http://www.bdu.ac.in/schools/physics/physics/ Department of Physics Bharathidasan University Tiruchirappalli-620024 M.Sc. PHYSICS SYLLABI FOR THE COURSE S.NO. Course Code Course Title Credits I – Semester 1 CC01 Classical Mechanics 5 2 CC02 Mathematical Physics - I 5 3 CC03 Electronics – Theory 5 4 CC04 Numerical Methods : Theory 5 5 CC05L Electronics – Practice 4 II – Semester 6 CC06 Mathematical Physics - II 5 7 CC07 Quantum Mechanics 5 8 CC08 Thermal and Statistical Physics 5 9 CC09 Atomic and Molecular Physics 5 10 CC10L Numerical Methods: Practice 4 11 EDC (Extra Disciplinary Course) 2 III – Semester 12 CC11 Nuclear and Particle Physics 5 13 CC12 Condensed Matter Physics 4 14 CC13 Electromagnetic Theory 4 15 EC01 Nano Materials and Applications 4 16 CC14L Materials Science Laboratory 4 17 EDC (Extra Disciplinary Course) 2 IV – Semester 18 EC02 Nonlinear Dynamics 5 19 EC03 Advances in Laser Physics 4 20 EC04 Crystal Growth and Thin Film Physics 4 21 CC15P Project Viva-Voce Examination 4 Total 90
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and Kolmogorov-Arnold-Moser (KAM) Theorem - Attractors –Poincare maps- Henon-
Heiles-Hemiltonian problems.
Unit 5 : Relativistic Mechanics
Inertial and non-inertial reference frames - Addition of velocities, mass, energy - Mass-
Energy equivalence - Pseudo forces - Galilean & Lorentz transformations - Invariance of
Maxwell’s equations under Lorentz transformation - Lagrangianand Hamiltonian of
relativistic particles - problems.
Books for Study and Reference
1. H. Goldstein, C. Poole and J. Sofko, Classical Mechanics, 3
rd Edition, (Pearson
Education, New Delhi, 2011). 2. T. L. Chow, Classical Mechanics (John Wiley, New York, 1995). 3. N.C.Rana and P.S.Joag, Classical Mechanics, (Tata Mc-Graw Hill, New Delhi,
curvilinear coordinates– Unit vectors in curvilinear coordinate system – Arc length and volume
element – The gradient, divergence, curl and Laplacian in Cylindrical and spherical polar
coordinates.
Unit 2: Linear vector spaces and Matrices
Definition of linear vector space – Examples – Linear independence–Basis and dimensions of a
vector space–Scalar product–Orthogonality of vectors– Linear transformation – Linear operator–
Matrix representation of a linear operator–Matrix algebra–Transpose of a matri–Hermitian
conjugate–Unitary matrix– Orthogonal matrix–The Inverse of a matrix –System of linear
equations–Eigenvaluesand eigenvectors of a square matrix–Cayley– Hamilton theorem–
Diagonalisation.
Unit 3: Ordinary Differential Equations First and second orderordinary differential equations with constant coefficients–Initial value problem–Method of finding solutions– Superposition principle–Wronskian-Second order
differential equations with variable coefficients–Definition of ordinary and singular points–Power Series Solution–Solutions about ordinary point and singular point–Frobenius Method.
Unit 4: Special functions
Strum-Liouville problem-Legendre, Bessel, Hermite and Laguerre differential equations–
Power series solutions–Generating functions – Recursion relations–Orthogonality relations-
Applications of special functions in physics. Unit 5: Beta, Gamma Functions Definition of gamma function–Fundamental property of gamma function and values of Gamma function – Definition of beta function – Different forms of beta function – Relationship between beta and gamma functions–Delta function–Basic properties-Introduction to linear partial differential equations-Solutions of Laplace, Poisson, Helmhotz and diffusion equations in Cartesian and polar co-ordinates.
theory – Feedback requirements – Relaxation oscillator.
Unit 3: Operational Amplifier (OpAmp) and its Applications OpAmp characteristics – DC & AC characteristics – basic applications – linear OpAmp circuits – Analog Multiplier and Divider – Frequency Doubling -Electronic Analog Computation – Active filters
Unit 4: Communication Electronics Modulations – Demodulation – Principle of Amplitude modulation, Frequency modulation and Phase Modulation – Simple circuits for AM and FM – Digital principles – Pulse modulation – APM, PPM, PWM and PCM.
Unit 5: Linear and Nonlinear Circuits VI characteristic of two terminal linear and nonlinear circuit elements – example – PWL circuit elements – Chua diode – autonomous and nonautonomous nonlinear circuits – Dynamics of Chuas and MLC circuits – Applications. Books for Study and Reference
1. J. Millman & C. C. Halkias, Electronic Devices and Circuits (TataMcGraw Hill, New Delhi, 1985).
2. G. Kennedy, Electronic Communication Systems, 3rd Ed. (Tata McGraw Hill, New
Delhi, 1994).
3. D. R. Choudhury & S. Jain Linear Integrated circuits (New Age International, New Delhi, 2001)
4. L. O. Chua, C. A. Desoer & E. S. Kuh Linear and Nonlinear circuits (McGraw Hill,
Singapore, 1987).
CC04 : NUMERICAL METHODS: THEORY Unit 1 : C++ Programming Constants and variables – I/O operators and statements – Header files – Main function – Conditional statements – Switch statement – Void function – Function programme – Loops: for, while and do while statements – Arrays – Break, continue and goto statements.
Unit 2 : Curve Fitting and Interpolation Curve fitting: Method of leastsquares – Normal equations – Straightlinefit – Exponential and powerlaw fits. Interpolation: Newton interpolation polynomial – Linear interpolation –Higherorder
Unit 3 : Solutions of Linear and Nonlinear Equations Simultaneous linear equations: Gauss elimination method – Jordan
′s modification –
Inverse of a matrix by GaussJordan method. Roots of nonlinear equations: NewtonRaphson method – Termination criteria – Pitfalls – Order of convergence.
Unit 4 : Numerical Integration and Differentiation Numerical Integration: NewtonCotes quadrature formula – Trapezoidal,Simpson’s 1/3 and 3/8 rules – Errors in the formulas – Composite Trapezoidal and Simpson’s rules – Errors in the formulas. Numerical Differentiation: First order derivative – Two and fourpoint formulas – Secondorder derivative – Three and fivepoint formulas.
Unit 5 : Numerical Solution of Ordinary Differential Equations Firstorder equations: Euler and improved Euler methods – Local andglobal truncation errors – Fourthorder RungeKutta method – Geometric description of the formula – Error Versus step size. Second order equations: Euler methods and Fourthorder RungeKuttamethod.
Books for Study and Reference
1. J. R. Hubbard, Programming with C++ (McGrawHill, New Delhi, 2006).
2. J. H. Mathews, Numerical Methods for Mathematics, Science and Engineering
(PrenticeHall of India, New Delhi, 1998).
CC06 : MATHEMATICAL PHYSICS – II Unit 1 : Green’s Function Techniques and Integral Equations
Green’s Functions – Properties – Methods of solutions in one, two and three dimensions
Applications – Linear integral equations Hilbert-Schmidt ker-nels – Fredholm alternative
– Neumann series – Applications.
Unit 2 : Complex Analysis
Complex functions and variables – Condition for a function to be analytic – Complex integration – Cauchy’s theorem – Cauchy’s integral formula – Taylor
expansion – Laurent series – Cauchys residue theorem – Computa-tions of residue –
Evaluation of integrals using residues. Unit 3 : Fourier Series Fourier Series : Determination of Fourier coefficients – Fourier series for periodic functions – Half-range series – Fourier cosine and Fourier sine series – Physical Applications.
Unit 4 : Fourier Transform Fourier Integral Theorem – Fourier cosine and sine – Integrals – Fourier transforms – Fourier cosine and sine Transforms – Physical applications – Heat equation (one dimension).
Unit 5 : Laplace Transform Properties of Laplace transform – Inverse Laplace transform – Laplace transform of derivatives – solution of second-order linear ordinary differ-ential equations by Laplace transform – Applications.
Books for Study and Reference
1. E. Kreyszig, Advanced Engineering Mathematics (Wiley Eastern, New Delhi, 1983)
2. L. A. Pipes and L. R. Harvill, Applied Mathematics for Engineers andPhysicists
(McGraw Hill, Singapore, 1970)
3. P. K. Chattopadhyay, Mathematical Physics (Wiley Eastern, New Delhi, 1992)
4. M. Hammernesh, Group Theory (Addision-Wesley, New York, 1962)
5. Harper, Introduction to Mathematical Physics (Prentice Hall of India, New Delhi,
1993) 6. H. K. Dass, Advanced Engineering Mathematics (S. Chand & Co., New Delhi,
1998) 7. K. Dass, Mathematical Physics, (S. Chand & Co., New Delhi, 2003)
CC07 : QUANTUM MECHANICS Unit 1 : The Schrodinger¨ Equation and operator formalism Time-dependent Schrodinger¨ equation – Physical meaning and conditions on admissible wave function – Consevation of probability– Expectation value – Ehrenfest
′ s theorem.
Operator Formulation: Linear operator – Adjoint and self-adjoint opera-tors –
Completeness – Physical interpretation of eigenvalues and eigen-functions –
Commutator – Simultaneous eigenfunctions – Heisenberg un-certainty relation. Unit 2 : Exactly Solvable Bound State Problems Linear harmonic oscillator: Eigenvalues and eigenfunctions by solving theone dimensional Schrodinger¨ equation and Abstract operator method – Particle in a box – Rectangular barrier potential – Tunnel effect. Unit 3 : Perturbation Theory Time-independent perturbation theory for non-degenerate states – Appli-cation to linear harmonic oscillator with perturbation – eFx and anhar-monic oscillator with perturbation x
3 and x
4 – Perturbation theory for de-generate states – Stark effect in hydrogen atom –
Time-dependent pertur-bation theory: Constant perturbation – Transition probability – Harmonic perturbation. Unit 4 : Scattering Theory
Classical definition of scattering cross-section – The scattering amplitude and scattering
cross-section in quantum mechanics – Green’s function for scattering amplitude – Born
approximation and its validity condition – Ap-plication to square-well, screened Coulomb
and Yukawa potentials – Par-tial wave analysis – Scattering by a perfectly rigid sphere. Unit 5 : Relativistic Quantum Mechanics Klein – Gordon equation for a free particle – Dirac equation for a free particle – Dirac matrices and their properties – Probability and current densities– Plane wave solutions – Negative energy states – Zitterbewe-gung: jitterly motion of a free particle – Spin of a Dirac particle.
Books for Study and Reference
1. L. Schiff, Quantum Mechanics (Tata McGraw Hill, New Delhi, 1968)
2. P. M. Mathews & K. Venkatesan, A Text Book of Quantum Mechanics (Tata McGraw Hill, New Delhi, 1987)
3. M. S. Rogalski & B. Palmer, Quantum Mechanics (Gordon & Breach, Amserdam,
1999)
CC08: THERMAL AND STATISTICAL PHYSICS
Unit I:Ensemble and equilibrium
Review of probability theory-Fundamental concepts of phase space–Microstates and
macrostates-Introduction to the concept of density of states-Statistical systems and
– Periodic table – Alkali type spectra – Equivalent electrons – Hund’s rule Unit 2 : Atoms in External Fields and Quantum Chemistry Atoms in External Fields: Zeeman and Paschen Back effect of one and two electron systems – Selection rules – Stark effect – Inner Shell vacancy – X-ray – Auger transitions – Compton effect.
Quantum Chemistry of Molecules: Covalent, ionic and van der Waal’s in-teractions – Born-Oppenheimer approximation – Heitler-London and Mole-cular orbital theories of H2 – Bonding and anti bonding MOs – Huckels molecular approximation – Application to butadiene and benzene. Unit 3 : Microwave & IR Spectroscopy
Rotational spectra of diatomic molecules – Intensity of spectral lines – Ef-fect of isotopic
substitution – The non-rigid rotor – Rotational spectra of poly atomic molecules – Linear,
symmetric top and asymmetric top mole-cules – Experimental techniques – Vibrating
diatomic molecule – Diatomic Vibrating rotator – Linear and symmetric top molecules –
Analysis by in-frared techniques – Characteristic and group frequencies. Unit 4 : Raman Spectroscopy Raman effect – Polarizability theory – Pure rotational Raman Spectrum – vibrational Raman Spectrum – diatomic molecules – Structure determina-tion from Raman & IR Spectrometer – Experimental Techniques. Unit 5 : Electronic Spectroscopy of Molecules Electronic spectra of diatomic molecules:- Intensity of spectral lines – The Franck-Condon principle – Dissociation energy and dissociation products – Rotational fine structure of electronic vibration transitions – Predissoci-ation.
Books for Study and Reference
1. C. N. Banwell, Fundamentals of Molecular Spectroscopy (McGraw-Hill, New York, 1981)
2. B. P. Straughan & S. Walker Spectroscopy: Vol. I (Chapman & Hall, 1976) 3. R. P. Feynman et al. The Feynman Lectures on Physics: Vol. III.
(Narosa Book Distributors, New Delhi, 1989) 4. A. K. Chandra, Introductory Quantum Chemistry (Tata McGraw Hill, New Delhi,
1989) 5. F. Pilar, Elementary Quantum Chemistry (McGraw Hill, New York, 1968) 6. I. N. Levine, Quantum Chemistry (Prentice-Hall of India, New Delhi, 1994) 7. A. Beiser, Concepts of Modern Physics (McGraw Hill, New York, 1995)
CC11 : NUCLEAR AND PARTICLE PHYSICS
Unit 1 :Basic Nuclear Properties and Nuclear Forces Ground state of deuteron – Magnetic dipole moment of deuteron – Properties of nuclear
6. A. Beiser, Concepts of Mordern Physics, 5th Ed. (McGraw-Hill, 1995)
CC12 : CONDENSED MATTER PHYSICS
Unit 1 : Crystal Structure Crystal classes and systemtry – 2D, 3D lattices – Bravais
lattices – Symmetry point groups – Space groups – Reciprocal lattice – Ewald’s sphere
construction – Braggs law – Atomic scattering factor – Diffraction – Structure factor –
Experimental techniques – Laue, Powder, Rotation methods - Nacl Bonding of common
crystal structures – CsCI & ZnS, Diamond – hcp ccp, random stacking and polytypism.
Unit 2 : Lattice Vibrations and Thermal Properties Vibration of monoatomic lattices –
Lattices with two atoms per primitive cell – Quantization of lattice vibrations – Phonon
momentum – Inelastic scattering of neutrons by phonons – Lattice heat capacity – Einstein
model – Density of modes in one-dimension and three- dimension – Debye model of the
lattice heat capacity – Thermal conductivity – Umklapp process
Unit 3 : Free Electron Theory, Energy Bands and Semiconductor Crystals Energy levels
and density of orbitals – Fermi-Dirac distribution – Free electron gas in three-dimensions
– Heat capacity of the electron gas – Electrical conductivity and Ohms law – Motion in
magnetic fields – Hall effect – Thermal conductivity of metals – Nearly free electron
model – Electron in a periodic potential – Semiconductors – Band gap – Effective mass –
Intrinsic carrier concentration.
Unit 4 : Diamagnetism, Paramagnetism, Ferromagnetism and Antiferromagnetism
Langevin classical theory of Diamagnetism and paramagnetism – Weiss theory –
Quantum theory of paramagnetism – Demagnetization of a paramagnetic salt –
Paramagnetic susceptibility of conduction electrons – Hund’s rules – Ferromagnetic order
– Curie point and the exchange integral – Temperature dependence of saturation
magnetization – Magnons – Antiferromagnetic order – Ferromagnetic domains – Origin of
domains – Coercive force and hysteresis.
Unit 5 : Dielectrics, Ferroelectrics and Superconductivity Macroscopic electric field –
Local electric field at an atom – Dielectric constant and polarizability – Clausius-Mossotti
equation – Polarization catastrophe – Ferroelectric domains – Occurrence of
Superconductivity – Meissner effect – Thermodynamics of superconducting transition –
London equation – Coherence length – BCS theory – Flux quantization – Type I and Type
II Superconductors – Josephson superconductor tunneling – DC and AC Josephson effect
– SQUID – Applications of superconductors.
Books for study and Reference
1. C. Kittel, Introduction to Solid State Physics, 5th Ed. (Wiley Eastern, New Delhi, 1977)
2. N. W. Ashcrof and N. D. Mermin, Solid State Physics (International Edition,
Philadelphia, 1976)
3. J. S. Blakemore, Solid State Physics, Second Edition (Cambridge University
Press, Cambridge, London, 1974)
4. A. J. Dekker, Solid State Physics (Mac Millan, Madras, 1971) 5. M. M.Woolfson, An
Introduction to X-ray Crystallography (Cambridge University Press, Cambridge, 1991)
6. T. P. Sheahen, Introduction to High-Temperature Superconductors (Plenum press, New
York, 1994)
7. S. O. Pillai, Solid State Physics (New Age International, New Delhi, 1995)
CC14 : ELECTROMAGNETIC THEORY Unit 1: Electrostatics Coulomb’s law – Gauss’ law – Divergence and curl of electrostatic field – Electric field and potential due to an electric dipole – Poisson and Laplace Equations – Boundary conditions and uniqueness theorem – Green’s theorem – Method of Images – Illustrations: Point charge in the presence of (i) a grounded conducting sphere (ii) an insulated conducting sphere (iii) a charged and insulated sphere – Conducting sphere in an uniform electric field.
Unit 2: Electrostatics of Macroscopic Media Electric qudrapole and multipole - Multipole expansion of electric field – Dielectric
polarization – External field of a dielectric medium – Electric field in a material medium –
Field due to a polarized sphere – Dielectric sphere in a uniform field Molecular field in
dielectric: The Claussis Mossotti relation – Electrostatic energy in dielectric media.
Unit 3: Magnetostatics Biot and Savart law – Force between current carrying conductors – Lorentz force Ampere’s law – Divergence and curl of magnetic induction – Comparison of electrostatics and magnetostatics – Magnetic vector potential – Magnetic field of a distant current loop – Magnetic field due to an infinite current carrying wire – Faraday’s law of induction – Self and Mutual Inductance.
Unit 4: Electromagnetics Maxwell’s displacement current – Maxwell equations and its derivation – Maxwell equations in free space, linear isotropic medium and harmonically varying fields – Conservation of energy (Poynting’s theorem) – Conservation of momentum for electromagnetic fields – Plane electromagnetic waves in (i) free space, (ii) nonconducting medium and (iii) conducting medium.
Unit 5: Wave Propagation
Polarization of electromagnetic waves (Linear, circular and elliptical polarization) –
Reflection and refraction of electromagnetic waves at a plane interface between dielectrics
– Fresnel’s equation – Total internal reflection – Propagation of electromagnetic waves
between parallel conducting medium – Waveguides (i) circular (ii) cylindrical and (iii)
rectangular.
Books for Study and Reference
1. J. D. Jackson, Classical Electrodynamics (Wiley Eastern Ltd., New Delhi, 1999) 2. D. Griffiths, Introduction to Electrodynamics (Prentice-Hall of India, New Delhi,
1999) 3. R. P. Feynman, R. B. Leighton and M. Sands, The Feynman Lectureson Physics: Vol.
II (Narosa Book Distributors, New Delhi, 1989) 4. Satya Prakash, Electromagnetic Theory and Electrodynamics (Kedar Nath Ram Nath,
Meerut, 2015)
EC01: NANO MATERIALS AND APPLICATIONS
I. NANOSCALE SYSTEMS: Length scales in physics, Surface-volume-ratio. Nanostructures:
3D, 2D and 1D nanostructures (nanodots, thin films and nanowires/ nanorods), Band structure
and density of states of materials at nanoscale, Size Effects in nano systems, Quantum
confinement: Applications of Schrödinger equation - Infinite potential well: particle in a box,
Quantum confinement of carriers in 3D, 2D, 1D nanostructures and its consequences.
II. SYNTHESIS OF NANOSTRUCTURE MATERIALS: Top down and Bottom up
approach, Photolithography, Ball milling. Gas phase condensation. Vacuum deposition. Physical