of dissociation energy of I2
3. Study of the arc spectra of iron, copper, Zinc and brass
4. Identification of elements by spectroscopic method.
5. Study of normal Zeeman effect
6. Measurements of wavelength of He-Ne laser light using ruler.
7. Hyperfine structure of spectral lines using FP etalon/LG plate.
8. GM counters characteristics.
9. AIO bands-photographing and analysis
10. Analysis of the given vibration-rotation spectrum
11. Interpretation of a Raman and IR spectra of simple of triatomic molecules
12. Dissociation energy of diatomic molecules- comparison of different
Spectroscopic methods
13. Analyses and, Identification of substances using XRD patterns using ASTM
cards.
14. Identification of elements from stellar spectra
15. Gaussian power distribution law using lasers.
16. Determination of Curie temperature.
17. Compton spectrometer using microwave and “ Tennis ball “ model.
PY - 2331
Solid State Physics Lab
[0 0 6 3]
1. Determinations of Lande’s ‘g’ factor for l RRH crystal using electron spin
resonance spectrometer (Electron Spin Resonance-ESR)
2. Determination of Fermi energy of metals
3. PN Junction Capacitance
4. Determination of transition temperature in ferrites
5. Magnetic susceptibility experiment using Quinke’s tube
6. Calibration of silicon resistance thermometer and measurement of temperature
from 77K to room temperature
7. Measurement of magneto resistance
8. Determination of transition temperature in ferroelectrics
9. Dispersion relation and cutoff frequency in the case of a mono-atomic lattice
using lattice dynamics kit
10. Dispersion relation, acoustical mode and optical mode of a diatomic lattice
using lattice dynamics kit.
Semester- II
PY 2113
ELECTRONICS
[3 1 0 4]
Network analysis
Review of network analysis and theorems. Thevenin’s theorem, Norton’s Theorem,
Superposition Theorem, Maximum power transfer Theorem.
Semiconductor devices and circuits
Characteristics of a pn junction. Clipping and clamping circuits. Response of RCdifferentiator and integrator circuits for sine, square and ramp wave signals. BJT, JFET and
MOSFET devices. Voltage divider bias. Small signal analysis of BJT and FET amplifiers
in CE/CS configuration. Comparison of CE/CS configuration with CB/CG and CC/CD
configurations. Frequency response of BJT amplifier. UJT characteristics and its use in a
relaxation oscillator. SCR characteristics and its use in ac power control.
Operational amplifiers and circuits
BJT differential amplifier. Operational amplifier - voltage/current feedback concepts
(series & parallel).
Inverting and noninverting configurations.
Basic applications of
opamps - comparator and Schmitt trigger. IC555 timer - monostable and a stable
multivibrators. Crystal oscillator using opamp. Voltage regulator using series transistor
and opamp with current limiting facility. Three terminal IC regulators. Switch mode
power supply (block diagram).
Digital electronics
Review of number systems, logic gates, latches and flipflops.. Simplification of logic
functions by Karnaugh maps. Tristate devices. Decoders and encoders. Multiplexers and
demultiplexers with applications.
Synchronous counter design.
Digital to analog
conversion with R/2R network. Analog to digital conversion using flash technique.
Reference Books:
1. Hayt W H, Kemmerly J E and Durbin S M, Engineering Circuit Analysis, VI Edn, McGraw-Hill (2002).
2. Boylestad R L, Introductory Circuit Analysis, VIII Edn, Prentice Hall (1997).
3. Boylestad R L & Nashelsky L, Electronic Devices & Circuit Theory, VIII Edn. Prentice Hall (2002).
4. Floyd T L, Electronic Devices, V Edn, Pearson Education Asia (2001).
5. Gayakwad R A, Opamps and Linear Integrated Circuits, III Edn. PHI (1993).
6. Floyd T L, Digital Fundamentals, VII Edn, Pearson Education Asia (2002).
PY 2212
QUANTUM MECHANICS
[3 1 0 4]
General formulation of quantum mechanics
Schrodinger wave equation - review of concepts of wave particle duality, matter waves,
wave packet and uncertainty principle. Schrodinger’s equation for free particle in one and
three dimensions - equation subject to forces. Probability interpretation of the wave
function, probability current density - normalisation of the wave function, box
normalisation, expectation values and Ehrenfest’s theorem.
Representation of states, dynamical variables - Adjoint of an operator.
problem - degeneracy. Eigenvalues and eigenfunctions.
Eigen value
The Dirac-delta function.
Completeness and normalisation of eigen functions. Closure. Physical interpretation of
eigen values, eigen functions and expansion coefficients. Momentum eigen functions.
Stationary states and eigen value problems
The time independent Schrodinger equation - particle in square well - bound states normalised states.
Potential step and rectangular potential barrier - reflection and
transmission coefficients - tunnelling of particles. Alpha decay.Simple harmonic oscillator
Schrodinger equation and energy eigen values - Energy eigen functions. Properties of
stationary states. Concept of parity. Rigid rotator. Particle in a central potential - radial
equation.Three-dimensional square well.
equation
-
energy
levels.
Stationary
The hydrogen atom - solution of the radial
state
wave
functions
-
bound
states.
Matrix formulation of Quantum Mechanics:
Hermitian and unitary Matrices, Transformation and diagonalization of Matrics, Function
of Matricies and matrices of infinite rank. Vector representation of states, transformation
of Hamiltonian with unitary matrix, representation of an operator, Hilbert space.. Dirac bra
and ket notation, projection operators, Schrodinger, Heisenberg and
interaction
pictures. Relationship between. Poisson brackets and commutation relations. Matrix theory
of Harmonic oscillator
Symmetry in Quantum Mechanics
Unitary operators for space and time translations. Symmetry and degeneracy, Rotation and
angular momentum; Commutation relations, eigenvalue spectrum, angular momentum
matrices of J +, J-, Jz, J2.
Concept of spin, Pauli spin matrices. Addition of angular momenta, Clebsch- Gordon
coefficients and their properties, recursion n relations. Matrix elements for rotated
state,
irreducible tensor operator, Wigner-Eckart theorem.
Rotation matrices and group aspects. Space inversion and time reversal: parity operator and
anti-linear operator. Dynamical symmetry of harmonic oscillator.
Applications: non-relativistic Hamiltonian for an electron with spin included.
C.G. coefficients of addition for j =1/2, 1/2; 1/2, 1; 1, 1.
Reference Books:
1. Powell and Crassman, Quantum Mechanics, Addison Wesley (1961).
2. Mathews P M and Venkatesan K, A Text Book of Quantum Mechanics, Tata McGraw Hill (1977).
3. Ghatak A K and Lokanathan S, Quantum Mechanics, III Edn., McMillan India (1985).
4. Sakurai J J, Modern Quantum Mechanics, Revised Edn., Addison Wesley (1994).
PY 2454 -Program
NANOSCIENCE AND NANOTECHNOLOGY- II [3 1 0 4]
Characterization Techniques for Nanomaterials
Characterization Techniques Related to Nanoscience and Nanotechnology: Compositional
surface analysis: XPS, SIMS Microscopies: optical microscopy, fluorescence, TEM, SEM,
Probe techniques: Scanning tunneling microscopy (STM), Atomic force microscopy
(AFM), Neutron Scattering and XRD, Spectroscopic Techniques: UV-visible, FT-IR,
Raman, NMR, ESR, Surface modification using ion beam, ion beam analysis technique:
Secondary ion mass and RBS.
Carbon Nanotubes and Fullerenes
Synthesis and purification of carbon nanotubes, Single-walled carbon nanotubes and
multiwalled carbon nanotubes, Structure-property relationships, Physical properties,
Applications, Bucky Balls, Importance and Properties of fullerenes, Application of
Fullerenes.
Applications of Nanomaterials
Garment industry, Rubber industry, Activated carbon industry, Electronics industry,
Nanotechnology in Energy Conversion and Storage, Nanoelectronic Devices,
Nanobiotechnology and Nanotechnology in Healthcare, Agricultural.
References:
1. Introduction to Nanotechnolology – Charles P. Poole Jr. et.al John Wiley & Sons
(Asia) Pte. Ltd.
2. Nanotechnology: Principles and Practices – Sulabha K. Kulkarni, Delhi.
3. Nanostructures and Nanomaterials: Synthesis, Properties and Application
Guozhong Cao, Imperial College Press, UK.
4. Nanostructured Materials and nanotechnology, Editor Hari Singh Nalwa
(Concise Edition) Academic Press.
5. Inorganic nanowires CRC Press M.Meyyappan and Mahendra K Surtkan
PY 2411
Nuclear and Radiation Physics
[3 1 0 4]
Passage of Radiation through Matter
Interaction of charged particles:
Energy loss of charged particles through matter. Bethe block ionization formula. RangeEnergy relation. Multiple coulomb scattering -p ß measurements, Bremsstrahlung and
Cerenkov radiations
Interaction - stopping power - energy loss characteristics, particle range - energy loss in
thin absorbers. Scaling laws. Interaction of fast electrons - specific energy loss. Electron
range and transmission curves.
Interaction of gamma rays:
Interaction mechanisms - photoelectric absorption, Compton scattering and pairproduction. Gamma ray attenuation - attenuation coefficients, absorber mass thickness,
cross sections. Interaction of neutrons - general properties - slows down interaction, fast
neutron interaction, neutron cross sections. Radiation exposure and dose – dose equivalent.
Nuclear detectors:
Gas filled counters, Nuclear Emulsions, Gaseous Ionization Detector:- Ionization and
Transport Phenomena in Gases, Transport of electrons and Ions in Gases. Avalanche
Multiplication, GM
Counters, Proportional counters, Multiwire proportional counters.
Scintillation detectors - different types of scintillators - photomultiplier tubes,
measurement with scintillation detectors - NaI(Tl), plastic scintillator - Scintillation
spectrometer. Spectrum analysis.
Semiconductor detectors :
Semiconductor properties - physics of semiconductor detectors - diffused junction,
surface barrier and ion-implanted detectors.
Si(Li), Ge(Li) and HPGe detectors -
semiconductor detector spectrometer. Pulse height analysis of spectrum, SSNTD,
Superheated drop detectors. Neutron detectors - Neutron detection from
nuclear
TLD,
reactions. BF3 counters, 3He counters, fission detectors, activation method for
neutron
flux measurement. Recoil counters - neutron time of flight technique
Accelerating Machines and General Characteristics of Detector:
Linear accelerators, Principle of orbital accelerators, Cyclotron, synchro-cyclotron,
modification with reference to magnetic field and frequency, Beam Collider.
Detector properties: - Sensitivity, Detector response, Energy resolution Response function
and time, Detector efficiency and Dead time.
Reference Books:
1. Marmier P. and Sheldon E., Physics of Nuclear & Particles, Vol.I & II
2. Lee S.Y., Accelerator Physics.
3. Persico E., Ferrari E, Sergre S. E., Principles of Particle Accelerators.
4. Green D, Principles of Particle Detector.
5. Knoll G. F., Radiation detection and measurement.
6. Burcham E., Nuclear & Particle Physics.
7. Ponearu D N and Greiner W, Experimental Techniques in Nuclear Physics,
Walter de Gruyter Berlin, (1997)
PY 2132
ELECTRONICS LAB
[Minimum 10 experiments to be performed]
1. Design of a regulated power supply
2. Design of a common emitter transistor amplifier
3. Design of a stable multivibrator
4. Design of monostable and Design of Bistable multivibrators
5. SCR Characteristics
6. Wein bridge Oscillator
7. Phase shift oscillator
8. Zener diode charecteristics and voltage regulation.
9. FET and MOSFET characteristics and application as an amplifier.
10. LOGIC GATES: TTL, NAND and NOR gates
11. Digital II: Combinational Logic. FLIP-FLOPS
12. Operational Amplifiers (741).
13. Differential amplifier
[0 0 8 4]
14. Experiment with Microprocessor kit
PY 2431
Nuclear Physics Lab
[0 0 8 4]
1. Dead time of GM tube by single source method and by double source method
2. Range of B particles using GM counter
3. Range and energy of Alpha particles by GM method
4. Inverse square law for Gamma radiation using GM Counter
5. Linear attenuation coefficient for γ- rays (GM).
6. Absorption of gamma rays by lead-mass absorption coefficient and half value
thickness of the absorber .
7. Absorption coefficient by equivalent thickness method using GM detector
8. Characteristics of scintillation counter
9. To determine the operating voltage if a –photomultiplier tube and to find the
Photo-peak efficiency of a Nal (Tl) crystal of given dimensions for gamma rays of
different energies.
10. Statistics of counting [ using G. M Counter ]
11. To determine the energy resolution of a Nal(Tl) detector and to show that it is
independent of the again of the amplifier.
Self Study course
III Semester
PY 2111
MATHEMATICAL PHYSICS
[3 1 0 4]
Integral Transforms and Fourier transformations:
Fourier series – Dirichlet’s conditions – Fourier series of even and odd functions Complex
form of Fourier series – Fourier integral and it’s complex form – Fourier transforms –
Fourier sine and cosine transforms – Convolution theorem and Parseval’s identity. Laplace
transform of elementary functions – Inverse Laplace transforms .Methods of finding Inverse
Laplace transforms – Heaviside expansion formula. Solutions of simple differential
equations
Curvilinear coordinates, Matrices:
Generalized coordinates - elements of curvilinear coordinates - transformation of coordinates
- orthogonal curvilinear coordinates - unit vectors - expression for arc
length,
volume
element. The gradient, divergence and curl in orthogonal curvilinear coordinates.
Laplacian in orthogonal curvilinear coordinates, spherical polar coordinates, cylindrical
coordinates.
Matrix representation of linear operators, Hermitian and unitary Solution of
system of linear equations – coordinate transformation.
Complex variables and integral transforms:
Review of functions of a complex variable – Cauchy Riemann conditions. Contour integrals.
Cauchy integral theorem, Cauchy integral formula. Taylor and
Laurentz series. Zero
isolated singular points, simple pole, mth order pole. Evaluation of residues. The Cauchy’s
residue theorem. The Cauchy principle value. Evaluation of different forms of definite
integrals.
Tensor analysis and group theory:
Introduction - rank of a tensor. Transformation of coordinates in linear spaces transformation law for the components of a second rank tensor. Contravarient and covariant
and mixed tensors - First rank tensor, higher rank tensors, symmetric and antisymmetric
tensors. Tensor algebra - outer product - contraction - inner product - quotient law. The
fundamental metric tensor - associate tensors.
Groups - subgroups - classes. Invarient subgroups - factor groups. Homomorphism and
Isomorphism. Group representation - reducible and irreducible representation. Schur’s
lemmas, orthogonality theorem.
Decomposing reducible representation into irreducible
ones. Construction of representations. Representation of groups and quantum mechanics.
Lie groups and Lie algebra. Three dimensional rotation group SO(3), SU(2) and SU(3)
groups.
Special functions:
Delta function and eview of power series method for ordinary differential equations
description of beta and gamma functions. Bessel functions – solution of Bessel’s equation
Neumann and Hankel functions – generating function and recurrence relations orthogonality
of Bessel functions – Spherical Bessel functions. Legendre polynomials solution of Legendre
equation – generating function and recurrence relations orthogonality property of Legendre
polynomials – associated Legendre polynomials and spherical harmonics. Solution of
Laguerre’s equation – Laguerre and associated Laguerre polynomials – Solution of Hermite
equation – Hermite polynomials – generating functions and recurrence relations.
Text and Reference Books:
1. Arfken G., Mathematical Methods for Physics, 4th edn., Academic press.
2. Joshi A. W., Matrices and Tensors for Physicists, Wiley Eastern.
3. Kreyzing E., Advanced Engineering Mathematics.
4. Rainville E. D., Special Functions.
5. Bell W. W., Special Functions.
6. Reily K. F. , Hobson M. P. and Bence S. J., Mathematical Methods for Physics and Engineering.
7. Boas M., Mathematics for Physics.
8. Churchill & Brown, Complex variables and applications,5th edn., McGrawHill.
9. Tung, Group theory in physics, World Scientific.
10. Ghatak et al, Mathematical physics, Macmillan.
11. Harper, Mathematical methods, PHI.
Self Study course
IV Semester
PY 2211
.
CLASSICAL ELECTRODYNAMICS [3 1 0 4]
Electrostatics: Electric field:
Gauss law, scalar potential, surface distribution of
charges
and
dipoles
and
discontinuities in the electric field and potential, Poisson and-Laplace equations, Green's
Theorem, Uniqueness of the solution with
Dirichlet or Neumann Boundary
Formal so1ution of Electrostatic Boundary value problem with
conditions,
Green's Function,
Electrostatic potential energy and energy density, capacitance.
Boundary- Value Problems in Electrostatics:
Methods of Images, Point charge in the presence of a grounded conducting sphere point
charge in the presence of a charge insulated conducting sphere, Point charge near a
conducting sphere at fixed potential, conducting sphere in a uniform electric field
by method of images, Green function for the sphere, General solution for the potential,
Conducting sphere with Hemispheres at different potential, orthogonal functions and
expansion.
Magnetostatics:
Biot, and Savart law, the differential equation of magnetostatics and Ampere's law, Vector
potential and Magnetic induction for a circular current loop, Magnetic fields of a localized
current distribution, Magnetic moment, Force and torque on and energy of a localized
current distribution in an external magnetic induction, Macroscopic equations.Boundary
conditions on B and H. Methods of solving Boundary-value problems in magneto statics,
Uniformly magnetized sphere, Magnetized sphere in an external field, Permanent magnets,
Magnetic shielding, spherical shell of permeable material in an uniform field.
Multipoles, Electrostatics of Macroscopic Media Dielectrics:
Multipole expansion, multipole expansion of the energy of a charge distribution in an
external field, Elementary treatment of electrostatics with permeable media, Boundary value
problems with dielectrics. Molar polarizability, and electric susceptibility. Models for
molecular polarizability, Electro-static energy in dielectric media.
Time varying fields, Maxwell's equations Conservation Laws:
Energy in a magnetic field, Vector and Scalar potentials. Gauge transformations, Lorentz
gauge, Coulomb gauge, Green functions for the wave equation, Derivation of the equations
of Macroscopic Electromagnetism, Poyntings theorem and conservations of energy and
momentum for a system of charged particles. Conservation laws for macroscopic media.
Electromagnetic field tensor. Transformation of four, potentials and four currents. Tensor
description of Maxwell's equation.
Plane Electromagnetic Waves and Wave Equation:
Plane wave in a nonconducting medium. Frequency dispersion characteristics of dielecttics,
conductors and plasmas, waves in a conducting or dissipative medium, superposition of
waves in one dimension, group velocity, casualty connection between D and E. KramersKroning relation. .
Reference Books:
1. Jackson J.D., Classical Electrodynamics.
2. Panofsky and Philips, Classical Electricity and Magnetism.
.
3. Griffiths, Introduction to Electrodynamics.
4. Landau and Lifshitz, Classical Theory of Field.
5. Landau and Lifshitz, Electrodynamics of Continuous Media.
6. Reitz and Milford, Foundations of electromagnetic theory, Addison Wesley.