Graduate Quantum Mechanics II
                Physics 522.004  (CRN 36885)

                Syllabus:  Angular momentum,  the hydrogen atom,  time-independent perturbation theory,  time-dependent perturbation theory,  identical particles,  helium, the hydrogen molecule, scattering theory,  quantization of the electromagnetic field,  the interaction of photons with atoms,  the Dirac equation,  quantization of the electron-positron field,  neutrinos and their oscillations.

                Because the students of 521 have purchased Messiah's two-volume treatise on quantum mechanics, the textbook for the course will be  volume 2 of Messiah.  There are better books, however.  Four of them are Quantum Mechanics by Cohen-Tannoudji, et al.,  Modern Quantum Mechanics by Sakurai,  Quantum Physics by Le Bellac,  and Quantum Mechanics (non-relativistic theory) by Landau and Lifshitz.

                Grades will be based exclusively upon the homework.   Mr.  Hannes Schenck is the grader:  hschenck@unm.edu and room 1144 in the northwest wing.

                My e-mail address is cahill@unm.edu.  You may reach me at 277-5318 and at 204-5448.  I am available most afternoons and evenings.

                Classes meet on Mondays and Wednesdays from 3:30 to 4:45 PM in room 184.

                Here are some of my notes on quantum mechanics:

•  Translations in space and time.
•  Schroedinger's equation and how states change with time.
•  Ehrenfest's theorem.
•  Bohr frequencies.
•  The virial theorem.
•  Supersymmetric quantum mechanics.
•  Summary of translations in space and time.
•  Rotations.
•  Lie algebra of rotation group.
•  Chapter 2 of these notes is on group theory and Lie algebras.
•  2x2 and 3x3 rotation matrices.
  
•  Orbital angular momentum in spherical coordinates.
  
•  Addition of angular momenta.
•  Example: adding two j = 1/2's.
  
•  Example: adding of two j=1's.
•  Isospin.
•  Example: Adding L and S.
  
•  The two-body problem.
•  Central potentials.
•  The hydrogen atom.
•  A relativistic particle in an electromagnetic field.
  
•  An electron in an electromagnetic field.
•  First-order perturbation theory and the linear Stark effect.
•  Higher-order perturbation theory of non-degenerate levels.
•  The quadratic Stark effect in the ground state of hydrogen.
•  Higher-order perturbation theory for a degenerate level. (New, improved!)
  
•  Fine Structure and the Spin-Orbit Effect in Alkali Atoms.
•  The variational method.
  
•  Identical particles (Cohen-Tannoudji).
•  Identical particles (my take).
•  Creation and annihilation operators for identical particles.
  
•  Helium.
•  Potential scattering.
  
•  Scattering.
• Scattering of identical particles.
• Absorptive scattering and the optical theorem.
• S-wave scattering off a square-well potential.
  
• Le Bellac's discussion of the S-matrix.
• Time-dependent perturbation theory.
• Fermi's golden rule.
• Light and atoms in SI units.
• Spontaneous emission.
• Spontaneous emission and the lifetime of the 2p state of atomic hydrogen in SI units.
• Ionization of atomic hydrogen in SI units.
• Hamiltonian of free, vacuum QED.
• Rayleigh and Thomson scattering (JJS)
• Thomson scattering.
• Rayleigh scattering.
• QED.
• Learning about Spin-One-Half Fields.      Erratum
• Compton Scattering.
• The Feynman rules for QED.
  

        Here's a video of the demonstration of the Lie algebra of the rotation group, which is described in the notes on rotations.
      
         Homework 1 due on 9 February: do these problems.    Solutions.
         Homework 2 due on 18 Feb: do these problems.    Solutions.
         Homework 3 due on 23 March: do these problems.   Solutions.
         Homework 4 due on 8 April: do these problems.   Solutions.
         Homework 5 due on 22 April: do these problems.   Solutions.
         Homework 6 due on May 6th: do these problems.   Solutions.
         Homework 7 due on May 13th: do these problems.   Solutions.

•      Video of lecture of 26 Jan. 2009 on the Lie algebra of the rotation group SO(3).
•      Video of lecture of 28 Jan. 2009 on matrix elements of angular-momentum operators and on orbital angular momentum in spherical coordinates.
•      Video of lecture of 2 Feb. 2009  on why massless particles have only two spin states instead of the 2j+1 that massive particles have and on the addition of angular momenta.  Please ignore three instances of "0 =" near the end of this lecture.
•     Video of lecture of 4 Feb. 2009  on 2x2 and 3x3 rotation matrices, on examples of adding angular momenta: adding two j=1/2 angular momenta and adding two j = 1 angular momenta, on isospin, and on two examples of the use of isospin:  the deuteron and nucleon-nucleon scattering. 
  
•    Video of lecture of 9 Feb. 2009 on adding L + S, the two-body problem, and central potentials.
•    Video of lecture of 11 Feb. 2009 on central potentials and the hydrogen atom.
  
•    Video of lecture of 16 Feb. 2009 on the hydrogen atom, on the action and hamiltonian of a relativistic charged particle in an electromagnetic field, and on a hydrogen atom in a magnetic field.
•    Video of lecture of 18 Feb. 2009 on a hydrogen atom in a static magnetic field and in a static electric field, on first-order perturbation theory, and on the linear Stark effect.
•    Video of lecture of 23 Feb. 2009 on higher-order, non-degenerate perturbation theory.
•    Video of lecture of 25 Feb. 2009 on higher-order degenerate perturbation theory.
•   Video of lecture of 9 March 2009 on a better way of doing higher-order degenerate-state perturbation theory and on the spin-orbit effect in alkali atoms.
  
•   Video of lecture of 11 March 2009 on identical particles.
•   Video of lecture of 23 March 2009 on identical particles, atoms, the variational method, and helium.
•   Video of lecture of 25 March 2009 on helium and potential scattering.
•   Video of lecture of 30 March 2009 on potential scattering.
•   Video of 1 April 2009 on partial waves and the optical theorem.
•   Video of lecture of 6 April 2009 on the scattering of identical particles, Glauber's eikonal approximation, and the Lippmann-Schwinger formalism.
•   Video of lecture of 8 April 2009 on absorptive scattering, the optical theorem, scattering off a square well and a hard sphere, poles in the s-wave S-matrix element, and bound states.
•   Video of lecture of 13 April 2009 on time-dependent perturbation theory, the time-energy uncertainty principle, and Fermi's golden rule.
•   Video of lecture of 15 April 2009 on the quantization of the electromagnetic field.
•   Video of lecture of 20 April 2009 on the x-section for the absorption of a photon by a hydrogen atom.
•   Video of lecture of 22 April 2009 on spontaneous emission and the lifetime of the 2p state of atomic hydrogen.
•   Video of lecture of 27 April 2009 on the hamiltonian of free, vacuum QED and the ionization of atomic hydrogen.
•   Video of lecture of 29 April 2009 on Thomson scattering.
  
•   Video of lecture of 4 May 2009 on how creation and annihilation operators are related to the quantum mechanics of identical particles, on Thomson scattering, and on Rayleigh scattering.
•   Video of lecture of 6 May 2009 on Rayleigh scattering.
•   Video of lecture of 11 May 2009 on QED and Compton scattering.
•  Video of lecture of 13 May 2009 on Compton scattering.
•  Part 2 of same video on Compton scattering and other QED processes.