Download M.Sc. (Physics)

Structure and Syllabi for M.SC Physics (Non – Semester)
I year
I.1 Classical Mechanics and Statistical Mechanics
I.2 Mathematical Physics
I.3 Digital Electronics and Microprocessor
I.4 Electromagnetic Theory
I.5 Solid State Pysics
I.6 Nuclear Physics
I.7 Practical I – Electronics
I.8 Viva-voce
II Year
1. Quantum Mechanics
2. Numerical Methods
3. Spectroscopy
4. Laser and Opto- Electronics
5. Advanced Nuclear Physics
6. Practical II – Non Electronics
7. Practical III – Computer and Microprocessor
8. Viva-Voce
Each Theory paper and each practical paper (For practical Record Mark 20 +
Examination 80) and each Viva-voce carries 100 marks. The theory examinations are of
three hours duration each. The practical examinations are of four hours duration each.
Total marks: 1600
Question papers: The paper will consist of Part A and Part B. There will be 5 questions in
Part A with internal choice. Each question carries 8 marks. (5X8=40 marks). There will
be 5 questions in Part B with internal choice. Each question carries 12 marks (5X12=60
marks). Each question in Part A and Part B will be from the same unit.
I.1 CLASSICAL MECHANICS AND STATISTICAL MECHANICS
Unit I Newtonian mechanics of single and many body systems – conservation laws-work
energy theorem – constraints- De’Alembert’s principle and Lagrangian equation –
application of Lagrangian equation to simple pendulum and Atwood’s machine –
variational principle – derivation of Lagrangian equation fromHamilton’s principle.
Unit II Hamilton’s equation from variational principle –principle of leastaction –
canonical transformation – generating function – group properties- Poisson’s bracketand
theorem – angular momentum Poisson bracket – Hamilton Jacobi equation- Hamilton’s
principle functions – application to harmonic oscillator.
Unit III Rigid body motion – spinning top motion – independent coordinate of
rigidbodies- orthogonal transformation – central force problem – definitions and
characteristics – equation of motion and first integrals – Kepler’s problems- Inverse
square law of forces – motion in time in Kepler’s problem – scattering in a central force
field.
Unit IV Contact between statistical and thernmodynamics of the system – classical ideal
gas- Gibb’s paradox – microcanonical ensemble – phase space- trajectory and density of
states – canonical and grand canonical ensembles – micro and macro states – Stiriling’s
formula – most probable distributions – M.B. distribution – law of equipartition of
energy.
Unit V Bose-Eistein statics- black body radiation and photon statistics – specific heat of
solids – Dulong and Petits law – Einstein’s theory of specific heat – Debye’s theory of
specific heat – BE condensation – Fermi Dirac statistics – equation of states of ideal gashigh temperature and low density – low temperature and high density – theory of electron
gas – statistics of occupation number – calculation of thermodynamic quantities.
Books for study and reference
1.Classical Mechanics – N.C. Rana and P.S. Joag (Tata Mc Graw – Hill, 1991)
2.Classical Mechanics – H. Goldstein (Addition Wesley, 1980)
3. Principles of Mechanics – Synge and Griffith
4. Introduction to Classical Mechanics- R.G. Takwale and P.S. Puranik
5. Thermodynamics – Searls and Salinger
6. Statistical Mechanics, by Kerson and K. Huang
7. Statistical Mechanics, by R.K. Pathria
8. Statistical Mechanics, by sears and zymanski
9. Statistical Pysics, by A.K. Agarwal and Melvin Eisner
1.2 Mathematical Physics
Unit I Vector spaces and tensors – linear independence – inner product – Schwartz
inequality – matrix representation of vector and linear operators with respect to basis –
change of basis – Schmidt orthogonalization – matrices – matrix multiplication- rotation
matrices – eigen values and eigen vectors – concepts of orthogonal sets of functions –
tensors- basic ideas of contravariant – covariant and mixed tensors.
Unit II
Power serious solution – power serious solution of – Legendre – Hermite – Lageurre –
Hermite Polynomials – recurrence relations – generating functions – Rodrigues functions
– orthogonality conditions.
Unit III
Partial differential equations – separation of variables – heat conduction problem. –
variable liear flow – two and three dimensional heat flow – temperature inside circular
and rectangular plates – cooling of hot brick – electrical analogy of heat flow – current
density and
total current in a wire – skin effect- vibration of stretched string and
membrane.
Unit IV
Complex variables –function of a complex variable – analytical function – Cauchy –
Rheinman equation – Cauchys integral theorem and formula – Tayor’s and Laurent’s
expansion – residue theorem and application – conformal mapping – basic concepts –
mapping by w=az +b and w = exp(z).
Unit V Probability and statistics – discrete probability distribution – combinations and
permutations – Stirling’s approximation for factorials of large numbers – continuous
distribution – binomial distribution – Poisson’s distribution – normal distribution – curve
fitting – least square analysis.
Books for study and reference
1. Matrices and Tensors – Joshi
2. Vector and Tensors – Spiegel – Schaum Series
3. Applied Mathematics for Physicists and Engineers – Pipes and Harwill
1. Complex variables – Spiegel – Schaum Series
2. Mathematical Physics – Eugine Butkov
I.3 DIGITAL ELECTRONICS AND MICROPROCESSORS
Unit 1 Logic gates – block diagram – truth table – Exor gate – equivalent functions –
combinational logic- half adder /subtactor – full adder / subtactor – DeMorgan’s laws –
Boolean algebra – Karnaugh maps – max and min terms – encoders and decoders –
multiplexers and demultiplexers.
Unit II Sequential logic – Flip flops – sequential circuit analysis – state diagram – state
equation – registers – shift registers – counters – up-down counters – decade counters –
timing sequences – the memory unit – Random Access Memory(RAM) – magnetic core
memory.
Unit III Common microprocessor characteristic – pin diagram and functions for generic
microprocessor – microprocessor architecture – the intel 8085 microprocessor – the 8085
pin diagram and functions – 8085 architecture – different addressing modes – 8085
instruction set – arithmetic, logical and branch instructions – the 8085 stack, I/O and
control instructions.
Unit IV Programming the 8085 microprocessor – 8 bit addition, subtraction,
multiplication and division-looping programs – sum of data maximum, minimum values
of the given array – ascending / descending – data transfer – 16 bit addition – relay
generation – multiple precision arithmetic – decimal arithmetic – subroutine programs –
ASCII to decimal multiple precision addition subroutine.
Unit V
Timing diagram – instruction cycle, machine cycle, R/W cycle – m interfacing the
microprocessor – interfacing with ROM – interfacing with RAM – I/O interfacing basics.
Books for study and reference
1. Digital Principles and Applications – A.P. Malvino and D.P. Leach.
2. Digital Computer Electronics – Malvino.
3. Digital Logic and Computer Design – M. Morris Mano
4. Microprocessor
Architecture,Programming
and
Applications
with
the
8085/8080A- R.S. Gaonkar.
5. Microprocessors – Mathur.
Electromagnetic theory
Unit I Electrostatics – Field and potential due to a point charge – line charge – surface
charge and volume charge – divergence and curl of electrostatic field – energy due to
point charge distribution and continuous charge distribution – Poisson equation and
Laplace equation – electrostatic boundary condition – separation of variables – Cartesian
and spherical coordinates – multipole and dipole – problems in dipole interaction –
electro static fields in matter – dielectrics – dipoles induced in polarisability –
polarisability tensor – electric field produced by uniform polarized sphere – field inside
dielectric – Gauss law with
dielectric – susceptibility – permeability and dielectic
constant – susceptibility tensor field inside a linear dielectric sphere when placed in a
electric field – force on a charge outside a linear dielectric slab – energy in a dielectric
system – forces on dielectrics – connection between polarisability and susceptibility.
Unit II Magnetostatics – Lorentz force – cyclotron motion – continuity equation – Biot
and Savart’s law for line, surface and volume currents – divergence and curl of B –
Ampere’s law – applications – magnetic vector potential – multipole expansion of vector
potential – Dia, para and Ferromagnetics – torques and forces on magnetic dipoles –
magnetic field of a uniformly magnetized sphere – magnetic susceptibility and
permeability in linear media and non linear media – ferromagnetism.
Unit III Ohm’s law – Faraday’s – electromagnetic inductance – energy in magnetic field
– Maxwell’s equations - boundary conditions – scalar and vector potentials – gauge
transformation – Coulomb gauge and Lorentz gauge – energy and momentum in
electrodynamics – Maxwell’s stress tensor – conservation of momentum.
Unit IV : Electromagnetic waves – the wave equation- oolarization – reflection and
transmission- boundary conditions – electromagnetic waves in non conducting media –
propagation through linear media – reflection and transmission at normal incidence and
oblique incidence – electromagnetic waves in conductors – reflection and transmission at
conducting surface – plasma wave guides – TE waves in rectangular wave guidescoaxial transmission line.
UnitV : Electromagnetic radiation – retarded potential and advanced potential – electric
and magnetic dipole radiation – radiation from point charge – fields of a point charge
Bremsstrauhlung, Synchrotron radiation and Cerenkov radiation.
Books for study and reference
1. Classical Electrodynamics – J.D. Jackson
2. Foundation of electromagnetic theory – Rietz, Milford and Griffith.
3. Electromagnetic fields and waves – P. Lorrain and D. Corson.
I.5 Solid State Physics
Unit I Crystals lattices – two and three dimensional lattice types – Simple crystal
structure – reciprocal lattice – Brillouin sones – structure factor of the basis – atomic
scattering factor – cohesive energy – compressibility and bulk modulus – dielectric and
ferroelectric properties of crystals – local electric field at an atom – Lorentz field –
different types of polarization – complex dielectric constants – Clausius – Mosetti
relation.
Unit II Phonons and lattice vibrations – quantization of lattice vibrations – vibrations of
monoatomic lattices – lattice with two atoms per primitive cell – lattice heat capacity –
Einstein and Debye’s models – density of states - - anharmonic crystal
- their
interactions – lattice thermal conductivity – Umplkapp process.
Unit III Energy bands – nearly free electron model – Bloch function – Kroneig – Penny
model – waveequation of electrons in a periodic potential – number of orbitals in a band
– effective mass – classification of solids- free electron gas – heat capacity of electron
gas – motion in magnetic fields – Hall effect.
- L.V. Azaroff
Unit IV Magnetism – Langevin’s theory of paramagnetism – quantum theory of
paramagnetism – Hund’s rules – paramagnetic susceptibility of conduction electrons –
weiss theory of ferromagnetism – ferromagnetic order – Curie point – spin waves –
quantization of spin waves – magnons – ferri, antiferri and antiferro magnetism.
Unit V Super conductivity – Meissner effect – heat capacity – energy gap – isotopic
effect – thermodynamics of the super – conducting transitions – London equations – BCs
theory
–
Type
I
and
Books for study and reference
1. Introduction to Solids – L.V. Azaroff
type
II
super
conductors.
2. Introduction to Solid State Physics – Charles Kittel V edition.
3. Elementary Solid Stae Physics – Ali Omar.
4. Soild State Physics – A.J. Dekkar.
Nuclear Physics’
Unit I
Elementary particles : Classification of elementary particles and types of interaction of
elementary particles – Leptons – Hadrons – Mesons – Hyperons – strange particles –
conservation laws – CPT theorem – Quark model – Gellmann –Okubo mass formula –
SU3 multipet – Baryon octet and baryon decouplet – Mesons nonet – elementary idea of
Gauge bosons.
Unit II Nuclear decay: Gamow’s theory of alpha decay – Fermi’s theory of beta decay –
Curie plot – shape of beta ray spectrum – parity violation in beta decay – Fermi and
Gamow Teller selection rules – multipole radiation – selection rules – internal
conversion – nuclear isomerism.
Unit III Nuclear models: Liquid drop model, Bohr – Wheeler theory of fission –evidence
for shell effect – shell model – spin –oribit coupling – angular momentum and parity of
nuclear ground state –magnetic moment and Schmidt lines – collective model of Bohr.
Unit IV Ground state of deuteron – excited states – magnetic moment and quadrupole
moment of deuteron – n-p scattering and p-p scattering – effective range theory – meson
theory of nuclear force – Compound nuclear theory – Reciprocity theorem – Resonance
scattering – Breit – Wignerr one level formula.
Unit V Neutron sources – classification of neutrons – energy distribution of thermal
neutrons – neutron diffusion – current density – leakage rate – therma neutron diffusion –
fast neutron diffusion – Fermi age equation – nuclear chain reaction – four factor formula
– critical size of a reactor – classification of reactors – thermal reactors – power reactor
research reaction – breeder reaction.
Books for study and reference
1. Nuclear physics – D.C. Tayal
2. Elements of Nuclear Physics – M.L. Pandya and R.P.S. Yadav
3. Nuclear Physics – Irwin Kaplan.
4. Introduction to Nuclear Physics – Herald Enge
5. Nuclear Physics – Roy and Nigam
6. Nuclear Physics – Cohen
1.7. Practical Physics (electronics)
1. Characteristics of Op-AMP – 741
2. Characteristics of SCR
3.Characteristics of UJT and construction of relaxation oscillator
4. Active filters implementation using 741 (second order)
5. A/D conversion
6. D/A conversion (v/f and v/f converters)
7. mod counters using 7490
8. Mod counter using 7473
9. BCD to 7 segment display
10. Schmidt trigger using transistors
11. Schmidt trigger using 555 and 741
12. Shift registers
13. Ring counters
14. Full adder /subtracter
15. Wave shaping using 741-square, triangle
16. JK, RS and D f/f
17. Experimental verification of Thevenin’s and Norton’s theorem.
18. Constant current source implementation using transistor (Evaluate output impedence)
19. Constant current source implementation using OP-AMP (Evaluate output impedence)
20.Transistor regulated voltage source. (evaluate output impedence)
21. CMRR in differential amplifiers . (Transistors).
II.1 Quantum Mechanics
Unit I Schrodinger equation – Free particle in one dimension – Generalization to three
dimension – Schrodinger equation for a particular subjected to a force – continuity
equation – normalization – probability interpretation – conservation of probability –
ehrenfast theorem – time independent Schrodinger equation – particle in a square well
potential – bound states in a square well E<o – non localized state E>o – Adjoint and self
– adjoint operators – eigenvalue problem – degeneracy – eigenvalues and eigenfunctions
of self adjoint operators – uncertaintly principle – proof – commutation relations.
Unit II Angular momentum in quantum mechanics – central force problems – addition of
angular momenta – exactly solvable eigenvalue problems – the simple harmonic
oscillator – Hydrogen atom – rigid rotator – Schrodinger, Heisenberg and interaction
pictures – matrix theory of harmonic oscillator – Raising and lowering operators.
Unit III Stationary perturbation theory – I and II order perturbation – perturbation of
oscillator – Zeeman effect without electron spin – variation method – ground state of
helium – WKB approximation – Time dependent perturbation theory – Fermi Golden
rule.
Unit IV
Scattering theory – kinematics of scattering process – scattering amplitudes and
scattering cross section – partial wave analysis from simple potentials – phase shift
scattering amplitude in terms of phase shift – Optical theorem – Born approximation –
Scattering by a perfectly rigid system – Square well, Coulom and Yukawa potentials.
U n it V
Semiclassical theory of radiation – Einstein’s coefficients for spontaneous and stimulated
emission of radiation – relations between them – transition probability for absorption and
induced emission – Kleiin Gordon equation – difficulties – Dirac equation – Dirac
matrices and their properties – Free particle solution of Dirac equation – negative energy
state – positrons – spin angular momentum and magnetic moment of electron in a
magnetic field.
Books for study and reference
1. Quantum Mechanics – Matthews and Venkatesan
2. Quantum Mechanics – L.I. Schiff
3. Quantum Mechanics – Satyaprakash
4. Quantum Mechanics- Lee.
5. Quantum Mechanics – A.P. Messiah.
II.2. Numerical Methods
Unit I Transcendental and polynomial equations – the bisection method – iteration
methods based on first degree equations – the Newton – Raphson method – iterative
method based on second degree equations – the Muller method – rate of convergence –
polyn mial equations – Birge – Vieta method – Baiston method.
Unit II
System of linear algebraic equations – eigenvalue problems – Gauss elimination method
– pivoing – Gauss Jordan elimination method – triangularisation method – Gauss Seidal
procedure – matrix inversion – eigenvalues and eigenvectors – jacobi method for
symmetric matrices.
Unit III Interpolation techniques – finite difference operators – forward and backward
differences – Lagrange and Newton interpolation – higher order interpolation –
interpolating polynomial using finite differences – approximations – least squares
approximation .
Unit IV
Numerical differentiation and integration – methods based on interpolation – methods
based on finite differences – methods based on undetermined multipliers – integration by
trapezoidal method – Simpson’s 1/3 and 3/8 rules – Lobatto integration method – double
integration.
Unit V
Ordinary differential equations – numerical methods – Euler’s method – backward
Euler’s method – single step method – Taylor’s series method – predictor – corrector
formula- Runge – Kutta methods (second and fourth order) – multi – step method: Adam
– Moulton method.
Books for study and reference:
1. Numerical methods for scientific and engineering computations – N.R. Jain ,
S.P.K. Iyengar and R.K. Jain.
2. Numerical mathematical analysis – James and Scarborough.
3. Numerical methods – Venkatraman
4. Introductory methods of numerival analysis – Sastry
5. Numerical analck effect ysis – Rajaram.
II.3 Spectroscopy
Unit I Quantum states of one electron atom – atomic orbitals – Hydrogen spectrum –
Pauli’s principle – spectra of alkali elements – spin –orbit interaction and fine structure in
alkali spectra – equivalent and non-equivalent electrons – normal and anomalous Zeeman
effect – Paschen Back effect – Stark effect – two electron systems – interaction energy in
LS JJ coupling.
Unit II
Rorational spectroscopy – classification of molecules – diatomic symmetric top,
asymmetric top and spherical top molecules – rotational spectra – diatomic molecule as a
rigid rotator and non rigid rotator – effect of isotopic substitution – intensities of
rotational lines – experimental techniques in microwave spectroscopy – Stark modulated
microwave spectrometer.
Unit III Vibrational spectroscopy – vibrational energy of a diatomic molecule – diatomic
molecule as a simple harmonic oscillator – energy levels and spectrum – Morse potential
energy curve – molecules as vibrating rotator – vibraional spectra of polyatomic
molecules – overtone and combination bands – practical aspects of infrared spectroscopy
– sources , monochromators, thermal detectors and amplifiers – double beam
spectrophotometers – FI –IR spectrometer.
Unit Iv
Rman spectroscopy – classical and quantum theories of Raman effect – polarizability
tensor – pure rotational spectra for linear molecules – vibrational Raman spectra – rule of
mutual exclusion – rotational Raman spectra – structure determination from Raman and
IR spectra – experimental Raman spectroscopy – sources – detectors – calibration.
Unit V Resonance spectroscopy – spin and applied field – interaction between spin and
magnetic field – population of energy levels – the Larmor precession – relaxation times –
FT spectroscopy in NMR –n spin –spin relaxation – spin – lattice relaxation – NMR
spectroscopy for hydrogen nuclei – the chemical shift – the coupling constant – coupling
between several nuclei – chemical analysis by NMR techniques – exchange phenomena
basic ideas of ESR, NQR and Mossbauer spectroscopy.
Books for study and reference’
1. Fundamentals of Molecular spectroscopy – C.N. Banwell.
2. spectroscopy Vol I & II – B.P. Straughan and S. Walker
3. Introduction to Atomic Spectra – H.E. While
4. IR and Raman Spectroscopy – Herzberg.
II. 4 Laser and optoelectronics
Unit I Light wave fundamentals – electro magnetic waves – dispersion – pulse distortion
– information rate – polarization – resonant cavities – reflection at a plane boundaries –
critical angle – reflections.
Unit II Integrated optic wave guides – dielectric slab wave guide – modes in the
symmetric slab wave guide – modes in the asymmetric slab wave guide – coupling to the
wave guide – integrated optic networks – optic fibre wave guides – step index fibre –
graded index fibre – attenuation – modes in step index fibre and graded index fibre –
pulse distortion – information rate – optic fibre cables.
Ud YAG LASER, Neodymium glass LASER, HE –Ne LASER, CO@ LASER, LASER
diodes, operating characteristics, light detectors, principles of photodectection, PMT, PIN
photo diode, avalanche photo diode CCd.
Unit IV Couples and connectors – connector principles – fibre and preparation, splices,
connectors, source coupling, modulation, LED modulation and circuits, analog
modulation formats, digital modulation formats, optic heterodyne receivers, holography.
Uni V Harmonic generation – 2nd and 3rd harmonic generation – phase matching – optical
mixing – parametric generation of light – cell focusing of light.
Books for study and reference
1. Fibre optic communications – Joseph C Palaias
2. LASERS and non-linear optics – BB Laud.
11.5 Advanced Nuclear Physics
Unit I : Addition of angular momentum – Clebsch – Gordan coefficients – symmetry
properties – evaluation of Clebsch – Gordan coefficients in simple cases – rotational
matrices forspinors – spherical tensors – rotation matrices – Wigner Eckart theorem –
simple applications.
Unit II
Nilsson model – collective model of Bohr – Mottelson – rotation and vibration – residual
interaction – 018 energy level calculations – two centre shell model.
Unit III Strutinsky’s prescription – shell effect – potential energy surfaces – nuclear
moment of inertia – cranking model – pairing correlation in nuclei – BCS theory.
Unit Iv
Nuclear stress – backbending – high spin states – hot nuclei – statistical theory – nuclear
level density – thermal fluctuations – giant dipole resonance.
Unit V
Characteristic of accelerators – beam modulation – column structure – electrostatic
accelerators – Van de Graff accelerator – tandem principle – pelletron – AVF cyclotron –
principles of phase shift.
Books for study and Reference
6. Nuclear Physics – Roy and Nigam.
7. Introduction to Nuclear Physics – Herald Enge.
8. Nuclear Physics – D.C. Tayal
9. Nuclear Physics – S.B. Patel
10. Nuclear Physics- Irwin Kaplan.
II. 6 Practical physics ( Non – Electronics)
Any 12 experiments
1. Hall effect
2. Di-electric constant of liquids
3. Ultrasonic diffraction
4. Susceptibility – Guoy’s method
5. Susceptibility – Quinke’s method
6. Michaelson’s interferometer
7. Four probe measurement of conductivity
8. Equipotential plot in an electrolytic tant ‘
9. Band gap measurement in semiconductors
10. Elliptical fringes
11. Hyperbolic fringes
12. Mutual inductance variation with distance and angle.
13. Hartman’s constant – spectrometer
14. Cauchys constant – spectrometer (curve fitting)
15. Hollow prism – variation of refractive index with concentration
16. XRD – analysis given film
17. Constant deviation spectrograph.
18. Grating oblique incidence
19. Hysterisis curve (B-H)
20. Babinets compensator.
II.7 Practical Physics (Computational Techniques)
Any 12 experiments
Group A Microprocessors (any 6)
1. Sorting
2. Square root of a number
3. Matrix addition (sum of column vectors)
4. Wave form generation
5. Fibinocci series generation
6. Transpose of 3X3 matrix
7. Delay generation
8. Search of number of occurance of a given number
9. displaying a series (sequence 0 through f sequentially)
10. Multiplication and division
Group B Computer programming (Fortran 77/C++) any 6
11. Numerical integration – Evaluate the area of a circle of unit radium
12. Matrix inverse
13. Determinant of a matrix
14. Solve a second order differential equation eg.
(D*D+2*K*d*+w*w)=y=a*sin(t) using Runge Kutta method
15. Find the roots of a transcendental equation using Newton Ralpson method
16. Generate Fibinocci series
17. Find the sum of the sine series and compare with the real value.
18. solve a simultaneous equation of 3e unknowns
19. Fit a straight line to a given set of data. Use the method of least squares.
20. Write the values of x,sin(x), sin(x*x) into a file. Find the area under the
21. Curve y = sin (x*x) in the region between x=0 and pi. Use Simpson’s rule.