Submitted by admin_sps on 17 August, 2020 - 15:22

Course No:

P475

Credit:

8

Prerequisites:

P302 (Quantum Mechanics II)

Approval:

UG-Elective

Syllabus:

(42 Lectures + 14 Tutorial) PART I: Quantum entanglement & applications:

- Density matrices
- Tensor product and entangled states coherent and squeezed states; Bell basis
- Quantum teleportation
- EPR and Bells inequalities
- Shannon entropy: Qbits, introduction to quantum computing principles; measurement and decoherence

*References: *

- Entangled systems by Jurgen Audretsch
- Density Matrix Theory and Applications by Karl Blum
- Quantum Mechanics by Leonard Susskind
- Modern Quantum Mechanics by J. J Sakurai

PART II: Introduction to many particle QM:

- Creation/ Annihilation operators; Symmetization/Antisymertization; many body operators, Boson/Fermion coherent states, Grassmann algebra and Gaussian integrals using coherent states.
- Dynamical variables and dynamics of identical particles
- Applications to many body systems: Angular momentum of system of identical particles, first order perturbation in many body systems, introduction to Hartree-Fock methods.

*References: *

- Quantum Mechanics Merzbacher (Chapters 21 and 22)
- Quantum many particle systems J. W. Negele and H. Orland (Chapter 1)
- Quantum Mechanics Schiff (Chapter 14)
- Elements of Advanced Quantum Theory by J. M. Ziman (Chapters 1,2 and 5)
- Modern Quantum Mechanics by J. J Sakurai

PART III: Symmetries in QM

- Group representation, Point group symmetry, Lie Groups; Schur lemma, orthogonality theorems, irreducible representations, accidental degeneracies; Irreducible tensor operators and direct product representations, Wigner Eckart theorem;
- Applications including molecular orbitals, space time symmetries of Bloch states; normal model of vibrations; characters of angular momentum states; SU(2), SU(3) representations

*References: *

- Group Theory by M Tinkham
- Group Theory by Hamermesh
- Lie Algebras in Particle Physics: from Isospin To Unified Theories by Howard Geogie
- Group theory and Chemistry by Bishop
- Topics in Condensed MatterTheoryby MicheleCini
- Elements of Advanced Quantum Theory by J. M. Ziman (chapters 7)
- SolidState Physics by Ashcroft and Mermin

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