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.
Student wishing to major in physics are required to take, in the first semester, the introductory course in calculus (Calculus I) offered by the Mathematics Department. In addition they may consider taking the foundation course Quantitative Reasoning & Mathematical Thinking. These courses will introduce the student to the kind of thinking that is expected in physics, but without the full mathematical and experimental accouterments of the compulsory courses in the major sequence.
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.
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 and Optics, Quantum Mechanics I, and Statistical Mechanics, and three accompanying labs. Anyone majoring in physics is expected to be thorough in these areas.
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.
Number of courses required for a major in physics: 15 (13 mandatory and 2 elective). Students are of course free to take as many of the electives as they wish.
Recommended Additional Courses:
Introduction to Programming, offered by the Department of Computer Science.
Calculus II: Multivariable Calculus, offered by the Department of Mathematics.
Probability & Statistics, offered by the Department of Computer Science.
Linear Algebra, offered by the Department of Mathematics.
To minor in physics a student must do six courses in physics. Of these the two gateway courses – Mathematical and Computational Toolkit and Introduction to Physics Through Experiments – are compulsory. At least two more courses should be taken from among the compulsory courses offered in semesters 3, 4, and 5. The remaining two may be either other compulsory courses offered or elective courses offered by the Physics Department or cross-listed with Physics.
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.
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.
Duration - Theory: two lectures a week each lasting 1.5 hours. Lab: one 3-hour lab session per week (plus lab time available for students to complete their work.)
Mathematical Physics I: Mathematical & Computational Toolkit
The purpose of this course is to prepare students for Classical Mechanics and Electricity & Magnetism in Light of Relativity, and through this process to introduce them to the conversation between mathematics and physical ideas that is called theoretical physics.
Recommended course content: Functions. Integration and differential in physical settings. Taylor series. Awareness of dimensions, time-scales, length-scales, etc in equations. Setting up Newton’s second law as a differential equation. First- and second-order ordinary differential equations with constant coefficients. Numerical methods for solving differential equations. Systems of equations and matrix methods. The idea of a partial differential equation. Functions of more than one variable. Scalar and vector fields. Vector analysis. Introduction to four-vectors in Minkowski space.
Pre-requisite: Calculus I.
References: Mathematical Tools for Physics, by J Nearing, Basic Training in Mathematics: A Fitness Program for Science Students, by R Shankar, Introduction to Electrodynamics, by D J Griffiths, and Vector Analysis, by M Spiegel and M Lipschutz.
Physics Lab I: Introduction to Physics through Experiments
The idea behind this course is to help students, using simple and interesting experiments, to acquire the skills, protocols, and attitudes required to perform and design experiments and to analyze observations successfully, so that they become a part of his/her mind-set.
Pre-requisite: none.
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-requisite: Mathematical & Computational Toolkit.
References: Classical Mechanics, by J R Taylor, Introduction to Classical Mechanics: With Problems and Solutions, by D Morin, An Introduction to Mechanics, by D Kleppner and R J Kolenkow, Classical Mechanics: the Theoretical Minimum, by L Susskind and G Hrabovsky; The Feynman Lectures in Physics vol 1, by R Feynman.
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-requisite: Mathematical and Computational Toolkit.
References: Electricity & Magnetism, by E M Purcell, Principles of Electrodynamics, by M Schwartz, Introduction to Electrodynamics, by D J Griffiths, and The Feynman Lectures in Physics vol 2, by R Feynman.
Physics Lab II
Experiments in classical mechanics and electricity & magnetism.
Pre-requisite: Physics Lab I.
Mathematical Physics II
The course continues with the laying the mathematical foundation of theoretical physics.
Recommended course content: Ordinary differential equations: Frobenius and other methods. Fourier series, Legendre, Laguerre, and Hermite polynomials, Bessel Functions. Beta and Gamma functions. Partial differential equations: Laplace’s equation, classical wave equation, diffusion equation. Fourier and Laplace transforms. Introduction to vector spaces for quantum mechanics.
Pre-requisite: Mathematical & Computational Toolkit.
References: Mathematical Tools for Physics, by J Nearing, Basic Training in Mathematics: A Fitness Program for Science Students, by R Shankar, Physical Mathematics, by Kevin Cahill, Introduction to Electrodynamics, by D J Griffiths, and Complex Variables and Applications, by J W Brown and R V Chruchill.
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 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.
References: Waves, by F S Crawford, Waves and Oscillations, by R Fitzpatrick, Introduction to Electrodynamics, by D J Griffiths, Optics, by E Hecht, and Principles of Optics, by E Wolf and M Born.
Thermal & Statistical 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 transformation. Boltzmann statistics. Micro-canonical and canonical ensemble. Random walks and Brownian motion.
Pre-requisite: Calculus I; some understanding of partial derivatives would be useful.
References: An Introduction to Thermal Physics, by D Schroeder, Concepts in Thermal Physics, by S J Blundell and K M Blundell, Statistical and Thermal Physics: with Computer Applications, H Gould and J Tobochnik, Entropy, Order Parameters and Complexity, by J P Sethna, and Elements of Non-equilibrium Statistical Mechanics, by V Balakrishnan.
Physics Lab III
Experiments in oscillations, waves, optics, Brownian motion, heat.
Pre-requisite: Physics Lab I.
Quantum Mechanics I
There are several approaches to teaching quantum mechanics at the undergraduate level. In this course a modern approach using vector spaces and spin-½ particles will be followed. This approach takes one straight to the heart of the quantum conundrum and reveals the subject it all its extraordinariness, without in any way being inaccessible to those who some training in linear algebra and partial differential equations.
Recommended course content: Review of linear algebra in the context of QM. Stern-Gerlach experiments. Basis. Angular momentum. Time evolution. A system of two spin-½ particles. Wave mechanics in one dimension. The one-dimensional harmonic oscillator.
Pre-requisite: Mathematical Physics II; it is strongly recommended that students take Linear Algebra, offered by the Department of Mathematics, before enrolling for this course.
References: A Modern Approach to Quantum Mechanics, by J Townsend, Quantum Mechanics, by L Susskind, and Principles of Quantum Mechanics, by R Shankar.
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-requisite: Thermal & Statistical Physics.
References: Fundamentals of Statistical and Thermal Physics, by F Reif, Statistical Physics, by L D Landau and E M Lifshitz, Statistical and Thermal Physics: with Computer Applications, H Gould and J Tobochnik, and Entropy, Order Parameters and Complexity, by J P Sethna.
Physics Lab IV
Experiments on electronics and the properties of matter.
Pre-requisite: Physics Lab I.
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.
Mathematical Physics III
Complex analysis in physics. Integral transforms. Green’s functions. Introduction to tensor analysis and group theory in physics. Pre-requisite: Mathematical Physics II.
References: Mathematics for Physics by M Stone and P Goldbart, Mathematical Methods for Physicists by G B Arfken, Physical Mathematics, by Kevin Cahill, Complex Variables and Applications, by J W Brown and R V Chruchill, and Mathematics for Physicists by P Dennery and A Krzywicki.
Quantum Mechanics II
A second course each in quantum mechanics is advisable for those wishing to pursue theoretical physics. Pre-requisite: Quantum Mechanics I.
Recommended course content: Review of basic quantum mechanics. Translational and rotational symmetry in the two-body problem. Bound states in central potentials. Time-independent perturbations.
Advanced Classical Mechanics & Electrodynamics
A second course each in classical mechanics and electrodynamics is advisable for those wishing to pursue theoretical physics. This course will be divided between advanced classical mechanics and electrodynamics and explore unifying principles.
Pre-requisite: Classical Mechanics, Electricity & Magnetism in Light of Relativity, and Mathematical Physics II.
Recommended course content: Review of Lagrangian and Hamiltonian mechanics. Canonical transformations. The Hamilton-Jacobi equation. Lagrangian mechanics for continuous systems.
The tensor formulation of Maxwell’s equations. Energy and momentum in the electromagnetic field. Transmission of electromagnetic waves in waveguides. Radiation by accelerated charges. The Lagrangian for the electromagnetic field.
The Physics of Einstein’s Miraculous Year
This course will be based on the papers published by Einstein in 1905. In that year he proposed the special theory of relativity (using Maxwell’s Equations); used the phenomenon of Brownian motion to place the atomic hypothesis on a firm foundation and, at the same time, derived the first fluctuation-dissipation relation; and explained the photoelectric effect using Planck’s new idea of the quantum of light. Einstein’s papers should be entirely within reach for anyone who has done the mandatory physics courses at Ashoka.
Pre-requisites: Mathematical and Computational Toolkit, and Electricity & Magnetism in Light of Relativity.
Astrophysics & Cosmology
To be decided.
Biophysics
To be decided.
Electronics & Instrumentation
To be decided.
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