Course Syllabus

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Instructor :Jay Sau

Webpage: http://www2.physics.umd.edu/~jaydsau/

email: jaydsau@umd.edu

Office: Toll Building 2308

Lectures: Toll 1204. Monday and Wednesday (10am - 10:50 am), Friday (10am - 11:50am).

Office hours: Monday 3:00 pm

TA: Yiming Cai (email: yimingcai01@gmail.com)

Textbooks: Chapters 1 to 4 of Modern Quantum Mechanics, J. J. Sakurai and Napolitano  (denoted by SAK) and

                    Quantum processes, systems and information, B. Schumacher and M. Westmoreland (denoted by SCH)

Homework Paper or email submission (to TA please)

Exams take-home Midterm  (October 22nd to 29th) and take home Final (beginning of December)

Grade information: Weekly assigments due Friday (total weight 20% of grade). One random problem will be picked and graded for the class (due to limited TA hours). Midterm (30% of grade) and Final (50% of grade)

Course outline (suggestions welcome):

  •  Stern Gerlach experiment, Hilbert space and probability postulate (kets, bras and operators), matrix representations
  •  measurements (eigenvalues and eigenvectors), Uncertainty relations
  •  Classical versus quantum probability (density matrices and entropy)
  •  Applications of quantum indeterminacy (quantum random numbers and cryptography)
  •  Composite systems, entanglement (entropy) and the EPR paradox (Bell's inequality)
  •  Unitary time dynamics of discrete systems - Schrodinger and Heisenberg representations - Bloch sphere dynamics
  •  Continuous variable Hilbert spaces (position and momenta)
  •  Time-dynamics of continuous systems - Heisenberg's equation and Schrodinger's wave-equation (classical limit)
  •  Review elementary solutions of Schrodinger's wave equation (harmonic oscillator, square well, linear potential)
  •  WKB semiclassical approximation, Adiabatic dynamics (Berry phase)
  •   Propagators and feynman path integrals, gauge potential, Aharnov-Bohm effect, diamagnetism in superconductors, monopoles
  •   Rotations as generators of angular momenta, SO(3) versus SU(2), angular momentum algebra, rotation matrices, spherical harmonics, schwinger bosons
  •  Schrodinger equation for central potentials (3D harmonic oscillator, SO(4) solution to hydrogen atom)
  •  Tensor operators and the Wigner-Eckart theorem
  •  Symmetry and conservation laws for continuous and discrete symmetry - translation and parity violation
  •  Time reversal symmetry and Kramer's theorem

Course timeline (specific topics by chapters as course progresses): time_line_quantum.htm

Course Summary:

Date Details Due