Aug-Dec 2020

Course description:

• Mathematical preliminaries of quantum mechanics: Linear Algebra; Hilbert spaces (states and operators).
• Heisenberg and Schrodinger pictures.
• Symmetries: Role of symmetries and types (space-time and internal, discrete and continuous); Symmetries and quantum numbers; Simple examples of symmetry (Translation, parity, time-reversal); Rotations and representation theory of Angular momentum; Creation and annihilation operator formalism for a simple harmonic oscillator.
• Perturbation Theory
• Scattering

We will also study some additional topics, including some elements of quantum information theory.

Textbook:

Modern Quantum Mechanics by Sakurai.

Evaluation: 

The grading would be done on the basis of the following weightage :

• Assignments (every other week approximately): 50%  

⇒ ONLY students who are crediting need to submit the assignments. Those who are auditing should be present in the tutorials and join the discussions to make sure that they have done the calculations correctly for the assignments.

⇒ Delay in submission: Delay in the submission of the assignment beyond the deadline would attract a penalty of 10% per day unless due to exceptional circumstances with prior knowledge of the TA and/or Instructor. No assignment will be accepted after the corresponding tutorial has been conducted by the TAs.   

⇒ Collaborations in assignments: You are encouraged to discuss with your classmates, but not copy. Any signatures of copying will be penalised by putting a total score of zero for the relevant assignment.

• End semester Exam (Take home, the details of the format to be decided): 40%   

⇒ Collaboration for the Exam: As will be elaborated in the question paper, NO collaborations are allowed in the exam. Any sign of copying would lead to cancellation of the exam (a zero will be recorded) and will be reported to the graduate studies cell.

• Impromptu class test/quiz (typically once a month, to be announced at the beginning of the class): 10% 

⇒ All students present would need to participate.

Course description:

This is an introductory course on the foundations of mechanics, focusing mainly on classical mechanics. The laws of classical mechanics are most simply expressed and studied in the language of symplectic geometry. This course can also be viewed as an introduction to symplectic geometry. The role of symmetry in studying mechanical systems will be emphasized.

The core syllabus will consist of Lagrangian mechanics, Hamiltonian mechanics, Hamilton-Jacobi theory, moment maps, and symplectic reduction. Additional topics will be drawn from integrable systems, quantum mechanics, hydrodynamics, and classical field theory.

Prerequisites:

Calculus on manifolds; rudiments of Lie theory (the equivalent of Chapter 1, Chapter 2, and Section 4.1 of [AM78]).

Textbook:

The course will not follow any particular textbook.

References:

[AM78] Ralph Abraham and Jerrold E. Marsden, Foundations of mechanics, Benjamin/Cummings Publishing Co., Inc., Advanced Book Program, Reading, Mass., 1978.

[Arn89] Vladimir I. Arnol’d, Mathematical methods of classical mechanics, Graduate Texts in Mathematics, vol. 60, Springer-Verlag, New York, 1989.

[CdS01] Ana Cannas da Silva, Lectures on symplectic geometry, Lecture Notes in Mathematics, vol. 1764, Springer-Verlag, Berlin, 2001.

[MR99] Jerrold E. Marsden and Tudor S. Ratiu, Introduction to mechanics and symmetry, second ed., Texts in Applied Mathematics, vol. 17, Springer-Verlag, New York, 1999.

Evaluation:

The final grade will be based on homework assignments (60% of the grade) and on two exams (40% of the grade). Both exams will carry equal weight.