Physics is many things to many people. It is a doorway to some of the most beautiful and profound phenomena in the universe, e.g. black holes, supernovae, Bose-Einstein condensates, superconductors. It is a driver of lifestyle-changing technology, e.g. engines, electricity, and transistors. And it is a powerful way of perceiving and analysing problems that can be applied in various domains, both within and outside standard physics. The beauty and profundity of the phenomena studied by physicists offer romance and excite passion; the utility of its discoveries and the power of its methods arouse interest. These methods can be very intricate and demanding: theoretical physics requires a skilful combination of physical and mathematical thinking, and experimental physics requires some of this along with the ability to turn tentative ideas into physical devices that can put those ideas to the test. The successful practice of physics demands mathematical and mechanical adroitness, persistence, and great imagination. Fortunately, the physicist’s imagination is nourished not just by physics but also by other areas of human enquiry and thought, of the kind that an Ashoka undergraduate is expected to encounter.
With all of this in mind, the physics programme has been designed to: (i) allow students wishing to major in physics to discover real physics and make a wise choice, in the first two semesters; (ii) provide a thorough training in fundamental physics, in the following three semesters; and (iii) bring together everything learnt earlier, and give students the option to pursue more advanced courses in physics or branch out into other areas, in the final semester. The idea is to accompany those wishing to become professional physicists as they take the first steps in that direction, and to introduce everyone who goes through the programme to the physicist’s way of thinking.
Mathematical level: All theory courses are calculus-based. The level of mathematical sophistication will increase progressively. The mathematical-physics courses will be application-oriented rather than proof-oriented. A student should have studied Mathematics at the +2 level in school. Those who do not have the requisite mathematics training should take the mathematics Foundation Course and the Calculus course as early as possible.
Labs: All lab courses will involve extensive use of instruments to make observations. These experiments will in general illustrate ideas studied in the accompanying theory courses.
The use of computers: All theory courses will include computational exercises, generally using the programming language Python. Labs will also require the use of computers.
Theory courses: Two lectures a week each lasting 1.5 hours.
Laboratory courses: One 3-hour lab session per week (plus one optional 3-hour lab session for students to complete their work.)
Major, Minor, and Concentration
Students wishing to major, minor, or pursue a concentration in Physics are expected to take the introductory course in calculus (Calculus I) offered by the Mathematics Department. Students wishing to major in Physics should plan to take it in their first semester.
Number of courses required to major in physics: 15
100 credits (FCs + CCs + Major courses + other courses)
Of these, the 13 courses of the core curriculum are mandatory, and 2 electives may be chosen of those offered. Students are of course free to take as many of the electives as they wish.
Number of courses required to minor in physics: 6(24 credits)
Of these the two gateway courses – Mathematical Physics I: Mathematical and Computational Toolkit and Lab 1:An Introduction to Physics through Experiments – are compulsory.
At least two more courses should be taken from among the core courses offered in semesters 3, 4, and 5, provided appropriate prerequisites have been satisfied for these courses (recommended courses: Classical Mechanics and Thermal Physics).
The remaining two may be either other compulsory or elective courses offered by the Physics Department or cross-listed with Physics, provided appropriate prerequisites have been satisfied. In place of one elective course, a student may take an Independent Study Module (ISM) of equivalent credit.
Number of courses required for a concentration in physics: 4 (16 credits)
Of these the two gateway courses – Mathematical Physics I: Mathematical and Computational Toolkit and Lab 1:An Introduction to Physics through Experiments – are compulsory.
At least two more courses should be taken from among the core courses offered in semesters 3, 4, and 5, provided appropriate prerequisites have been satisfied for these courses (recommended courses: Classical Mechanics and Thermal Physics)
Semesters 1 and 2: Discovering College-level Physics
Students wishing to major in physics are expected to take, in the first semester, the introductory course in calculus offered by the Mathematics Department.
The physics-major sequence begins in semester 2, with two courses, one in theoretical physics and the other in experimental physics. The first purpose of these courses is to provide an experience of college-level physics on the basis of which a student can decide whether or not to major in physics, i.e. they are gateway courses. The second purpose of these courses is to serve as an introduction to the physicist’s way of thinking about problems and solving them, something that has proved useful not just to physicists but also to those in other disciplines that make use of quantitative methods and experiments, e.g. mathematics, computer science, economics, psychology, and biology.
Semesters 3, 4, and 5: The Physics Core
The physics courses in semesters 3, 4, and 5 form the core of the physicist’s undergraduate canon: Mathematical Physics II, Classical Mechanics, Electricity & Magnetism in Light of Relativity, Thermal & Statistical Physics, Oscillations, Waves & Optics, Quantum Mechanics I, and Statistical Mechanics, and three accompanying labs. Anyone majoring in physics is expected to be thorough in these areas.
Semester 6: Choosing a Direction and Bringing Physics Together
In semester 6 there will one required course that bring together all the physics learnt in earlier semesters, so that the student leaves with a view of physics as an integrated subject: The Physics of Matter. In addition there will be one more elective course.
Recommended Additional Courses:
Linear Algebra, offered by the Department of Mathematics.
This course aims to familiarise the student with a variety of mathematical techniques which every student of physics should be conversant with. Having taken the course you should be comfortable with casting a wide variety of physics problems in mathematical language and being able to analyse and solve them subsequently. The course will also include an introduction to programming with Python. Within the physics curriculum at Ashoka university, this course is an essential prerequisite for Classical Mechanics and Electricity and Magnetism in Light of Relativity offered in the third semester.
Recommended course content: Brief review of basic calculus: Differentiation and integration, derivative as a rate of change, setting up a differential equation for physical problems. Taylor series. Basic ideas of vector spaces and linear algebra: Eigenvalues and eigenvectors. Characteristic equation, completeness and orthonormality. Functions of more than one variable: Basic idea of partial derivatives. Line, surface, and volume integrals. Vector Analysis: Gradient, Divergence and Curl, Differential Vector identities. Applications to Electromagnetism.
Pre-requisites: Students who have not done mathematics at the 12th-grade level are required to take Calculus I.
Taught at the level of:Basic Multivariable Calculus (J E Marsden, A Tromba, and A Weinstein), Vector Analysis (M Spiegel, M Lipschutz), Mathematical Methods for Scientists & Engineers (D A McQuarrie).
PHY1010 – Physics Lab I: An Introduction to Physics through Experiments
The goal of this introductory lab is to help students develop the skills needed for experimental physics. Students will be introduced to the basic concepts of data collection, analysis, and interpretation over the span of the course by working on different experimental problems which have been carefully selected to represent different branches of physics.
Graphing data and describing the relationships between quantities both in one's own words and in terms of the mathematical relationship between the variables is essential. The distinction between experimental uncertainties and mistakes in reading or recording information will be stressed, to highlight the possibilities and the limitations of the process of measurement.
PHY2210 – Classical Mechanics
Newtonian mechanics and an introduction to Lagrangian and Hamiltonian mechanics. Newtonian mechanics is, both historically and otherwise, the starting point of all of physics. The Lagrangian and Hamiltonian formulations of classical mechanics allow a more profound vision of the subject while also introducing the language in which much of higher-level theoretical physics is expressed.
Recommended course content: Frames of reference and Galilean relativity. Newton’s laws. Momentum. Work and Energy. Collisions. The harmonic oscillator. Rotation and angular momentum. Central-force motion. The principle of least action. Introduction to the calculus of variations. Lagrangian mechanics. Non-inertial frames of reference. Hamiltonian mechanics and phase space.
Pre-requisites: Mathematical Physics I (Mathematical & Computational Toolkit).
Taught at the level of:Classical Mechanics (D Gregory), Classical Dynamics of Particles and Systems (S T Thornton and J B Marion).
PHY2310 – Electricity & Magnetism in Light of Relativity
The beautiful theory of electricity and magnetism is, with classical mechanics, the heart of classical physics. What is often not appreciated at the undergraduate level is that electricity and magnetism are related in a way that reveals the structure of space-time. In this course relativity will be used from the beginning to relate electric and magnetic fields, so that their unity, as components of the electromagnetic field are revealed and used in the study of Maxwell’s Equations.
Recommended course content: Frames of reference and Einsteinian relativity. Charge. Lorentz invariance of charge and its consequences. Electrostatics. Conductors. Electric currents and magnetic fields. Electromagnetic induction. Maxwell’s equations. The potential formulation. Transformation of Maxwell’s equations between inertial frames. The idea of the electromagnetic field tensor. Electric and magnetic fields in various media.
Pre-requisites:Mathematical Physics I (Mathematical and Computational Toolkit).
Taught at the level of:Introduction to Electrodynamics (D J Griffiths), Electricity & Magnetism (E M Purcell).
PHY2010 – Physics Lab II: Classical Mechanics and Electromagnetism
Designed to accompany the theory courses Classical Mechanics and Electricity & Magnetism in Light of Relativity, this laboratory course explores their experimental foundations.
Students will be introduced to video-analysis and modelling to study elastic and inelastic collisions, uniformly accelerated motion, and terminal velocity. In addition, students will also be introduced to physical systems exhibiting electromagnetic damping, resonant electronics circuits, and two-dimensional electrostatics.
Pre-requisites:Physics Lab I.
PHY2110 – Mathematical Physics II
This mathematical physics course aims to be an introduction to differential equations. Besides standard topics in ordinary and partial differential equations, nonlinear dynamical systems will be studied and nonlinear ODEs will be analysed using geometric and computational tools.
Recommended course content:
Ordinary differential equations: First order equations, integrating factors. Second order equations. Frobenius and other methods, singular points. Special Functions (Legendre, Bessel, Hermite, Laguerre). Fourier series. Partial differential equations: Laplace’s equation, classical wave equation, diffusion equation. Dynamical systems: Nonlinear ODEs. Flows and vector fields, phase space analysis.
Pre-requisites:Mathematical Physics I (Mathematical & Computational Toolkit).
Taught at the level of:Differential Equations with Applications and Historical Notes (G F Simmons), Nonlinear Dynamics and Chaos (S Strogatz).
PHY2410 – Oscillations, Waves & Optics
Oscillatory phenomena appear in all areas of physics, both classical and quantum (to the point where a famous textbook begins by saying that the domain of physics is all phenomena that can be reduced to coupled oscillators). The methods used to study oscillatory motion are powerful and wide-ranging in their utility.
Recommended course content: The harmonic oscillator. Coupled oscillators. Oscillations of a string and of a circular drum-skin. Sounds waves in solids, liquids, and gases. Torsional oscillations. Doppler effect for sound waves. Wave-fronts and rays. Beats. Phase and group velocities. Pulses and wave packets. Dispersion relations. Waves in dispersive systems. Electromagnetic waves in vacuum, dielectric media, conductors, and plasmas. Doppler effect for light. Fresnel’s laws of reflection and refraction. Classical optics: interference, and Fraunhofer and Fresnel diffraction. Lasers. Optical devices: prisms; lenses; mirrors; telescopes; microscopes; diffraction gratings.
Pre-requisites:Classical Mechanics and Electricity & Magnetism in Light of Relativity.
Taught at the level of:Waves (F S Crawford), Introduction to Electrodynamics (D J Griffiths).
PHY2610 – Thermal Physics
An integrated approach to thermodynamics, kinetic theory, and basic statistical mechanics. Physical quantities like temperature, entropy, and free energy, and phenomena like heat flow make sense only in systems with large numbers of particles. The basic methods used to study such systems will be established in this course. This course will also be useful to biology majors; the mathematical pre-requisites have been adjusted accordingly.
Recommended course content: Thermal equilibrium. The first law. Ideal gas. Transport phenomena. The second law. The Carnot engine. Thermodynamic identities. Helmholtz and Gibbs free energies. Chemical potential. Phase transformations. Boltzmann statistics. Random walks and Brownian motion.
Pre-requisites: Non-physics majors are required to take Calculus I. Physics majors are required to take Mathematical Physics I (Mathematical & Computational Toolkit).
Taught at the level of:An Introduction to Thermal Physics (D Schroeder), Concepts in Thermal Physics (S J Blundell and K M Blundell).
Designed to accompany the theory courses Thermal Physics and Oscillations, Waves & Optics, this laboratory course explores their experimental foundations.
Students will be introduced to the properties of light as a wave: interference, diffraction, and polarisation, through conceptually rich experiments like the Michelson Interferometer. In addition, mechanical systems which exhibit oscillatory behaviour, like coupled pendula and capillary waves, will also be studied. Students will also be introduced to ideas of thermometry and calibration.
Pre-requisites:Physics Lab I.
PHY3510 – Quantum Mechanics
This course is an introduction to Quantum Mechanics (QM). Starting with a historical introduction and motivation, it goes on to introduce probability amplitudes as the fundamental physical basis for QM. Using the Dirac bra-ket notation, the fundamental postulates are then introduced and their consequences worked out. The basic physical concepts are illustrated through spin-½ systems and one-dimensional wave mechanics. Symmetries and Conservation laws in QM are discussed, an introduction to the basic theory of angular momentum and spin is given, and the course culminates with the first major triumph of QM - a quantum mechanical understanding of the hydrogen atom.
Recommended course content: Review of linear algebra in the context of QM. Postulates. Uncertainty Principle. Ehrenfest Theorem. Wave mechanics in one dimension. The one-dimensional harmonic oscillator. Symmetries, angular momentum. Spin-½ systems, Stern-Gerlach experiments. Hydrogen Atom
Pre-requisites:Classical Mechanics, Mathematical Physics II
Strongly recommended:Linear Algebra (Department of Mathematics).
Taught at the level of:Principles of Quantum Mechanics (R Shankar), Introduction to Quantum Mechanics (D J Griffiths).
PHY3610 – Statistical Mechanics
Statistical mechanics allows one to solve problems involving large numbers of particles by exploiting statistical regularities. When combined with quantum mechanics, it helps physicists to understand some of the most fascinating phenomena in the universe.
Recommended course content: Classical statistical physics. Classical theory of radiation. Quantum theory of radiation. Quantum statistical physics: Fermi-Dirac and Bose-Einstein distributions. Applications.
Pre-requisites:Thermal & Statistical Physics.
Taught at the level of:Fundamentals of Statistical and Thermal Physics (F Reif).
Designed to accompany the two theory courses Quantum Mechanics and Statistical Mechanics, this laboratory course explores their experimental foundations.
Students will be introduced to some of the experiments which required Quantum Mechanics in order to be explained, notably discrete atomic spectra and the Zeeman Effect. The lab will also contain experiments on Brownian Motion and the determination of other properties of matter like magnetic susceptibility.
Pre-requisites:Physics Lab I.
PHY3710 – The Physics of Matter
In real physical systems the various areas of fundamental physics that are studied separately in semesters 3-5 are usually required all at once. The purpose of this course is to show how fundamental physics can be used to study a number of interesting phenomena.
Recommended course content: Elastic properties of solids. Crystals and band structure. Semiconductors, insulators, and conductors. Electronic devices. Superconductivity. Glasses and amorphous materials. Liquids. Colloids. Polymers. Bose-Einstein condensation. The Chandrasekhar mass limit: white-dwarf and neutron stars.
Pre-requisites: All mandatory courses in the physics-major sequence.
PHY3150/PHY6150 – Computational Physics
This course focuses on developing an algorithmic approach to problem solving, and on the translation of algorithms to working computer codes. The course starts from the basics of computations and errors, and then discusses both deterministic problems and those involving random numbers, like Monte Carlo.
Taught at the level of:Computational Physics: Problem Solving with Computers (R H Landau, M J Paez, and C C Bordeianu), Numerical Recipes: The Art of Scientific Computing (W H Press, S A Teukolsky, W T Vetterling, B P Flannery).
PHY3520 – Quantum Mechanics II
A second course in quantum mechanics is advisable for those wishing to pursue theoretical physics.
Recommended course content:
Many particle systems and identical particles: fermions and bosons. Approximation methods: Variational method, WKB, Time-independent and time-dependent perturbation theory: Stark and Zeeman effect. Adiabatic approximation. Theory of Angular Momentum in more detail than in the previous QM course. Addition of Angular Momenta, Hydrogen atom fine structure. Scatttering Theory: Born approximation, partial wave analysis.
Pre-requisites:Quantum Mechanics I.
PHY3110 – Mathematical Physics III
This mathematical physics course will develop the use of complex analysis in physics. It will develop the subject from an application point of view, and discuss its applications in Fourier transforms, Laplace transforms, Green's functions, differential equations, special functions, etc. It will be useful for those wishing to pursue theoretical physics.
Pre-requisites:Mathematical Physics I (Mathematical and Computational Toolkit) and Mathematical Physics II.
Taught at the level of: To be decided.
PHY4720/PHY6720 – Soft-Matter Physics
The course will provide a birds-eye view of soft matter physics, concentrating on physical ideas and building up the mathematical description. Examples will include: Polymers: DNA, proteins, plastics, fabrics; Gels: jelly, rubber; Suspensions/Dispersions (one phase in another): river water, blood; Surfactant solutions: detergents, shampoos; Emulsions and foams: paint, shaving cream; Liquid crystals: displays; Greases, pastes, powders, granular media; Colloids (suspensions of small particles in a medium): Milk; Membranes: Cell membranes and Magnetorheological fluids.
Pre-requisites: Statistical mechanics
The aim of cosmology is to apply laws of physics to the universe as a whole. Observations tells us that the universe is neither eternal nor static, and therefore it raises questions as to when and how did the universe start? What did it look like in the past? How will it evolve in the future? Aim of this course is to use all the physics that you have learned as an undergraduate to try and answer these questions.
The student will have a fairly deep understanding the origin and evolution of the universe, and will be exposed to the outstanding unsolved problems.
In absence of any general framework (no non-equilibrium analogue of entropy), there are several broad approaches to study non-equilibrium systems. This course will discuss these general approaches like Langevin equation, Fokker-Planck formalism, Martin-Siggia-Rose field theory, master equation, Boltzmann equation, and hydrodynamics. Some of the well-established results like the fluctuation-dissipation theorem, linear response theory, etc., will also be covered. Time permitting, a few specific model systems will be discussed, especially to introduce the idea of the renormalization group.
Reif, Fundamentals of statistical and thermal physics
Chaikin-Lubensky: Principles of condensed matter physics
V Balakrishnan, Langevin equation
G Mazenko, Nonequilibrium statistical mechanics
PHY-6150/4150 - Symmetry in Physics: Lie algebras, groups and representations
This graduate level course will focus on the physics of symmetry using the mathematics of group theory and representation theory. Symmetry is a fundamental concept throughout physics, be it particle physics and field theory, condensed matter physics, cosmology, quantum mechanics/quantum information or atomic and molecular physics.
The basic concepts of geometrical symmetry, finite groups and their representations will be covered. A physically oriented introduction will be given to Lie algebras and Lie groups and their representations. The emphasis throughout will be on the particular rather than the general. Familiar concepts from quantum mechanics will be used repeatedly - for example, the hydrogen atom spectrum and its symmetries will arise repeatedly during the study of Lie groups. Rather than develop the general theory of semi-simple compact Lie groups, the important concepts will be illustrated through particular examples. For example, the groups SO(2), SO(3), SU(2), SU(3) etc. as they arise in physics and their unique and distinctive features and representations.
Pre-requisites: Quantum Mechanics
References: Group theory in a nutshell for physicists, by A. Zee
Group Theory and Physics, S. Sternberg
Shattered Symmetry, by P. Thyssen and A. Ceulemans, Quantum Mechanics: Symmetries, by W. Greiner
Cross-Listed Elective Courses
PHY1001/ MAT1001: Linear Algebra (cross-listed with Department of Mathematics)
PHY3513/ PHY6313/ BIO3513/ BIO6313: Computational and Mathematical Biology (cross-listed with the Department of Biology)
PHY301/ BIO211: Biophysics (cross-listed with the Department of Biology)
PHY3020/ BIO3020: Ecology (cross-listed with the Department of Biology)
PHY3314/BIO3314: Forces and Motion in Biology (cross-listed with the Department of Biology)
PHY1208/ CS1208: Probability and Statistics (cross-listed with the Department of Computer Science)
PHY1101/ CS1101: Introduction to Programming (cross-listed with the Department of Computer Science)
PHY1390/ CS1390: Introduction to Machine Learning (cross-listed with the Department of Computer Science)
PHY3901/ ES3901: Remote Sensing(cross-listed with the Department of Environmental Studies)
Critical Thinking Seminars
CT165 – Order-of-Magnitude Physics
Order-of-Magntiude Physics is a Critical Thinking Seminar in which simple examples will be used to illustrate the conceptual lenses through which a typical physicist looks at phenomena and the associations that arise naturally in her mind when she does that. In other words, students will learn to see the world through the eye of a physicist.
Students will be encouraged not to remember what they know but to re-examine it. A little knowledge of physics and mathematics may be helpful, but too much knowledge is likely to be a hindrance. Students will be required to solve problems and make presentations in the class.
Information for the Physics ASP
The fourth year ASP provides the opportunity for students to study physics at a level more advanced than the usual undergraduate level. Alternatively, students wishing to broaden their education further can use it to take a minor/concentration in any other subject or simply take whatever courses in any department they wish to.
The advanced major is for students intending to pursue higher studies and research in physics. It would enable them to take some advanced physics courses as well as get an idea of research through the capstone project/thesis.
Students are required to take 16 credits in the 7th semester of which the capstone project comprises 8 credits. Likewise in the 8th semester, they take 16 credits with the capstone thesis comprising 8 credits. Over the whole year (2 semesters), it is recommended that they take 2 physics electives (8 credits) . Two courses (8 credits) may be taken from outside the department.
Capstone Project and Thesis
Interested students should talk to prospective advisors about possible projects in their 6th semester. After mutual agreement - the advisor agrees to guide the student and the student agrees to work on one of the projects suggested by the advisor - students should start with necessary background reading / preliminary work over the summer before the start of the fourth year.
At the end of the 7th semester the project would be assessed with a presentation and report - this will be evaluated by the physics faculty. Students without satisfactory progress at this stage may not continue for the thesis subsequently.
At the end of the 8th semester the thesis has to be submitted and defended before a panel which may also include some external members. It is mandatory to successfully complete the capstone project and thesis to be eligible for the advanced major.
Other Options (Minor/Concentration)
Students not opting for the advanced major can take courses as per their interest in the fourth year. It is recommended that physics majors take two physics electives over the year. Those minoring in physics (or taking it as a concentration) may take physics courses accordingly to meet the necessary requirements.
PhD in the Physics Department
The Department of Physics at Ashoka University invites applications for its PhD program, starting in the spring semester (January) 2021. Currently, we invite applications only in experimental soft-condensed matter physics. The Department's work in this area is described in more detail in the faculty profiles listed below.
The Ashoka Physics Journal is an initiative started by the Physics Society and is a joint effort by both students majoring in physics and other departments. They were ably supported by the professors of the physics department in this endeavour. This journal is a small attempt by the students to provide glimpses of just how exciting the field of physics can be and also to popularise physics across various disciplines.