PHY 511/512: Quantum Mechanics I,II
Instructor: Dr. Alexander (Sasha) Abanov,
Fall 2010 / Spring 2011, Stony Brook
Tue, Thu: 9:50-11:10, in P-122
alexandre.abanov @ sunysb.edu
Teaching Assistant: Xu-Gang He
hexugang @ gmail.com
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.
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%).
Syllabus of QM I (Fall 2010)
Homework 11, due on Tuesday, February 15
Homework 12, due on Tuesday, February 22
Orbital Angular Momentum and addition of angular momenta.
Homework 13, due on Tuesday, March 1
Angular Momentum. Density matrix.
Homework 14, due on Tuesday, March 8
Density matrix. Symmetry in quantum mechanics.
Homework 15, due on Tuesday, March 15
Homework 16, due on Thursday, March 24
Time-independent perturbation theory.
Homework 17, due on Tuesday, April 5
Time-independent perturbation theory.
Homework 18, due on Tuesday, April 12
Two-level system. Time-dependent perturbation theory.
Homework 19, due on Thursday, April 28
Time-dependent perturbation theory. WKB.
Homework 20, due on Thursday, May 5
WKB, path integrals
Homework 21, due on Friday, May 13, noon
Identical particles, Born approximation in scattering.
Quantum Mechanics,3rd edition,
Wiley, 1997, ISBN: 978-0471887027.
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.
D. J. Griffiths,
Introduction to Quantum Mechanics., Benjamin Cummings, 2004, ISBN 978-0131118928.
Introductory Quantum Mechanics, 4th edition,
Addison Wesley, 2002, ISBN: 978-0805387148.
Principles of Quantum Mechanics,
Springer, 1994, ISBN: 978-0306447907.
- 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.
- 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.
- Time-independent perturbation theory: nondegenerate and degenerate cases.
- Atomic terms.
- Time-dependent perturbation theory.
- Sudden perturbations.
- Semiclassical approximation.
- The WKB method.
- Bound states: Bohr-Sommerfeld quantization rule.
- Penetration through (reflection from) a potential barrier.
- Symmetric double-well potential.
- Resonant transmission.
- Reflection above the barrier. Classical complex paths.
- Adiabatic theory. Berry's phase.
- Path integrals.
- Introduction to path integrals.
- Scattering theory.
- Scattering cross section, differential cross section and scattering amplitude.
- The Lippmann-Schwinger equation.
- The Born approximation.
- Scattering matrix.
- The method of partial waves.
- Identical particles and spin.
- The permutation symmetry
- The symmetrization postulate. Fermi-Dirac and Bose-Einstein statistics.
- Exchange interaction.
- Introduction into relativistic quantum mechanics.
- Measurements in quantum mechanics.
Syllabus of the course QM II
Stony Brook University Syllabus Statement
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Last updated May 12, 2011