AMAT 41413: Quantum Mechanics and Quantum Field Theory

Course Code : AMAT 41413

Title               : Quantum Mechanics and Quantum Field Theory

Pre-requisites : AMAT 11223, PMAT 21263

Learning Outcomes:  

At the end of this course, the student should be able to

1. understand and explain the differences between classical and quantum mechanics

2. solve time-dependent and time-independent Schrodinger equation for some basic, physically important types of potentials

3. interpret the wave function and apply operators to it obtain information about particle’s physical properties such as position, momentum and energy

4. understand the role of uncertainty in quantum physics and use the commutation relations of operators to determine whether or not two physical properties can be simultaneously measured

5. relate the matrix formalism to the use of basis states, and solve simple problems in that formalism

6. demonstrate an understanding of field quantization and the expansion of the scattering matrix

7. understand relativistic wave equations 8. describe spin zero and spin half fields.

Course Contents:

Quantum Mechanics:

• Introduction to Quantum mechanics: Review of Finite systems and commutator brackets, Quantum mechanics in Hilbert space, Axiomatic structure of quantum mechanics, Heisenberg and interaction picture, Complete set of observables, Observables and their expectation values.

Schrodinger’s Equation: 

• Schrodinger’s time -independent and time -dependent equations in one dimension, potential well, potential barrier and tunnelling, simple harmonic oscillator, Schrödinger’s equation in three dimensions, particle in a three dimensional box, Hydrogen atom, Completely continuous operators, uncertainty principle, scattering theory of two particles, potential scattering

Quantum Field Theory: 

• Quantization, Relativistic wave equation, Spin zero fields and spin ½ fields, Momentum and angular momentum operators, Phase factor, Conventions between the spinners, Two - component theory.

Method of Teaching and Learning : A combination of lectures and tutorial discussions.

Assessment : Based on tutorials, tests and end of course examination.

Recommended Reading :

1. Schiff, L.I. (4th Ed., 2014). Quantum Mechanics, McGraw-Hill India.

2. Prugovecki, E. (2nd Ed., 2013). Quantum Mechanics in Hilbert Space, Dover Publication.

3. Liboff, R.L. (4th Ed., 2011). Introductory Quantum Mechanics, Pearson India.

4. Baggot, J. (1997). The meaning of Quantum Theory, Oxford University Press.

5. Sakurai, J.J. (2013). Advanced Quantum Mechanics, Replica Press (P) LTD, India.

6. Lee, T.D. (1981). Particle Physics and Introduction to Field Theory, Harwood Academics.