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.

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.