| Department of Physics

B.Sc. (Research) in Physics

Degree Requirement

151

Total Credits

97

Core Credits

12

Major Electives

42

CCC + UWE credits

Core & Elective Courses

Core Courses

Course code
Title
Credit
CHY111
Chemical Principles
5

This course will focus on introductory chemical principles, including periodicity, chemical bonding, molecular structure, equilibrium and the relationship between structure and properties. Students will explore stoichiometric relationships in solution and gas systems which are the basis for quantifying the results of chemical reactions. Understanding chemical reactivity leads directly into discussion of equilibrium and thermodynamics, two of the most important ideas in chemistry. Equilibrium, especially acid/base applications, explores the extent of reactions while thermodynamics helps us understand if a reaction will happen. The aim of the laboratory will be to develop your experimental skills, especially your ability to perform meaningful experiments, analyze data, and interpret observations. This is a required course for Chemistry majors, but also satisfies UWE requirements for non-majors.

COURSE CONTENT:

  1. Atomic structure, Periodic table, VSEPR, Molecular Orbital theory, and biochemistry:
    1. Introduction: why chemistry in engineering? Concept of atom, molecules, Rutherford’s atomic model, Bohr’s model of an atom, wave model, classical and quantum mechanics, wave particle duality of electrons, Heisenberg’s uncertainty principle, Quantum-Mechanical Model of Atom, Double Slit Experiment for Electrons, The Bohr Theory of the Hydrogen atoms, de Broglie wavelength, Periodic Table.
    2. Schrodinger equation (origin of quantization), Concept of Atomic Orbitals, representation of electrons move in three-dimensional space, wave function (Y), Radial and angular part of wave function, radial and angular nodes, Shape of orbitals, the principal (n), angular (l), and magnetic (m) quantum numbers, Pauli exclusion principle.
    3. Orbital Angular Momentum (l), Spin Angular Momentum (s), spin-orbit coupling, HUND’s Rule, The aufbau principle, Penetration, Shielding Effect, Effective Nuclear Charge, Slater’s rule.
    4. Periodic properties, Ionization Energies of Elements, Electron affinities of elements, Periodic Variation of Physical Properties such as metallic character of the elements, melting point of an atom, ionic and covalent nature of a molecule, reactivity of hydrides, oxides and halides of the elements.
    5. Lewis structures, Valence shell electron pair repulsion (VSEPR), Valence-Bond theory (VB), Orbital Overlap, Hybridization, Molecular Orbital Theory (MO) of homo-nuclear and hetero-nuclear diatomic molecules, bonding and anti-bonding orbitals.
    6. Biochemistry: Importance of metals in biological systems, Fe in biological systems, Hemoglobin, Iron Storage protein - Ferritin]

2. Introduction to various analytical techniques:

UV-Visible Spectroscopy, IR Spectroscopy, NMR spectroscopy, X-Ray crystallography

Spectroscopy: Regions of Electromagnetic Radiation, Infra-Red (IR) Spectroscopy or Vibrational Spectroscopy of Harmonic oscillators, degree of freedom, Stretching and Bending, Infrared Spectra of different functional groups such as OH, NH2, CO2H etc., UV-Vis Spectroscopy of organic molecules, Electronic Transitions, Beer-Lambert Law, Chromophores, principles of NMR spectroscopy, 1H and 13C-NMR, chemical shift, integration, multiplicity,

X-ray crystallography: X-ray diffraction, Bragg’s Law, Crystal systems and Bravais Lattices

  1. The Principles of Chemical Equilibrium, kinetics and intermolecular forces:
  • Heat & Work; State Functions
  • Laws of thermodynamics
  • Probability and Entropy
  • Thermodynamic and Kinetic Stability
  • Determination of rate, order and rate laws
  • Free Energy, Chemical Potential, Electronegativity
  • Phase Rule/Equilibrium
  • Activation Energy; Arrhenius equation
  • Catalysis: types; kinetics and mechanisms
  • Electrochemistry
  • Inter-molecular forces

 4. Introduction to organic chemistry, functional group and physical properties of organic compounds, substitution and elimination reaction, name reactions and stereochemistry

Texts & References:

  1. Chemical Principles - Richard E. Dickerson, Harry B. Gray, Jr. Gilbert P. Haight
  2. Valence - Charles A. Coulson [ELBS /Oxford Univ. Press]
  3. Valence Theory - J. N. Murrell, S. F. A. Kettle, J. M. Tedder [ELBS/Wiley]
  4. Physical Chemistry - P. W. Atkins [3rd Ed. ELBS]
  5. Physical Chemistry - Gilbert W. Castellan [Addison Wesley, 1983]
  6. Physical Chemistry: A Molecular Approach -Donald A. McQuarrie, J.D . Simon
  7. Inorganic Chemistry:  Duward Shriver and Peter Atkins.
  8. Inorganic Chemistry: Principles of Structure and Reactivity by James E. Huheey,
  9. Ellen A. Keiter and Richard L. Keiter.
  10. Inorganic Chemistry: Catherine Housecroft, Alan G. Sharpe.
  11. Atkins' Physical Chemistry, Peter W. Atkins, Julio de Paula.
  12. Strategic Applications of Named Reactions in Organic Synthesis, Author: Kurti Laszlo et.al
  13. Classics in Stereoselective Synthesis, Author: Carreira Erick M & Kvaerno Lisbet
  14. Molecular Orbitals and Organic Chemical Reactions Student Edition, Author: Fleming Ian
  15. Logic of Chemical Synthesis, Author: Corey E. J. & Xue-Min Cheng
  16. Art of Writing Reasonable Organic Reaction Mechanisms /2nd Edn., Author: Grossman Robert B.
  17. Organic Synthesis: The Disconnection Approach/ 2nd Edn., Author: Warrer Stuart & Wyatt Paul

Other reading materials will be assigned as and when required.

Prerequisite: None.

MAT101
Calculus I
4

Core course for B.Sc. (Research) programs in Mathematics, Physics and Economics. Optional course for B.Sc. (Research) Chemistry.

Credits (Lec:Tut:Lab)= 3:1:0 (3 lectures and 1 tutorial weekly)

Prerequisites: Class XII mathematics or MAT 020 (Elementary Calculus)

Overview:  This course covers one variable calculus and applications. It provides a base for subsequent courses in advanced vector calculus and real analysis as well as for applications in probability, differential equations, optimization, etc. One of the themes of the course is to bring more rigour to the formulas and techniques students may have learned in school.

Detailed Syllabus:

  1. Real Number System: The axioms for N and R, mathematical induction.
  2. Integration: Area as a set function, integration of step functions, upper and lower integrals, integrability of bounded monotone functions, basic properties of integration, polynomials, trigonometric functions.
  3. Continuous Functions: Functions, limits, continuity, Intermediate Value Theorem, Extreme Value Theorem, integrability of continuous functions, Mean Value Theorem for integrals.
  4. Differentiation: Tangent line, rates of change, derivative as function, algebra of derivatives, implicit differentiation, related rates, linear approximation, differentiation of inverse functions, derivatives of standard functions (polynomials, rational functions, trigonometric and inverse trigonometric functions), absolute and local extrema, First Derivative Test, Rolle's Theorem, Mean Value Theorem, concavity, Second Derivative Test, curve sketching.
  5. Fundamental Theorem of Calculus: Antiderivatives, Indefinite Integrals, Fundamental Theorem of Calculus, Logarithm and Exponential functions, techniques of integration.
  6. Polynomial Approximations: Taylor polynomials, remainder formula, indeterminate forms and L'Hopital's rule, limits involving infinity, improper integrals.
  7. Ordinary Differential Equations: 1st order and separable, logistic growth, 1st order and linear.

References:

  1. Calculus, Volume I, by Tom M Apostol, Wiley.
  2. Introduction to Calculus and Analysis I by Richard Courant and Fritz John, Springer
  3. Essential Calculus – Early Transcendentals, by James Stewart. Cengage, India Edition.
  4. Calculus with Analytic Geometry by G F Simmons, McGraw-Hill

Past Instructors: Amber Habib, Debashish Bose

MAT102
Calculus II
4

Core course for B.Sc. (Research) programs in Mathematics, Physics. Optional course for B.Sc. (Research) Chemistry.

Credits (Lec:Tut:Lab)= 3:1:0 (3 lectures and 1 tutorial weekly)

Prerequisites: MAT 101 (Calculus I)

Overview: The first part is an introduction to multivariable differential calculus. The second part covers sequences and series of numbers and functions. The concepts and techniques covered here are used extensively in the social and natural sciences as well as in engineering.

Detailed Syllabus:

  1. Differential calculus in several variables: Functions of several variables, level curves and surfaces, limits and continuity, partial derivatives, tangent planes, chain rule, directional derivatives, gradient, Lagrange multipliers, extreme values and saddle points, 2nd derivative test
  2. Sequences and Series: Limits of sequences, algebra of limits, series, divergence test, comparison and limit comparison tests, integral test, alternating series test, absolute convergence, root & ratio tests, Abel and Dirichlet tests, power series, Taylor series, Fourier Series.

References:

  • Calculus, Volume II, by Tom M Apostol, Wiley.
  • Essential Calculus – Early Transcendentals by James Stewart, Cengage, India Edition.
  • Calculus and Analytic Geometry by G B Thomas and R L Finney, 9th edition, Pearson.
  • Basic Multivariable Calculus by J E Marsden, A J Tromba and A Weinstein, 1st edition, Springer (India), 2011.
  • Calculus by Ken Binmore and Joan Davies, 1st edition, Cambridge, 2010.

Past Instructors: Amber Habib, Debashish Bose

 

PHY103
Fundamentals of Physics I
5

This is an introductory course for students majoring in physics or those who are planning to take physics as their minor.  It will provide an introduction to Newtonian mechanics, Lagrangian Methods, and to the Special Theory of Relativity.  

 Physics and its relation to other sciences.  
 Time and Distance. Frames of reference and the inertial frames of reference.  
  Vector Analysis, Coordinate systems, Dimensional Analysis  
 Newton’s laws of motion in one dimension.  
 Rotational invariance. Newtons’s laws of motion in three dimension  
 Conservation of energy and momentum.  
 Oscillations.  
 The Lagrangian method.  
 Rotation in two dimensions. Rotation in three dimensions.
 Central forces  
 The Special Theory of Relativity.  Space-Time and four vectors.  
 Accelerating frames of reference

PHY104
Fundamentals of Physics II
5

Vector Analysis 
Electrostatics: Electric Field, Divergence and Curl of Electrostatic Fields, Electric Potential, Work and Energy in Electrostatics, Conductors 
Potentials: Laplace's Equation, Method of Images, Multipole Expansion 
Electric Fields in Matter: Polarization, Field of a Polarized Object, Electric Displacement, Linear Dielectrics 
Magnetostatics: Lorentz Force Law, Biot-Savart law, Divergence and Curl of Magenetic Field, Magnetic Vector Potential 
Magnetic Fields in Matter: Magnetization, Field of a Magnetized Object, Auxiliary Field, Linear and Nonlinear Media 
Electrodynamics: Electromotive Force, Electromagnet Induction, Maxwell's Equations 
Conservation Laws: Charge and Energy, Momentum, Work 
Electromagnetic Waves: Waves in One Dimension, Electromagnetic Waves in Vacuum, Electromagnetic Waves in matter

PHY105
Introduction to Computational Physics I
3

Introduction to Python: General information, Operators, Functions, Modules, Arrays, Formatting, Printing output, Writing a program
Approximation of a function: Interpolation, Least-squares Approximation              
Roots of Equations: Method of Bisection, Method based on Linear Interpolation,              
Newton-Raphson Method              
Numerical Differentiation: Finite Difference Approximation              
Numerical Integration: Trapezoidal Rule, Simpson's Rule              
Ordinary Differential Equations: Taylor Series Method, Runge-Kutta Methods, Shooting Method

PHY106
Introduction to Computational Physics II
3

1.Systems of Linear Algebraic Equations: Gauss Elimination Method, LU              
decomposition, Choleski’s Decomposition Method, Symmetric and Banded Coefficient Matrices, Pivoting, Matrix Inversion, Iterative Methods 
 
2.Symmetric Matrix Eigenvalue Problems: Jacobi Method, Power and Inverse Power Methods, Eigenvalues of Symmetric Tridiagonal Matrices, Computation of Eigenvectors    
3. Two-Point Boundary Value Problems: Shooting Method 
4. Solution of Partial Differential Equations: Separation of variables, Finite            
Difference Method, The Relaxation Method, The matrix method for difference Equations.

PHY201
Fundamentals of Thermal Physics
4

 1. The Kinetic Theory of Gases Macroscopic and  microscopic description of matter, thermodynamic variables of a system, State function, exact and inexact differentials, Basic assumptions of the kinetic theory, Ideal gas approximation, deduction of perfect gas laws, Maxwell’s distribution law, root mean square and most probable speeds. Collision probability, Mean free path from Maxwell’s distribution. Degrees of freedom, equipartition of energy. Nature of intermolecular interaction : isotherms of real gases. van der-Waals equation of state.   
2. Transport Phenomena  Viscosity, thermal conduction and diffusion in gases. Brownian Motion: Einstein’s theory, Perrin’s work, determination of Avogardo number.   
3. Thermodynamics of Photon Gas  Spectral emissive and absorptive powers, Kirchoff’s law of blackbody radiation, energy density, radiation pressure. Stefan-Boltzmann law, Planck’s law   
4. First Law of Thermodynamics Zeroth law and the concept of temperature. Thermodynamic equilibrium, internal energy, external work, quasistatic process, first law of thermodynamics and applications including magnetic systems, specific heats and their ratio, isothermal and adiabatic changes in perfect and real gases.  
5. The Second Law of Thermodynamics and its Statistical Interpretation (a) Second law of thermodynamics: different formulations and their equivalence (b) Entropy: The statistical postulate. (c) Equilibrium of an isolated system: Temperature (d) Illustration: The Schottky defects. (e) Equilibrium of a system in a heat bath: Boltzmann distribution; Kinetic interpretation of the Boltzmann distribution.  
6. Thermodynamic Functions  Enthalpy, Helmholtz and Gibbs’ free energies; Chemical potential, Maxwell’s relations; thermodynamic equilibrium and free energies.  
7. Change of State  Equilibrium between phases, triple point, Gibbs’ phase rule and simple applications. First and higher order phase transitions, The phase equilibrium and the ClausiusClapeyron equation,. JouleThomson effect, third law of thermodynamics  
8. Applications of Thermodynamics. (a) Heat engines and Refrigerators: Derivation of limits on efficiency from the laws of thermodynamics; Carnot cycle; realistic cycles for internal combustion engines, steam engines, and refrigeration (b) Thermodynamics of rubber bands: Gibbs free energy, Entropy (c). Paramagnetism: A paramagnetic solid in a heat bath. The heat capacity and the entropy. An isolated paramagnetic solid.  Negative temperature.

PHY202
Introduction to Quantum Mechanics
4

1. Quantum and Classical Behavior 
a) Experiments with bullet, waves and electrons 
b) Probability Amplitude 
c) The two-slit interference pattern 
d) Identical particles 

2. Base States 
a) Filtering atoms with a Stern-Gerlach apparatus 
b) Base states 
c) Interfering amplitudes 
d) Transferring to different bases 
e) Base states of spin one-half particle 

3. Dependence of Amplitude on Time 
a) The Hamiltonian Matrix 
b) The Ammonia Maser 
c) Other Two State Systems: The Hydrogen Molecule, The Benzene Molecule, Neutrino 
d) Oscillations
e) The Pauli spin matrices and the Hamiltonian of a spin-half particle in an external 
f) magnetic field 
g) Generalization to N-state system 

4. Propagation in a Crystal Lattice 
a) States for an electron in a one-dimensional lattice 
b) An electron in a three-dimensional lattice 
c) Scattering by imperfections in the lattice 
d) Trapping by a lattice imperfection 
e) Semiconductors and the transistor 

5. Symmetry, Conservation Laws and Angular-Momentum 
a) Symmetry and conservation 
b) The conservation laws 
c) Polarized light 
d) The annihilation of positronium 
e) Entangled states and Bell’s theorem 

6. Dependence of Amplitude on Position 
a) Amplitudes on a line 
b) The wave function 
c) The Schrödinger equation in one dimension

PHY203
Introduction to Mathematical Physics I
3

(a) Linear transformations of the plane    
i. Affine planes and vector spaces    
ii. Vector spaces and their affine spaces    
iii. Euclidean and affine transformations  
 iv. Representing linear transformations by matrices    
v. Areas and determinants  

(b) Eigenvectors and eigenvalues    
i. Conformal linear transformations    
ii. Eigenvectors and eigenvalues  
 iii. Markov processes  

(c) Linear differential equations in the plane    
i. Functions of matrices    
ii. Computing the exponential of a matrix    
iii. Differential equation and phase portraits    
iv. Applications of differential equations  
                
 (d) Scalar products    
i. The Euclidean scalar product    
ii. Quadratic forms and symmetric matrices    
iii. Normal modes 
iv. Normal modes in higher dimensions    
v. Special relativity: The Poincare’ group and the Galilean group   
(e) Calculus in the plane
i. The differential calculus and the examples of the chain rule: the Born approximation and Kepler motion  
ii. Partial derivatives and differential forms.  
iii. The pullback notation  
iv. Taylor’s formula  
v. Lagrange multiplier  

(f) Double integrals  
i. Exterior derivative  
ii. Two-forms
iii. Pullback and integration for two-forms  
iv. Two-forms in three space  
v. Green’s theorem in the plane

PHY204
Introduction to Mathematical Physics II
3

1. Functions of a complex variable 
(a) Elementary properties of analytic functions 
(b) Integration in the complex plane 
(c) Analytic functions 
(d) Calculus of residues: applications 
(e) Periodic functions: Fourier series 
(f) Gamma function 

2. Differential Equations: analytical methods 
(a) Linear differential equations and their power series solutions 
(b) Legendre’s equation 
(c) Bessel’s equation 
(d) Hypergeometric equation 

3. Hilbert Spaces 
(a) Infinite-dimensional vector spaces 
(b) Function spaces 
(c) Fourier series 
(d) Fourier integral and integral transforms 
(e) Orthogonal polynomials 

4. Partial differential equations 
(a) Linear first-order equations 
(b)The Laplacian and the Green function for Laplace’s equation 
(c) Time-dependent partial differential equations: The diffusion 
equation and the Schrödinger equation 
(d) Nonlinear partial differential equations and solitons

PHY205
Waves and Oscillations
4

1. Oscillations of Systems with Many Degrees of Freedom
(a) Review of the Harmonic Oscillator
(b) Systems with More than One Degree of Freedom
(c) Linearity, Normal Modes and the Matrix Equation of Motion
(d) Forced Oscillations and Resonance is Systems with More than One Degree of Freedom
(e) The Infinite System and Translational Invariance
(f) Forced Oscillations and Boundary Conditions

2. Traveling Waves
(a) The Continuum Limit of a Discrete System
(b) Longitudinal Oscillations and Sound
(c) Harmonic Traveling Waves in One Dimension Phase Velocity
(d) Index of Refraction and Dispersion
(e) Impedance and Energy Flux

3. Modulations, Pulses, and Wave Packets
(a) Group Velocity
(b) Pulses
(c) Fourier Analysis of Pulses
(d) Fourier Analysis of Traveling Wave Packet

4. Waves in Two and Three Dimensions
(a) Harmonic Plane Waves and the Propagation Vector
(b) Water Waves
(c) Electromagnetic Waves
(d) Radiation from a Point Charge

 
5. Polarization
(a) Description of Polarized States
(b) Production of Polarized Transverse Waves
(c) Double Refraction
(d) Bandwidth, Coherence Time, and Polarization

6. Interference and Diffraction
(a) Interference between Two Coherent Point Sources
(b) Interference between Two Independent Sources
(c) How Large Can a “Point” Light Source Be?
(d) Angular Width of a “Beam” of Traveling Waves
(e) Diffraction and Huygen’s Principle
(f) Geometrical Optics

PHY206
Electronics I
4

Review from Fundamentals of Physics-II, Galvanometer to Ammeter and Voltmeter, Meaning of Network, Voltage and Current dividers, Voltage and Current source, Impedance Matching. Network Theorems. Thermionic Emission: Richardson’s equation, Child-Langmuir Law, Brief introduction on Valves, deflection sensitivity in electric and magnetic fields, Cathode Ray Oscilloscope, Lissajous figures. 
Basic concepts of semiconductors, conduction and doping, PN junction, diode characteristics, forward bias, reverse bias, static and dynamic resistance, junction capacitance, equivalent circuit, Zener and avalanche breakdown, Heterojunction; Diode circuits - Rectifiers half wave and full wave efficiency and ripple factor, Voltage multiplier, clipper and clamper circuits. 
Bipolar Junction transistor, the transistor action, transistor current components, Modes of operation, common base, common emitter and common collector configurations, Current voltage characteristics of CB, CE, CC configuration, current gain , and Early effect, DC load line, Q-point, saturation and cut-off regions; 
Transistor biasing - Base bias, Emitter bias, Transistor switch, Voltage divider bias, Self bias, Collector feedback bias. Stability factor. Field Effect Transistors, MOSFET, HEMT and MOSFET as Capacitor. AC Models - ac resistance of the emitter diode, ac input impedance, ac load-line, ac-equivalent circuits - T- model, π-model. 
Amplifier: types with uses, Transistor as an amplifier using h-parameters, comparison of amplifier configurations, simplified h-model; Voltage amplifiers voltage gain, DC, RC, transformer coupled amplifiers, frequency response of RC coupled amplifiers, cascading CE & CC amplifiers, Darlington pair. Feedback: Positive and negative feedback-advantages of negative feedback-input and output resistances-voltage series and current series feedback-frequency response of amplifiers with and without feedback. Power amplifiers - Class A, Class B, Class C amplifiers, Push pull amplifiers. Oscillators, Wien bridge oscillator, Colpitt oscillator, phase shift oscillator, resonant circuit oscillators, crystal oscillator. 
Operational Amplifier: characteristics, applications like adder, differentiator, integrator, and voltage comparator.

PHY208
Advanced Experimental Physics I
3

PHY 208 is an advanced lab course which aims to offer an experiential learning through a wide range of experiments and projects based on Thermodynamics, Optics and Modern Physics.

PHY301
Classical Mechanics
4

Introduction to dynamical systems, degree of freedom, time evolution 
                 Lagrangian formulation of mechanics 
                 Noether's Theory: Symmetry and conservation laws 
                 Hamiltionian formulation of mechanics 
                 Phase space and Liouville's theorem: applications to statistical mechanics 
                 Poisson Bracket: Symmetry, rotation generators 
                 Small Oscillations: normal modes, normal coordinates, vibration of molecules 
                 Rotation and rigid body motion: Euler angles and applications

PHY302
Statistical Physics
4

1. The Fundamentals of Statistical Mechanics 
1. Introduction 
2. The Microcanonical Ensemble. 
3. Entropy and Temperature 
4. The Canonical Ensemble 
5. The Partition Function , Energy and Fluctuations, Entropy, Free Energy 
6. The Chemical Potential 
7. Grand Canonical Ensemble, Grand Canonical Potential, Extensive and Intensive Quantities 

2. Classical Gases. 
1. Ideal Gas, Equipartition of Energy, Boltzmann's Constant, Gibbs's Paradox 
2. Maxwell Distribution, Kinetic Theory 
3. Diatomic Gas, Interacting Gas, Mayer f Function, Virial Coecient 

van der Waals Equation of State, The Cluster Expansion. 
3. Quntum Statistical Mechanics 
1. The Postulate of Quantum Statistical Mechanics 
2. Density Matrix 
3. Ensembles in Quantum Statistical Mechanics 
4. The Third Law of Thermodynamics 
5. Fermi Systems, Bose Systems. 
4. Phase Transitions 
1. Liquid-Gas Transition, Phase Equilibrium, The Clausius-Clapeyron Equation,The Critical Point 
2. The Ising Model, Mean Field Theory, Critical Exponents, Validity of Mean Field Theory. 
3. Some Exact Results for the Ising Model, The Ising Model in d= 1 Dimensions 2d Ising Model. 
4. Landau Theory, Second Order Phase Transitions, First Order Phase Transitions, 
5. Landau-Ginzburg Theory, Correlations, Fluctuations.

PHY303
Classical Electrodynamics
4

Overview: This course is one step ahead towards understanding some oldest phenomena of nature that mankind has ever sought after since Benjamin Franklin’s “lightning” experiment in early eighteenth century. The course begins with discussion on basic theoretical framework of electrodynamics, the Maxwell’s equations and new phenomena with respect to field theoretical questions (energy, momentum of the field) and its application to establish optics as well as in sector of practical applications (wave guides and resonant cavities) are investigated thereon.  
Unit 1: Review of Maxwell’s equations, The Poynting vector, The Maxwellian stress tensor. Unit-2: Electromagnetic waves in vacuum, Polarization of plane waves, Electromagnetic waves in matter, frequency dependence of conductivity, frequency dependence of polarizability, frequency dependence of refractive index. Laws of Reflection and Refraction of Electromagnetic waves, Wave guides, boundary conditions, classification of fields in wave guides, phase velocity and group velocity, resonant cavities.   
 Unit-3: Moving charges in vacuum, gauge transformation, the time dependent Green function, The Lienard-Wiechert potentials, Lienard-Wiechert fields, application to fields- radiation from a charged particle, Antennas, Radiation by multipole moments, Electric dipole radiation, Complete fields of a time-dependent electric dipole, Magnetic dipole radiation.  
Unit-4: Lorentz transformations, Four vectors and four tensors, The field equations and the field tensor, Maxwell’s equations for covariant notation. Relativistic covariant Lagrangian formalism, Covariant Lagrangian formalism for relativistic point charges, The energy-momentum tensor, Conservation laws.

PHY304
Condensed Matter Physics
4

1. Invitation to Condensed Matter Physics 
2. Geometrical Description of Crystals and Scattering 
3. The Sommerfeld Free Electron Theory of Metals 
4. One Electron Theory and Energy Bands 
5. Lattice Dynamics of Crystals : Phonons

PHY305
Quantum Mechanics I
4

Overview  This course (Quantum Mechanics – I) aims to follow up the development in Introduction to Quantum Mechanics (PHY202) with more advanced topics in the fundamental subject of Quantum Mechanics, like representation theory and the Schrödinger, Heisenberg and Interaction (Dirac) pictures, Theory of Angular Momentum, and Time-Independent and Time-Dependent Approximation Methods like Perturbation theory and the Variational Principle. (Some advanced optional topics are marked with * in the syllabus.) It starts with reviewing the basic concepts and surprizes in Quantum Mechanics (QM) with the prototypical example of Photon Polarization in great detail. This course together with the next advanced course (PHY306 : Quantum mechanics – II) is based mainly on the set of celebrated Lecture Notes in QM by Gordon Baym, which formed the subject matter of the Graduate level QM course at the University of Illinois at Urbana-Champaign, and hence would ideally prepare the students at a Graduate QM level, ready to go into research, and ideal for students interested to go into the 4th year extension into B.Sc. Research. It can also be of interest to certain students in Chemistry, Mathematics or some branches of Engineering, provided they have the necessary background.  
In addition to the above mentioned precursor course on Basic QM, a background in Basic Electromagnetism and Some Mathematical Methods relating especially to Linear Algebra would be useful, but not an absolute necessity.

PHY306
Quantum Mechanics II
4

1. Advanced Angular Momentum Theory 
2. Advanced Topics in Perturbation Theory 
3. Identical Particles and Second Quantization 
4. Central Potentials and Potential Scattering Theory 
5. Interaction of Radiation with Matter 
6. Symmetries in Quantum Mechanics

PHY307
Electronics - II
4

Overview Digital Electronics is an advanced course for students in which rigorous scientific approach driven hands-on training is provided on handling and designing basic components in digital electronic devices.  The pre-requisite for this course is well-versed understanding of analog electronic systems as offered through courses like PHY206, PHY104 etc. At the end of this course, students are expected to demonstrate competency in handling and designing digital devices.   Detailed Syllabus Introduction of Digital Systems comparing Analog Systems, Logic Levels: Introduction to Number System: Binary, Decimal and BCD, Logic Gates and discussion up to 3/4 input, Truth Table, Boolean Algebra, Boolean Circuit simplifications using algebra, Handling an unknown digital circuit through Truth table, De Morgan’s Theorems, Sum of Products (SOP) & POS, Introduction of Karnaugh Map: Need beyond Truth Table, Circuits simplification through K-map, Parity Checker, K-map working examples, K-map simplification using Max terms, Don’t care condition using Max terms/Min terms, Comparator and Gate circuit as memory: NOT gate Latch, S-R Latch, Clock Input and Clocked S-R Latch as Flip-Flop, D-Flip Flop & J-K Flip-Flop, Multiplexer and Demultiplexer, Synchronous counters, Shift Register, Examples of comparative circuits between Synchronous counters and shift 
register, Difference between systematic and non-systematic counting: Introduction to Ripple Counter, Ripple counter concludes, Examples of Ripple and Synchronous Counters, D/A converter with examples, A/D converter with examples, Logic family: TTL and CMOS

PHY308
Advanced Experimental Physics - II
3

PHY 308 is a lab course offering an opportunity for hands-on learning through physics experiments based on various physics concepts covering Condensed matter physics and interaction of matter and energy.

PHY499
Undergraduate Thesis
12

Undergraduate thesis is a research project, spread over two consecutive semesters, in which students will work extensively on a research problem of current interest under the guidance of a faculty member.

Elective Courses

Course code
Title
Credit
PHY255
Introduction to Biophysics
3

1. Introduction: Definition of biophysics, why to study, examples.   
2. Thermodynamics: Entropy, Enthalpy, The free energy of a system, Chemical potential, Redox potential, Bioenergetics  
3. Biophysical properties: Brownian motion, Osmosis, Dialysis, Colloids 
4. Membrane biophysics: Structure of bio-membrane. Structure-function relation. 
5. Application of Radiation to Biological system: Introduction, particles and radiations of significance, physical and biological half-lives, macroscopic absorption of radiation, activity and measurements, units of dose, relative biological effectiveness and action of radiation at molecular level. 
6. Experimental methods in biophysics:  (a) Microscope: Light characteristics, microscopes- compound, phase contrast, polarization, fluorescent and electron microscopes – Transmission Electron Microscope, Scanning Electron Microscope, and Scanning tunneling electron microscope, Atomic Force Microscopy 
(b) Spectroscopy: Electronic structure of atoms, Bond formation, hybridization of orbitals, Molecular orbitals, Bond energy, Ultraviolet & Visible spectroscopy-Beer Lamberts law- spectrophotometer. Infrared spectroscopy, Raman spectra, Circular Dichroism, Fluorescence spectroscopy, NMR spectroscopy.

PHY402
Classical Theory of Fields
3

This course has two parts. The first part reformulates classical electrodynamics as a field theory. The second part introduces general theory of relativity.

PHY406
Advanced Quantum Mechanics
3

This course introduces a student to relativistic quantum mechanics. It includes The Dirac equation and an introduction to quantum electrodynamics.

PHY408
Advanced Condensed Matter Physics
3

This is an advanced course in condensed matter emphasizing the special properties of solids: magnetism, super fluidity and superconductivity, dielectrics and ferroelectrics.

PHY409
Quantum Field Theory
3

Review of Klein-Gordon and Dirac equations Solutions of Dirac Equation, Properties of Dirac matrices Free Klein Gordon Field Theory  
Self-Interacting Scalar Field Theory           
Complex Scalar Field Theory                     
Dirac Field Theory                    
Feynman diagrams

PHY410
Introduction to High Energy Particle Physics
3

This course introduces the experimental results and the theoretical concepts that lead to the formulation of the standard model of particle physics

PHY411
Classical Field theory and general relativity
3

The first part of this course reformulates classical electrodynamics as a field theory and the second part introduces general theory of relativity.

PHY412
Introduction to Experimental Techniques in Particle Physics
3

This course introduces the student to detectors, data analysis and other experimental techniques used in experimental particle physics.

PHY413
General Theory of Relativity
3

We begin with an overview of special theory of relativity and proceed to give the definitions of tensor, connection, parallel transport and covariant differential with the aim of providing the description of gravity as arising from a curve space. From Riemann geometry and the Christoffel symbols we move to geodesic equations and to Riemann tensor outlining its various properties. We explain how one can formulate Einstein equations from fundamental principles. We also derive the Einstein equations from the least action principle applied to the Einstein-Hilbert action. We define the energy-momentum tensor for matter and show that it obeys a conservation law. We take up the study of the black hole type solution and derive the one for Schwarzschild black hole. We touch upon the Birkhoff theorem and explain the important differences between energy-momentum conservation laws in the absence and in the presence of the dynamical gravity. We discuss gravitational waves and give an introduction to cosmology including cosmic microwave background radiation, dark matter and dark energy.

PHY414
Computational and Numerical Analysis
3

Numeric and computational techniques to calculate roots of polynomials and other nonlinear functions; determinants, eigenvalues, and eigenvectors, solutions to differential equations; applications of FFT, finite difference expressions, interpolation and approximation, numerical differentiation and integration, by emphasizing on the algorithms and their implementation in the FORTRAN program language.

PHY415
Non-linear dynamics
3

Nonlinear dynamics will deal with fundamental properties of nonlinear systems and the question of non-integrability.

This course provides a broad introduction and familiarity to the field of nonlinear dynamics and chaos. It takes an intuitive approach and focuses on both the analytical and the computational tools that are important in the study of nonlinear dynamical systems.

PHY417
Topics in Quantum Many Body Th
3

This course (Topics in Quantum Many-Body Theory) aims to introduce the student with ample knowledge of Quantum Mechanics (qualified all of IQM, QM-I and QM-II) to the complexity of the many-body problem, mainly in the field of Condensed Matter Physics, though some of the methods go well beyond the scope of Condensed Matter Physics. Many-body Physics is the study of systems with a very large number of coupled degrees of freedom, typically involving a system of many (often ~ Avogadro’s Number ~ 1023) interacting particles. An exact solution of this would ideally involve the solution of ~ coupled Schrödinger Equations, which is essentially and unsolved problem! So the methods of Many-body Physics involve making useful and valid approximations to extract useful information about the system, without having to do a full exact solution of the many-body problem. This could involve, for example, the reduction of the fully interacting problem to a non-interacting or weakly interacting problem via certain “canonical transformations”. The prototypical example in this case is the resolution of the complex motion of crystal lattices into independent and non-interacting oscillator modes called “Phonons”, in the harmonic approximation. The interactions between these Phonons when anharmonic effects are included is weak, compared to that between the original lattice atoms. Similarly “elementary excitations” of the strongly coupled Heisenberg Spins on a lattice, are non-interacting spin-waves or “magnons”, to a first approximation, and magnon-magnon interactions are relatively weak.

This course will familiarize students with the concepts of “Elementary Excitations” in many-body systems, like “quasi-particles” and “collective excitations” etc. Also the concepts of “Broken Symmetry” and the idea of “Emergent Complexity” will be emphasized, following the prophetic article “More is Different” by P.W. Anderson. It also inspects Spin Systems and related complexities in some detail. Other approximations and methods of calculations like “Mean-field Theories”, “Green’s Functions and the Renormalization method” etc. will be dealt with. “Linear Response Theory” and “Kubo Formulae” that connects theory to experiments will also be covered. We will also try to cover “Many-body Perturbation Theory” and some aspects of “Strong Correlations”.

PHY451
Materials Characterization Techniques
3

This course covers the interaction of matter with photons, electrons and charge particles, and the related characterization techniques. The fundamentals of each technique will be discussed with suitable examples.