Semester: Jan-April, 2026
Course Description: This is a 3-credit elective course. The course begins with discussions of electromagnetic radiation, flux, luminosity, specific intensity, luminosity distance, angular diameter distance, Hubble expansion, FLRW cosmology, cosmological redshift, Type Ia supernovae, and the origin and properties of the Cosmic Microwave Background (CMB), including recombination and photon decoupling. The syllabus then introduces the major radiative processes in astrophysics, including Thomson scattering, synchrotron radiation, bremsstrahlung radiation, the photoelectric effect, inverse Compton scattering, and radiative transfer theory involving absorption, emission, scattering, optical depth, source functions, and formal solutions of the transfer equation. A major component of the course focuses on cosmic rays, including their discovery, composition, primary and secondary cosmic rays, transport equations, cosmic-ray spectra, acceleration mechanisms, supernova remnants as sources of Galactic cosmic rays, solar modulation, and ultra-high-energy cosmic rays together with the GZK cutoff. The course also introduces neutrino oscillations and the MSW effect, followed by an introduction to dark matter and the Galactic Center Excess. In addition, the course includes computational components using CRPropa and project-based explorations of contemporary problems in astroparticle physics.
Semester: Jan-April, 2026
Course Description: This is a 3-credit course offered to Btech 2nd year Students. This course introduces the mathematical structure and physical foundations of quantum mechanics using the language of Hilbert spaces, linear operators, orthonormal bases, and wavefunctions. The course begins with the postulates of quantum mechanics, state vectors, observables as Hermitian operators, projection operators, measurement theory, Born probability interpretation, expectation values, uncertainty relations, and the Schrödinger equation in both abstract Hilbert-space and position-space formulations. The formalism of basis transformations, momentum as the generator of translations, momentum-space wavefunctions, and completeness relations is developed in detail. Applications of the formalism include free particles, plane waves, Gaussian wave packets, probability current and continuity equation, infinite and finite square wells, stationary states, quantum superposition, time evolution of wave packets, scattering from finite potentials, transmission and reflection coefficients, and bound states in finite wells. The course further covers the quantum harmonic oscillator, angular momentum algebra, central potentials, the hydrogen atom, spin-1/2 systems, particles in weak magnetic fields, spin precession, two-level systems, and Rabi oscillations. Additional topics include symmetry, degeneracy, parity, normalization of bound and scattering states, and the physical interpretation of quantum dynamics and measurements.
Semester: July-Nov, 2025
Course Description: This is a 3-credit Lab course offered to Btech 4th year Students.
Course Description: This is a 3-credit course offered to first-year PhD students, serving as a comprehensive review of key topics in quantum mechanics. The course covers the following topics: 1. Bound state solutions of the hydrogen atom 2. Theory of angular momentum: - Clebsch-Gordan coefficients - Wigner-Eckart theorem 3. Time-independent perturbation theory: - Applications to the harmonic oscillator - Stark effect - Zeeman effect 4. Time-dependent perturbation theory: - Rabi oscillations - Fermi's golden rule - Ionization, absorption, and emission processes 5. Scattering theory: - T-matrix formalism - Lippmann-Schwinger equation - Born approximation - Partial wave analysis - Scattering states of the hydrogen atom 6. Relativistic quantum mechanics: - Klein-Gordon equation - Scalar field theory.