Details of PH3106 (Autumn 2013)
| Level: 3 | Type: Project | Credits: 3.0 |
| Course Code | Course Name | Instructor(s) |
|---|---|---|
| PH3106 | Reading Course | Prasanta K. Panigrahi |
| Syllabus |
|---|
| The Reading Course(s) for the 1st year IPhD students in Physics are aimed at the basics (on topics such as Quantum Mechanics, Statistical Mechanics, Classical Mechanics, Mathematical Methods in Physics etc) of the subject.
The level of the course is expected to be comparable to the level of 1st year IPhD core courses (3rd year BS-MS) or may be slightly advanced depending on the exposure and aptitude of the student. This semester (Aut13) the following faculty are offering Reading Courses (please contact the faculty member in person to decide on the topic): Ananda Dasgupta Subhasis Sinha Siddhartha Lal Rumi De Bhavtosh Bansal Narayan Banerjee Prasanta K. Panigrahi Dibyandu Nandi Rajesh Kumble Nayak Nirmalya Ghosh The syllabus(es): SUBHASIS SINHA: Approximation methods and applications of Quantum Mechanics Syllabus: 1. Creation annihilation operators of harmonic oscillator, coherent state, time evolution, number states, classical phase space description and classical fields in terms of coherent states, application: atom photon interaction and Jaynes Cummings model. 2. Semiclassical methods: WKB methods for 1d potential, Tunneling through a barrier, decay rate, alpha decay, tunneling in double well potential, eikonal approximation. 3. Semiclassical methods for many particle systems (non interacting): Thomas -Fermi method, semiclassical density of states, Wigner-Kirkwood expansion and extended Thomas-Fermi method, Applications: atoms, nuclear shell model, quantum dot. 4. Time dependent perturbation theory, interaction picture, time dependent variational methods Applications: two level systems, collective oscillations of nuclear models and trapped Bose-Einstein condensates, free expansion of condensate. 5. Path integral method: Free particle and harmonic oscillator References: Quantum Mechanics (Landau Lifshitz), Qualitative methods in Quantum theory (A. B. Migdal), practical quantum mechanics (S Flugge), Quantum Optics (D F Walls and G J Milburn) RUMI DE: Topic: Random walk and Diffusion Processes Syllabus: Probability distribution, random walk in 1D, 2D and 3D; Microscopic theory of diffusion, Fick's 1st and 2nd law; Diffusion to capture - probability and mean time to capture; Biased random walk, diffusion with drift- viscous drag, sedimentation; Diffusion-reaction systems and its application in pattern formation. stochastic processes Reference book: 1. Random walks in biology by H. Berg 2. Books on pattern formation and nonlinear dynamics 3. Stochastic processes in physics and chemistry by Van Kampen NARAYAN BANERJEE: Course Title: Elements of Differential Geometry Syllabus: 1. Elementary ideas: Open sets, topological spaces, mappings 2. Differentiable manifold: coordinates on manifolds, examples of manifolds, homeomorphism, diffeomorphism. 3. Differential forms: vectors, tangent spaces, tangent bundle. 1-forms, tensors, Lie derivative; wedge product; p-forms and p-vectors; Exterior derivative. Metric on a manifold; volume form 4. Examples of some applications: Lagrangian and Hamiltonian systems; thermodynamics; electrodynamics **5. Smooth maps: Pull back; Isometries and conformal maps. Suggested text: Geometrical Methods of Mathematical Physics: Bernard Schutz |
| References |
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| Suggested by the instructor. |
Course Credit Options
| Sl. No. | Programme | Semester No | Course Choice |
|---|---|---|---|
| 1 | IP | 1 | Elective |
| 2 | IP | 3 | Not Allowed |
| 3 | MS | 5 | Not Allowed |
| 4 | RS | 1 | Not Allowed |