August-December, 2025: 

Course: JT: 205: Quantum Mechanics 

Instructors: Dr. Abhishek Kumar and Prof. Swapan K Pati 

Syllabus: 

1. Waves & Particles, Basis sets, probability & superposition, wave equation Quantum Mechanical Postulates. 

2. Uncertainty principle, minimum uncertainty, Ehrenfest’s theorem. 

3. Free particle, particle in a box, probability current, classical limits, stationary states. 

4. Step potential, transmission and reflection coefficients, transfer matrix. 

5. Quantum Harmonic oscillator 

6. Delta-function potential, transmission and bound states. 

7. Particle in a box revisited; Stationary states, Fermi Sea, Density of States and Quantum confinement. 

8. Quantum Simple Harmomic Oscillator revsited; Operator arguments for constant energy separation and derivation of quantum classical correspondence. 2-dimensional simple Harmonic Oscillator - polar solutions, effect of magnetic field. 

9. Angular momentum operators, commutation relations, separation of variables, symmetries, addition of angular momentum, 3J and 6J symbols, various theorems. Importance of angular momentum in single electron and many electrons systems, spin variables, spin-spin interactions and magnetic structures. Unitary operation and time evolution. 

10. Hydrogen atom: spherical polar functions, functions without spherical symmetry, degeneracy. Bound states, tunneling and scattering. Various potentials and importance of Coulombic interactions in atoms. 

11. Variational Principle and approaches for many-electron systems. Timeindependent perturbation theory: non-degenerate and degenerate cases. Derivation of Operators corresponding to n’th order Perturbation Theory. 

12. Application of perturbation theory and variation Principles to derive the ground state energy of He atom. 

January-April, 2025:

Course: JT: 205: Solid State Physics-II 

Instructors: Prof. N S Vidyadhiraja and Prof. Swapan K Pati 

Syllabus:

1. Bondings: Covalent, Ionic, Metallic, van der Waals, Hydrogen bondings. Theoretical background and Experimental determinations. 

2. Magnetic Properties: Fundamental concepts, Magnetic interactions, various exchange interactions, Spin waves, Magnons, Magnetic Resonance Phenomena.

3. Magnetic Effects: Spin and spin variables, spin-spin interactions and magnetic structures. Unitary operation and time evolution. Generators and matrix elements of unitary representations; Addition of angular momenta, Clebsch-Gordon and Racah series, Wigner-Eckart theorem, and Lande-g-factor; Charged particle in a magnetic field; Aharanov-Bohm effect, Spin-orbit coupling. 

4. Boltzmann Transport Equations: General formalism and derivation from first principles, Dynamics of electrons, Electrical, Optical and Thermal Conductivities; Various Scattering processes and Mechanisms of Conductions. 

5. Semiconductors Physics: Electrons and Phonons at absolute zero and at finite temperatures in Metals, Semiconductors and Insulators; Direct and Indirect band Semiconductors; Inter and Intra band transitions; Various competing processes. 

6. Semiconductor Devices: Photoconductivity, Diffusion of charge carriers, p-n junctions, Various device physics, excess carriers, band inversion, defect scatterings and Carrier dynamics in device structures. 

7. Optical and Dielectric Properties: Ferroelectrics and Piezoelectrics; Static and dynamic Polarizabilities; Electronic and Ionic Polarizabilities; Free Carrier effects. 

8. Superconductivity: The basic phenomena, Theory of Superconductors, Second quantization, BCS theory, Josephson junctions. High-Tc superconductors, Manybody effects. 

9. Physics of correlated systems: Kondo Physics, Model Hamiltonians, Canonical transformations and Hilbert space methods-Schrieffer-Wolff transformation. 

10. Topological and disordered systems: Introduction to topology in condensed matter; Introduction to Anderson localization.

References

1. Charles Kittel, “Introduction to Solid State Physics”, 8th edition, Wiley 8th Edition (November, 2011); ISBN: 0471415267. 

2. N. Ashcroft and N. Mermin, “Solid State Physics” Revised Edition, Cengage Learning Asia Publication, Revised edition (June 30, 2016); ISBN: 9814369896 

3. M. E. Rose, “Elementary Theory of Angular Momentum”, Dover Publications (November, 20111); ISBN: 4866848064. 

4. G. D. Mahan, “Many-Particle Physics”, Springer Publication, 3rd ed. (October, 2000); ISBN: 0306463385. 

5. Philip Philips, “Advanced Solid State Physics”, Cambridge University Press; 2nd edition (April 9, 2012); ISBN: 0521194903 

6. Piers Coleman, “Introduction to Many-Body Physics”, Cambridge University Press

August-December, 2024:

Course: JT: 205: Quantum Mechanics 

Instructor: Prof. Swapan K Pati

Syllabus: 

1. Waves & Particles, Basis sets, probability & superposition, wave equation.

2. Matrix formulation, various operators and their properties, wave-particle duality, commutation relations, Heisenberg uncertainty.

3. Free particle, particle in a box, probability current, classical limits, stationary states, Fermi Sea, Density of States and Quantum confinement.

4. Harmonic oscillator - solution from various approaches; Operator arguments for constant energy separation and derivation of quantum classical correspondence. 2-dimensional simple Harmonic Oscillator - polar solutions, effect of magnetic field.

5. Angular momentum operators, commutation relations, separation of variables, symmetries, addition of angular momentum, 3J and 6J symbols, various theorems. Importance of angular momentum in single electron and many electrons systems, spin variables, spin-spin interactions and magnetic structures. Unitary operation and time evolution.

6. Hydrogen atom: spherical polar functions, functions without spherical symmetry, degeneracy. Bound states, tunneling and scattering. Various potentials and importance of Coulombic interactions in atoms.

7. Variational Principle and approaches for many-electron systems. Timeindependent perturbation theory: non-degenerate and degenerate cases. Derivation of Operators corresponding to n’th order Perturbation Theory.

8. Application of perturbation theory and variation Principles to derive the ground state energy of He atom.

References:

1. E. Merzbacher, Quantum Mechanics, John Wiley & Sons, 3rd edition, 1998.

2. C. Cohen-Tannoudji, B. Diu and F. Laloe, Quantum Mechanics Vol.1, John Wiley & Sons, 1977.

3. Arno Bohm, Quantum Mechanics: Foundations and Applications, Springer, 1993.

• JT-205: Quantum Mechanics, September - December, 2021.

• JNC-313: Applied Quantum Chemistry, August - December, 2020.

• JT-205: Quantum Mechanics, August - December, 2020.

• JNC-313: Applied Quantum Chemistry, August - December, 2019.

• JC-307: Physics of Materials, August - December, 2019

• JC-307: Physics of Materials, August - December, 2018.

• JT-205: Quantum Mechanics, August - December, 2016.

• JT-205: Quantum Mechanics, August - December, 2015.

• JT-205: Quantum Mechanics, August - December, 2014.

• JT-205: Quantum Mechanics, August - December, 2013.

• JT-205: Quantum Mechanics (jointly with Prof. N. S. Vidyadhiraja), August - December, 2011.

• JT-205: Quantum Mechanics, August - December, 2010.

• JT-205: Quantum Mechanics, August - December, 2009.

• JC-206: Basics in Nanoscience and Technology (jointly with Prof. G. U. Kulkarni), January - April, 2009.

• JC-301: Physical Chemistry (jointly with Prof. S. Balasubramanian), August - December, 2008.

• JT-205: Quantum Mechanics, August - December, 2008.

• JC-206: Basics in Nanoscience and Technology (jointly with Prof. G. U. Kulkarni), January - April, 2008.

• JC-301: Physical Chemistry (jointly with Prof. S. Balasubramanian), August - December, 2007.

• JT-203: Quantum Mechanics I, August - December, 2007.

• JC-206: Basics in Nanoscience and Technology (jointly with Prof. G. U. Kulkarni), January - April, 2007.

• JC-301: Physical Chemistry (jointly with Prof. S. Balasubramanian), August - December, 2006.

• JC-206: Basics in Nanoscience and Technology (jointly with Prof. G. U. Kulkarni), January - April, 2006.

• JT-303: Quantum Mechanics-II, January - April, 2006.

• JC-301: Physical Chemistry (jointly with Prof. S. Balasubramanian), August - December, 2005.

• JC-206: Basics in Nanoscience and Technology (jointly with Prof. G. U. Kulkarni), January - April, 2005.

• JC-301: Physical Chemistry (jointly with Prof. S. Balasubramanian), August - December, 2004.

• JT-303: Quantum Mechanics-II, January - April, 2003.

• JT-302: Topics in Condensed Matter Theory, January - April, 2002.

• JT 201: Solid State Physics (jointly with Prof. S. Narasimhan), August - December. 2001.