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Details of PH4101 (Autumn 2012)

Level: 4 Type: Theory Credits: 3.0

Course CodeCourse NameInstructor(s)
PH4101 Quantum Mechanics III Siddhartha Lal

Syllabus
Time evolution in quantum mechanics. The evolution of a Gaussian wave packet for a free particle and a harmonic oscillator. The Schroedinger, Heisenberg and interaction pictures. Propagator for the Schroedinger equation. Path integrals for quantum mechanics. Application to free particles and harmonic oscillator.



Time dependent perturbation theory. The Born and Dyson series. Fermi golden rule its scope and limitations. Atom-radiation interaction in the dipole approximation. Transition rates and selection rules.



A two level atom interacting with a quantized radiation field. Comparison between golden rule and exact treatment.



Scattering by a localized potential. Cross sections total and differential. The golden rule approximation. Scattering in a Yukawa potential field. The Rutherford scattering cross section. The Lippmann-Schwinger equation. The Born approximation. The transition operator. Partial waves. The optical theorem.



System of identical particles. The Helium atom. The Fock space representation of multi-particle states. Creation and annihilation operators. Representation of one and two body operators in Fock space. The second quantized form of the Schroedinger equation. The connection between spin and statistics.



Relativistic quantum mechanics. The Klein-Gordon and Dirac equations. Problems with one body relativistic quantum mechanics.



The Copenhagen and many-world interpretations of quantum mechanics. Hidden variables and Bell's inequalities. Violation of Bell's inequality in two-spin systems.



Two level systems and the qubit. Entanglement. Survey of basic notions of quantum information theory - quantum key distribution, quantum teleportation, quantum non-demolition measurements, quantum computation etc.







References


  1. R Shankar, Principles of quantum mechanics, Springer (1994).

  2. J. J. Sakurai, Modern quantum mechanics. Pearson Education Inc. (2004).

  3. J. S. Townsend, A modern approach to quantum mechanics, University Science Books( 2000)

  4. L. E. Ballentine, Quantum mechanics : a modern approach, World Scientific Publishing Company ( 1998).

  5. D. J. Griffiths, Introduction to Quantum Mechanics, Pearson Education Inc.(2005).

  6. B G Englert, Lectures on quantum mechanics (3 volumes), World Scientific (2006).

  7. A. Das and A. C. Melissinos, Quantum mechanics : a modern introduction, Routledge (1986).





Course Credit Options

Sl. No.ProgrammeSemester NoCourse Choice
1 IP 1 Not Allowed
2 IP 3 Not Allowed
3 MS 7 Not Allowed
4 RS 1 Not Allowed

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