PHY 511/512: Quantum Mechanics I,II
Fall 2009 / Spring 2010, Stony Brook
Tue, Thu: 11:20-12:40, in P-112
Under construction
Grades are posted to Solar System.
Merry Christmas and Happy New Year!
Instructor: Dr. Alexander (Sasha) Abanov,
Associate Professor
Office: B-102
Phone: 2-8174
E-mail:
alexandre.abanov @ sunysb.edu
Web page:
http://felix.physics.sunysb.edu/~abanov/
Teaching Assistant: Tin Sulejmanpasic
Office: C-123
Phone:
E-mail:
tin2019 @ gmail.com
Catalog description
First course in a two-part sequence. Topics include basic quantum physics and mathematical apparatus; application to one dimensional examples and simple systems. Symmetries, angular momentum, and spin. Additional topics as time permits.
Second course in a two-part sequence, covering variational principles, perturbation theory, relativistic quantum mechanics, quantization of the radiation field, many-body systems. Application to atoms, solids, nuclei and elementary particles, as time permits.
Grading
The final grade for this course will be based on grades for weekly
homeworks (25%), the grade for the midterm exam (30%),
and on the grade for the final exam (45%).
Topics
- Introduction
- Experimental motivations for quantum mechanics.
- Basics: Vector spaces, Hilbert spaces, Hermitian operators, eigenvalues and eigenstates.
- Dirac's bra and ket notations, wave functions, observables, probabilities, correspondence principle.
- Schrodinger equation.
- Simplest examples.
- Quantum mechanics in one dimension.
- Plane waves and quantum wells.
- Reflection and transmission.
- Harmonic oscillator.
- Energy and momentum.
- General properties of motion in 1D.
- Variational principle.
- Quantum mechanics in 2D.
- Separation of variables.
- Angular momentum in 2D.
- Free particle in a circular box. Zeros of Bessel's functions.
- Plane rotator and Aharonov-Bohm effect.
- Motion in magnetic field.
- Gauge invariance in quantum mechanics
- Current operator and continuity equation
- Aharonov-Bohm effect
- Landau levels. Landau gauge and radial gauge
- Ladder operator formalism for Landau levels
- Magnetic translations and magnetic rotations
- Dirac's monopole
- Theory of Angular Momentum.
- Quantum mechanics in 2D and 3D
- Rotational symmetry and angular momentum.
- Motion in central potential.
- Perturbation theory.
- Semiclassical approximation.
- Identical particles and spin.
Homeworks
-
Homework 1, due on Tuesday, September 15
(PDF )
-
Homework 2, due on Tuesday, September 22
(PDF )
-
Homework 3, due on Thursday, October 1
(PDF )
-
Homework 4, due on Tuesday, October 13
(PDF )
-
Homework 5, due on Tuesday, October 20
(PDF )
-
Homework 6, due on Tuesday, October 27
(PDF )
-
Homework 7, due on Tuesday, November 10
(PDF )
-
Homework 8, due on Tuesday, November 17
(PDF )
-
Homework 9, due on Tuesday, November 24
(PDF )
-
Homework 10, due on Thursday, December 3
(PDF )
-
Homework 11, due on Thursday, December 10
(PDF )
Recommended Books
-
J. Sakurai,
Modern Quantum Mechanics,
Addison Wesley, 1993, ISBN: 978-0201539295.
-
L. Landau and E. Lifshitz,
Quantum Mechanics, Non-relativistic theory., Butterworth-Heinemann, 1981, ISBN 978-0750635394.
-
E. Merzbacher,
Quantum Mechanics,3rd edition,
Wiley, 1997, ISBN: 978-0471887027.
Additional Books
-
R. Shankar,
Principles of Quantum Mechanics,
Springer, 1994, ISBN: 978-0306447907.
-
D. J. Griffiths,
Introduction to Quantum Mechanics., Benjamin Cummings, 2004, ISBN 978-0131118928.
-
R. Liboff,
Introductory Quantum Mechanics,4th edition,
Addison Wesley, 2002, ISBN: 978-0805387148.
Online resources
Stony Brook University Syllabus Statement
If you have a physical, psychological, medical, or learning
disability that may impact your course work, please contact
Disability Support Services at (631) 632-6748 or
http://studentaffairs.stonybrook.edu/dss/
. They will determine with
you what accommodations are necessary and appropriate. All
information and documentation is confidential.
Students who require assistance during emergency evacuation are
encouraged to discuss their needs with their professors and
Disability Support Services. For procedures and information go to the
following website:
http://www.sunysb.edu/ehs/fire/disabilities.shtml
Last updated December 9, 2009