 Course Catalog | Department of Physics

# Course Catalog

PHY481
Data Mining & its Applications
4.00
Course description not available.
PHY419
Intro to Density Functional...
3.00
Course description not available.
PHY101
Introduction to Physics I
4.00
The aim of this course is to bridge the gap between the various boards across the country at 10+2 level and bring everyone at the standard undergraduate level. All the engineering branches have their origin in the basic physical sciences. In this course we aim to understand the basic physical laws and to develop skills for application of various physical concepts to the science and engineering through problem solving. This will involve the use of elementary calculus like differentiation and integration.    Detailed Syllabus         Mechanics: The inertial reference frames, Newton’s laws of motion in vector notation, Conservation of energy, Application of Newton’s laws of motion, Dynamical stability of systems: Potential energy diagram, Collisions: Impulse, conservation of energy and linear, momentum, Conservation of angular momentum and rotation of rigid bodies in plane Thermal Physics: Averages, probability and probability distributions, Thermal equilibrium and macroscopic variables, Pressure of an ideal gas from Newton’s laws - the kinetic theory of gases. Maxwell’s velocity distribution, Laws of Thermodynamics and the statistical origin of the second law of thermodynamics, Application of thermodynamics: Efficiency of heat engines and air-conditioners, Thermodynamics of batteries and rubber bands
PHY102
Introduction to Physics II
5.00
This is a continuation of PHY 101 and is meant for engineers and non-physics majors. The course will introduce students to Electricity and Magnetism, Maxwell’s equations, Light as an electromagnetic wave, and Wave optics.  Electrodynamics:  Vector calculus: Gradient, Divergence, Curl and fundamental theorems of vector calculus. Basic laws in electricity and magnetism, Classical image problem, displacement current and continuity equation, Maxwell’s Equations, electromagnetic wave equation and its propagation in free space, conducting media and dielectric medium, Poynting theorem, Electromagnetic spectrum.  Wave Optics:  Interference of light waves: Young’s double slit experiment, displacement of fringes, Interference in thin films  Diffraction: Fresnel’s and Fraunhofer’s class of diffraction, diffraction from single, double & N- Slits, Gratings.  Polarization: Concept of Polarization in electromagnetic waves, types of polarized waves.
PHY103
Fundamentals of Physics I
5.00
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
5.00
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
3.00
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
3.00
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.
PHY108
Physics For Life
4.00
It will provide an introduction to Newtonian mechanics, Fluids, Thermodynamics, Electricity & Magnetism and Wave Optics.  1. Introduction: Relation of Physics with other sciences, Estimation and Units, Dimensional analysis, Vector and scalar.  2. Mechanics: Newton’s laws of motion in one dimension, work & energy in one dimension, Motion in two dimensions, Momentum, Rotational motion.  3. Fluids: Ideal fluid, Viscous fluid, Surface tension  4. Thermodynamics: Temperature, laws of thermodynamics, entropy  5. Electricity & Magnetism: Electric force & field, Energy & potential, Magnetic force & field, Electromagnetic induction  6. Wave optics: Interference, diffraction, Diffraction gratings, Polarization
PHY201
Fundamentals of Thermal Physics
4.00
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
4.00
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
3.00
(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
3.00
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
4.00
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
4.00
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.
PHY207
Abridge course for Minor students
4.00
PHY207 is a bridge course specially designed for students who have already taken PHY101 and PHY102 instead of PHY103 and PHY104. The course supplements and develops their understanding of Newtonian physics and classical electromagnetism.  The content is as follows:  Review of Newtonian mechanics  Solving planetary motion using a personal computer A brief introduction to Lagrangian formulation of mechanics Review of simple harmonic motion Introduction to coupled oscillators and normal modes Introduction to special theory of relativity, space-time diagrams and four vectors Review of electrostatics and magnetostatics Review of Maxwell’s equation Wave equation from Maxwell’s equation, plane wave solution, polarization Light as an electromagnetic wave
PHY208
3.00
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.
PHY255
Introduction to Biophysics
3.00
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.
PHY301
Classical Mechanics
4.00
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
4.00
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
4.00
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
4.00
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
4.00
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
4.00
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
4.00
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
3.00
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.
PHY315
Particle and Nuclear Physics
3.00
Particle and Nuclear Physics
PHY409
Quantum Field Theory
3.00
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
3.00
This course introduces the experimental results and the theoretical concepts that lead to the formulation of the standard model of particle physics
PHY413
General Theory of Relativity
3.00
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.
PHY416
Soft Matter Physics
3.00
Soft Matter Physics
PHY417
Topics in Quantum Many Body Th
3.00
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
3.00
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.
PHY499
12.00
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.
PHY415
Non-linear dynamics
3.00
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.
PHY414
Computational and Numerical Analysis
3.00
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.
PHY412
Introduction to Experimental Techniques in Particle Physics
3.00
This course introduces the student to detectors, data analysis and other experimental techniques used in experimental particle physics.
PHY411
Classical Field theory and general relativity
3.00
The first part of this course reformulates classical electrodynamics as a field theory and the second part introduces general theory of relativity.
PHY408
3.00
This is an advanced course in condensed matter emphasizing the special properties of solids: magnetism, super fluidity and superconductivity, dielectrics and ferroelectrics.
PHY406
3.00
This course introduces a student to relativistic quantum mechanics. It includes The Dirac equation and an introduction to quantum electrodynamics.
PHY402
Classical Theory of Fields
3.00
This course has two parts. The first part reformulates classical electrodynamics as a field theory. The second part introduces general theory of relativity.
PHY547
3.00
PHY501
Classical Mechanics
3.00
Classical Mechanics
PHY502
Classical Dynamics
3.00
Classical Dynamics
PHY503
Quantum Mechanics
3.00
Quantum Mechanics
PHY505
States of Matter
3.00
States of Matter
PHY506
Rev. Classical Mechanics
1.50
Review of Classical Mechanics
PHY507
Rev. Statistical Mechanics
1.50
Review of Statistical Mechanics
PHY508
Rev. Quantum Mechanics
1.50
Review of Quantum Mechanics
PHY509
Rev. Classical Electrodynamics
1.50
Review of Classical Electrodynamics
PHY548
3.00
PHY550
Solid State Physics
3.00
This course covers the application of concepts of classical mechanics, electrodynamics, quantum mechanics and statistical physics to study properties and structure of matter (solids and liquids). It also aims to develop an understanding of behavior of applied materials.
PHY551
NanoMaterial and NanoPhysics
3.00
This is an interdisciplinary advanced level Ph.D. course in which various nanomaterials processing techniques, including chemical and physical vapor deposition, lithography, self-assembly, and ion implantation will be introduced. Tools commonly used to characterize nanomaterials will be introduced. The structural, mechanical, optical and electronic properties which arise due to nano-scale structure will be discussed from the point of view of nano-scale devices and application.
PHY557
Prob, Stat, Mat Th.& App
3.00
Probability, Statistics, Matrix Theory and Applications
PHY563
Comptnl. & Numerical Analysis
3.00
This course develops the basic programming skills to perform numerical analysis of various physical phenomenon by emphasizing on the algorithms and their implementation in the FORTRAN program language.
PHY568
Physics Of Semiconductor Materials And Devices
3.00
The course covers the electric polarization and their types, dipoles, frequency and temperature dependence of polarization, local field and Clausius-Mossotti equation, dielectric constant, loss and breakdown; Applications of high-k materials, ferroelectricity, pyroelectricity and piezoelectricity, electrical memory/hysteresis loop, fatigue testing, pyro and piezo coefficients; Shape Memory alloys: types, working, properties, manufacturing and applications.
PHY569
Complex Fluids
3.00
Complex Fluids
PHY572
Soft Matter Physics
3.00
Soft Matter Physics
PHY573
Characterization Of Materials
3.00
Characterization Of Materials
PHY574
Materials Characterization Techniques I
3.00
This course covers the basic interaction of matter with photons, elastic and non–elastic scatterings, characterization techniques: Ultra-violet photoelectron spectroscopy (UPS), Raman spectroscopy, Extended X-ray absorption fine structure (XAFS), X-ray fluorescence, Fourier transform infrared spectroscopy (FTIR), UV- Visible spectroscopy, Photoluminescence (PL), Electroluminescence (EL) and Cathode luminescence (CL).
PHY575
Characterization of Materials II
3.00
This course covers the basic interaction of matter with electrons, neutrons, ions, energetic particles, elastic and non–elastic scatterings, and characterization techniques: Optical microscopy, Transmission electron microscopy (TEM), Scanning electron microscopy (SEM), Scanning probe microscopy (SPM), Atomic force microscopy (AFM), X-ray diffraction, Energy dispersive X-ray analysis. X- Ray photoelectron spectroscopy (XPS), Secondary ion mass spectrometry (SIMS).
PHY578
Introduction to Thin Films
3.00
This course covers the crystals structure, defects, bonding, phase diagram, kinetics, diffusion, nucleation and growth, trapping, surface diffusion, growth models, vacuum techniques; thin film deposition techniques: thermal evaporation, e-beam evaporation, sputtering, molecular beam epitaxy, chemical vapor deposition, pulsed laser deposition; thin film properties: materials surface, structural, mechanical, optical, electrical, magnetic properties; thin film based devises and applications.
PHY599
Explorations in Research
3.00
Explorations in Research
PHY588
Fundamentals of Ion-Solid Interactions
3.00
Introduction to ion beam processes, ion implanter and applications, interatomic potential, Thomas-Fermi statistical model, classical two-particle scattering theory, differential scattering cross-section, energy-loss process in solid, Fermi-teller model, ZBL universal scattering function, ion range & distribution, Straggling, radiation damage in solid, Thermal spikes, Mono-Carlo simulation, diffusion in solid, sputtering, applications of ion beam, ordering-disordering, alloying, Hume-Rothery rules, ion-mixing, phase transition, doping semiconductors, location of dopants via Rutherford backscattering and ion channeling.
PHY566
Introduction to String Theory
3.00
The aim of this course is to introduce the basic concepts of string theory by applying quantum mechanics to a relativistic string. In this manner the student will deepen his or her understanding of quantum mechanics and will also be able to appreciate the diverse areas of physics in which the mathematical description of a string like object is useful.
PHY564
3.00
This course gives an introduction to various simulation techniques such as Monte Carlo, Classical Molecular Dynamics, Quantum Simulations: time-independent Schrödinger equation in one dimension (radial or linear equations); scattering from a spherical potential, Born approximation, bound state solutions; single particle time-dependent Schrödinger equations; Hartree-Fock theory: restricted and unrestricted theory applied to atoms; Schrödinger equation in a basis: matrix operations, variational principle, density functional theory, quantum molecular dynamics.
PHY562
Experimental Techniques in Particle Physics
3.00
This course is intended to give an in-depth study of detector, data analysis and other experimental techniques used in particle physics. Modern particle detectors such as micro-pattern gaseous detectors, drift chambers, silicon detectors, calorimeters, Cherenkov detectors and others are discussed along with advanced statistical methods and data analysis techniques to extract results.
PHY560
Particle Physics Phenomenology
3.00
Introduction, decay rates and cross Sections, the Dirac equation and spin, interaction by particle exchange, electron – positron annihilation, electron – proton scattering, deep inelastic scattering, symmetries and the quark model, QCD and color, V-A and the weak interaction, leptonic weak interactions, the CKM matrix and CP violation, electroweak unification and the W and Z, tests of the standard model, the Higgs Boson and beyond.
PHY556
Introduction to Quantum Field Theory
3.00
This course introduces the techniques of quantum field theory and its application to condensed matter physics and particle physics.
PHY554
3.00
This course covers the critical phenomena, Landau-Ginzburg theory of phase transition, renormalisation group, time-dependent phenomena in condensed matter, Correlation and response, Langevin theory, Fokker Plank and Smoluchowski equations, broken symmetry, hydrodynamics of simple fluids, stochastic models and dynamical critical phenomena, nucleation and spinodal decomposition, and topological defects.
PHY558
Semiconductor Physics and Devices
3.00