PHY 511/512: Quantum Mechanics I,II
Fall 2010 / Spring 2011, Stony Brook
Tue, Thu: 11:2012:40, in P112
ATTENTION: A makeup class is scheduled on Tuesday, December 7, 5:306:50pm, in room B131
ATTENTION: Final exam is scheduled on Tuesday, December 14, 2:154:45pm, in room P112
Instructor: Dr. Alexander (Sasha) Abanov,
Associate Professor
Office: B102
Phone: 28174
Email:
alexandre.abanov @ sunysb.edu
Web page:
http://felix.physics.sunysb.edu/~abanov/
Teaching Assistant: Sooraj Radhakrishnan
Office: A105
Phone: 24070
Email:
sooraj9286 @ gmail.com
Catalog description
First course in a twopart 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 twopart sequence, covering variational principles, perturbation theory, relativistic quantum mechanics, quantization of the radiation field, manybody 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%).
Homeworks

Homework 1, due on Tuesday, September 21
(PDF )
Operators and Dirac notations.

Homework 2, due on Tuesday, September 28
(PDF )
Operators, Pauli matrices, spin 1/2 system.

Homework 3, due on Tuesday, October 5
(PDF )
Uncertainty relation, tensor product of Hilbert spaces.

Homework 4, due on Tuesday, October 12
(PDF )
Quantum dynamics. Math foundations.
Homework 5, due on Tuesday, October 19
(PDF )
Stationary Schrodinger equation in 1D. Some commutators.

Homework 6, due on Tuesday, October 26
(PDF )
Deltafunctional potentials.

Homework 7, due on Thursday, November 11
(PDF )
1D scattering. Harmonic oscillator.

Homework 8, due on Tuesday, November 23
(PDF )
Harmonic oscillator. Sudden perturbations.

Homework 9, due on Tuesday, November 30
(PDF )
Variational principle. 2D oscillator. Angular momentum.

Homework 10, due on Thursday, December 9
(PDF )
Plane rotator. Motion in e/m field. Landau levels.
Recommended Books

E. Merzbacher,
Quantum Mechanics,3rd edition,
Wiley, 1997, ISBN: 9780471887027.

J. Sakurai,
Modern Quantum Mechanics,
Addison Wesley, 1993, ISBN: 9780201539295.

L. Landau and E. Lifshitz,
Quantum Mechanics, Nonrelativistic theory., ButterworthHeinemann, 1981, ISBN 9780750635394.
Additional Books

D. J. Griffiths,
Introduction to Quantum Mechanics., Benjamin Cummings, 2004, ISBN 9780131118928.

R. Liboff,
Introductory Quantum Mechanics, 4th edition,
Addison Wesley, 2002, ISBN: 9780805387148.

R. Shankar,
Principles of Quantum Mechanics,
Springer, 1994, ISBN: 9780306447907.
Online resources
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 AharonovBohm effect.
 Motion in magnetic field.
 Gauge invariance in quantum mechanics
 Current operator and continuity equation
 AharonovBohm 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.
 Rotational symmetry and orbital angular momentum.
 Eigenvalues of angular momentum.
 Eigenfunctions of angular momentum.
 Addition of angular momenta.
 Symmetry in Quantum Mechanics.
 Motion in central potential.
 The spherical square well potential.
 The Coulomb potential: hydrogen atom
 Perturbation theory.
 Timeindependent perturbation theory: nondegenerate and degenerate cases.
 Atomic terms.
 Timedependent perturbation theory.
 Sudden perturbations.
 Semiclassical approximation.
 The WKB method.
 Bound states: BohrSommerfeld quantization rule.
 Penetration through (reflection from) a potential barrier.
 Symmetric doublewell potential.
 Resonant transmission.
 Reflection above the barrier. Classical complex paths.
 Adiabatic theory. Berry's phase.
 Path integrals.
 Propagators.
 Introduction to path integrals.
 Scattering theory.
 Scattering cross section, differential cross section and scattering amplitude.
 The LippmannSchwinger equation.
 The Born approximation.
 Scattering matrix.
 The method of partial waves.
 Identical particles and spin.
 The permutation symmetry
 The symmetrization postulate. FermiDirac and BoseEinstein statistics.
 Exchange interaction.
 Introduction into relativistic quantum mechanics.
 Measurements in quantum mechanics.
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) 6326748 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 6, 2010