Quantum Mechanics-I (PHYS-6119)

Course Importance: In this course, we review the fundamental ideas of quantum mechanics, introduce the path integral for a non-relativistic point particle, and use it to derive time-dependent perturbation theory and the Born series for non-relativistic scattering. The course concludes with an introduction to relativistic quantum mechanics and the ideas of quantum field theory. 

Learning Outcomes: This course examines the fundamental concepts and experimental techniques of quantum mechanics. Students will develop a self-critical perspective on the theoretical techniques to solve the problems. Rather the task is to develop reflective and critical skills for thinking about creative solutions for further higher studies and applications.

Course Contents:

1. Review of Concepts of Classical Mechanics: Historical Review (Experiments and Theories, Wave Aspects of Particles, Hilbert Space, and Wave Functions

2. Mathematical tools of Quantum Mechanics: The linear vector space, The Hilbert space, Dimensions, and basis of a vector space, Square integrable wave functions, Dirac notation, Operators, Representation in a discrete and continuous basis.

3. Basic Postulates of Quantum Mechanics: The state of a system, Observables, Measurement in Quantum Mechanics, Time Evolution of the System’s State (Time evolution operator, Stationary states: Time independent potentials), Conservation of probability, Time evolution of expectation values, Symmetries and Conservation Laws.

4. General Properties of one Dimensional Schrödinger Equation: bound states (discrete spectrum) and unbound states (continuous spectrum), mixed spectrum, symmetric potentials and parity, Properties of one-dimensional motion. The solution of Simple One Dimensional Systems: The free particle, The step potential, The potential barrier and well, The infinite square well potential, The finite square well potential, The harmonic oscillator

Suggested Books:

1. Introductory Quantum mechanics by R.L. Liboff, Addison Wesley Publishing Company, Reading Mass. (1980).

2. QUANTUM MECHANICS: Concepts and Applications by Nouredine Zettili, JOHN WILEY & SONS (2001)

3. A Modern Approach to Quantum Mechanics by J.S. TownsendMcGraw Hill Book Company,

Singapore (1992).

4. Quantum Mechanics: An Introduction by W. Greiner, Addison Wesley Publishing Company, Reading Mass. (1980).

5. Quantum Mechanics, Classical Results, Modern Systems, and Visualized Examples by Richard W. Robinett, Oxford University Press (2006).

6. Theory of Quantum by Bialynicki-Birula, M. Cieplak & J. Kaminski, Oxford University Press, New York (1992).

7. Relativistic Quantum Mechanics by W. GreinerSpringer Verlag, Berlin (1990).

8. Quantum Mechanics by F. Schwabe, Narosa Publishing House, New Delhi (1992).

9. Quantum Physics by S. Gasiorowicz, Wiley, (2003).

10. Introduction to Quantum Mechanics by David J. GriffithsPRENTICE Hall, Int., Inc, (2005).

ASSESSMENT CRITERIA:

Sessional 20 Marks

Mid Term exam: 30 marks

Final exam: 50 marks

CLASS TIMINGS:

MSc-2 

Monday                 2:00pm to 3:00pm

Thursday              3:00pm to 4:00pm  

Friday                   12:00pm to 1:00pm