PHY 511/512: Quantum Mechanics I,II
Fall 2009 / Spring 2010, Stony Brook
Tue, Thu: 9:50-11:10, in P-128

Under construction

ATTENTION: The final is on Thursday, May 13, P-128, 11:15am-1:45pm.
It is open book. You can use your notes,
homeworks with solutions and one textbook.
There will be four problems:

The last problem (number 5) of hw 22 is removed.
See the updated version hw22.pdf
The homework is due on Friday, May 7, until 5pm.
Please, bring it to my office (B-102).

Catalog description

Grading

Syllabus of the course (under construction)

Earlier Homeworks for QM I, PHY 511, (Fall 2009)

Homeworks

• Homework 12, due on Tuesday, February 9 (PDF )
  
  
• Homework 13, due on Tuesday, February 16 (PDF )
  
  
• Homework 14, due on Tuesday, February 23 (PDF )
  
  
• Homework 15, due on Tuesday, March 2 (PDF )
  
  
• Homework 16, due on Tuesday, March 9 (PDF )
  
  
• Homework 17, due on Tuesday, March 23 (PDF )
  
  
• Homework 18, due on Thursday, April 8 (PDF )
  
  
• Homework 19, due on Thursday, April 15 (PDF )
  
  
• Homework 20, due on Thursday, April 22 (PDF )
  
  
• Homework 21, due on Thursday, April 29 (PDF )
  
  
• Homework 22, due on Friday, May 7 (PDF )
  
  

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.
  • 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.
• Propagators.
• 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.

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

• K. K. Likharev's Lectures on Quantum Mechanics


• MIT Open Courseware, Quantum Theory I

Syllabus of the course (under construction)
Syllabus of QM I (Fall 2009)

Stony Brook University Syllabus Statement