PHY 511/512: Quantum Mechanics I,II
Fall 2010 / Spring 2011, Stony Brook
Tue, Thu: 11:20-12:40, in P-112
ATTENTION: A makeup class is scheduled on Tuesday, December 7, 5:30-6:50pm, in room B-131
ATTENTION: Final exam is scheduled on Tuesday, December 14, 2:15-4:45pm, in room P-112
Instructor: Dr. Alexander (Sasha) Abanov,
alexandre.abanov @ sunysb.edu
Teaching Assistant: Sooraj Radhakrishnan
sooraj9286 @ 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%).
Homework 1, due on Tuesday, September 21
Operators and Dirac notations.
Homework 2, due on Tuesday, September 28
Operators, Pauli matrices, spin 1/2 system.
Homework 3, due on Tuesday, October 5
Uncertainty relation, tensor product of Hilbert spaces.
Homework 4, due on Tuesday, October 12
Homework 5, due on Tuesday, October 19
Quantum dynamics. Math foundations.
Stationary Schrodinger equation in 1D. Some commutators.
Homework 6, due on Tuesday, October 26
Homework 7, due on Thursday, November 11
1D scattering. Harmonic oscillator.
Homework 8, due on Tuesday, November 23
Harmonic oscillator. Sudden perturbations.
Homework 9, due on Tuesday, November 30
Variational principle. 2D oscillator. Angular momentum.
Homework 10, due on Thursday, December 9
Plane rotator. Motion in e/m field. Landau levels.
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.
Stony Brook University Syllabus Statement
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Last updated December 6, 2010