PHYS622-0201: Introduction to Quantum Mechanics I-Fall 2015 jaydsau

PHYS622-0201: Introduction to Quantum Mechanics I-Fall 2015 jaydsau

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). Here is a link to Kristi's page who has kindly put her lecture notes online

Office hours: Fridday 3:00 pm

TA: Chang Hun Lee (changhun@umd.edu)

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 instructions: Paper in class or at instructor office or email submission to TA. Email homework should not be hand written

Exams take-home Midterm  (October 24th to 29th midnight) 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,
  •   Propagators and feynman path integrals, gauge potential, Aharonov-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:

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