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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