QUANTUM MECHANICS: Fall 2001 (501) and Spring 2002 (502).
Room 268 Serin
Office Hour: Tues 10am or by appointment.
Scope of Course. This course is aimed to provide an advanced
foundation for any research involving quantum mechanics. The course follows
develops Dirac's bra-ket approach, developing the formalism and providing
worked examples of some of the most recent lines of thought and applications
of quantum mechanics such as quantum computation, Berry's geometric phase,
2D electron gasses and Quantum Entanglement.
J. J. Sakurai Modern Quantum Mechanics (Addison Wesley, 1994)
R. Shankar Principles of Quantum Mechanics
G. Baym Lectures on Quantum Mechanics (Addison Wesley, 1990)
P.A.M. Dirac Quantum Mechanics (Cambridge)
Times: (501) 9:50-11:10 Mon and Wednesday in SEC 212 starting
Weds Sept 5th.
(502) 9.50-11:10 Mon and Wednesday in ARC 108 (Mon) and
212 (Weds) starting Weds Jan 23rd, 2002.
Assessment: Assessment will be made on the basis of weekly
assignments (502), a mid-term and final exam.
(Old assignments for 501).
Tentative Outline for the Course
Fundamental Concepts. Historical Background
Photon polarization and the Stern-Gerlach experiment; bra-ket formalism;
the Copenhagen interpretation- modern view of measurement theory- Elitzur-Vaidman
bomb problem; Uncertainty Principle; momentum and position representations.
Quantum Dynamics Hamiltonian as the generator of time-translation;
Schrödinger/Heisenberg ; Simple-harmonic oscillator; Schrödinger's
wave equation; Hydrogen atom and the Quantum Stadium; Propagators and Path
Integrals; Aharanov Bohm effect; Electron in a magnetic field and the fractional
quantum Hall Effect.
Angular Momentum Rotation group; SU(2) and SO(3); density matrices;
Addition of angular momentum; Berry Phases; EPR
Paradox and Bells inequality; Quantum
Teleportation. Vector and Tensor operators; Wigner Eckert Theorem and
Symmetries. Quantum vs classical symmetries. Discrete Symmetries.
Parity. Transformation of operators and states. Lattice translation:
conservation of crystal momentum and Bloch's theorem. Time-reversal symmetry.
Anti-unitary operators. Transformation of position, momentum
and orbital angular momentum. Transformation of spins under time-reversal.
Approximate methods: Perturbation Theory and Variational approach. Time
independent perturbation theory: 1st and 2nd order. Wavefunction renormalization.
Degenerate perturbation theory. Fine structure in Hydrogen-like
atoms. Zeeman effect. Van der Waals forces. Variational methods.
Time dependent potentials and the "interaction representation". Spin resonance
and the Maser. Time dependent perturbation theory: transition rate and
Golden Rule. Absorption and emission of radiation: dipole approximation.
Photo-electric effect. Line broadening and resonances.
Identical Particles . Exchange symmetry. Symmetrization postulate.
Pauli Exclusion principle. Two electron system. Helium atom. Occupation
number representation. Creation and annihilation operators. Fermions
and Bosons. Hamiltonian of many particles.
Scattering Theory. Separation of wave into incoming and scattered
components. Lippmann Schwinger equation. Scattering amplitude and
phase shift. Scattering cross-section. Born approximation.
Coulomb scattering. Beyond Born approximation. Optical Theorem. Phase
shift at high energy- eikonal approximation. Partial wave decomposition.
Calculation of phase shift. Hard sphere scattering. Low energy scattering
and bound states. Resonant scattering. Scattering of identical particles.
Symmetry in scattering. Time dependence in scattering. Inelastic
Relativistic Quantum Mechanics. Klein Gordon model and its
failure. Dirac equation. Concept of antiparticle.
Emergence of spin.