This page lists what was covered in lectures, reading assignments, and also archives handouts.
To bottom (most recent lectures)| Lecture | Date | Covered in lecture | Reading (not covered or partially covered) |
| 1.1 | 1/7 |
Class organization. First pretest . Rotations and the group SO(3). |
Section 3.1 and the first part of 3.3 I am doing more background group theory than in Sakurai, so you may want to look at some group theory texts. |
| 1.2 | 1/9 |
Finish discussion of SO(3) Rotation operators in QM Motivating using ang. mom. operator to generate them by analogy with generators of infinitessimal canonical transf. in Cl. Mech. |
For more on inf. can. transf. see Goldstein et al, Ch. 9 sec 4 |
| 1.3 | 1/11 |
Using definition of D(R) to determine ang. mom. commutation
relations, and also those of J with x and p. Vector operators I expect about half the class to be free for discussion, e.g. of HW1 |
|
| 2.1 | 1/14 |
Rotations in Spin Hilbert space (Sakurai 3.2) Experimental tests SU(2) versus SO(3) |
Read about the neutron interferometry experiment
in 3.2 to fill in details that I missed Read about Cayley-Klein parameters in 3.3 |
| 2.2 | 1/16 |
Why did we end up with SU(2) and not SO(3)? Representations of angular momentum (Sakurai 3.5) A little on Wigner functions |
HW2 involves some questions using mixed states. This was covered in 517. Please read Sakurai 3.4 if needed |
| 2.3 | 1/18 |
Wigner functions and Euler rotations Discussion of HWs |
Optional: read Sakurai 3.8, which describes a method to calculate Wigner functions in general |
| 3.1 | 1/21 | HOLIDAY! | |
| 3.2 | 1/23 |
Orbital angular momentum Spherical harmonics |
I skipped over many details, which you can find in Sakurai's discussion |
| 3.3 | 1/25 |
Loose ends of spherical harmonics Adding angular momenta---intro and starting an example |
Read "Spherical Harmonics as Rotation matrices" which
I didn't cover in detail Read first section of 3.7 (Addition of ang. mom.) |
| 4.1 | 1/28 |
Addition of ang. mom.--an example and sketch
of general method Introduction to spherical tensor operators |
Read "Clebsch-Gordon Coefficients and Rotation Matrices"--last section of 3.7 |
| 4.2 | 1/30 | Spherical tensor operators and the Wigner-Eckart theorem (Sakurai 3.10) | I sketched a proof using finite rotations; you should read Sakurai 3.10 for an equivalent proof using infinitesimal transformations, with all details included, and also read about the "Projection theorem". |
| 4.3 | 2/1 |
HW discussion session (run by Can) Derivation of Projection theorem |
|
| 5.1 | 2/4 |
Recap of 3-dim Schr. equations: general method and
solution for V=0 Infield's method of generating spherical Bessel fcns |
Sakurai assumes all this material, and gives a summary of
results in App. A Read Sakurai 4.1 for a nice summary of symmetries in QM Any standard grad or undergrad. QM text (except Sakurai) will have a more detailed discussion of 3-d Schr. eqn. |
| 5.2 | 2/6 |
Complete V=constant discussion (spherical well, completeness) Bound states of spinless hydrogen atom: Asymptotic form from WKB, sketch of dermination of energies, size of states from virial theorem. |
Again, see App. A for summary of results See any (other) standard text for details of Laguerre polynomials |
| 5.3 | 2/8 |
Discussion of HW4/5 Runge-Lenz vector and degeneracies in the spinless H-atom |
Derivation of Euler-Lagrange equation in
terms of Lagrange density Constructing normal coordinates explicitly (both in FW sec. 25) |
| 6.1 | 2/11 |
Review for midterm Discrete symmetries in QM: Parity (Sakurai 4.2) |
Read sakurai 4.3: discrete translation symmetry Will not be discussed in lectures. |
| 6.2 | 2/13 | MIDTERM | |
| 6.3 | 2/15 | Discussion session run by Can: questions on midterm, and anti-unitary operators | |
| 7.1 | 2/18 | HOLIDAY! | |
| 7.2 | 2/20 |
Time reversal invariance (Sakurai 4.4) Motion reversal operator, need for antiunitary operator, form for spinless particle |
|
| 7.3 | 2/22 |
Finish time reversal invariance: transformation of spin and angular momentum, Kramers degeneracy. |
Read the section in Sakurai 4.4 on spin-1/2, which gives a different way of calculating \theta, and some more applications |
| 8.1 | 2/25 | Time independent perturbation theory (non-degenerate case) |
Sakurai 5.1: parts I will not discuss
in class but which you should read: the 2x2 case and wavefunction renormalization. |
| 8.2 | 2/27 |
Time independent pert. theory (continued):
Brillouin-Wigner pert. theory; example
of quadratic Stark effect Linear Stark effect using degenerate time independent pert. theory |
Read Sakurai 5.2 for the formalization of the non-degenerate case, which we will discuss on Friday. |
| 8.3 | 2/29 |
Formalism of degenerate PT including second order
term (Sakurai 5.2) Application to n=2 Stark effect (calculating polarizability) Sakurai problem 5.12 |
For fun: show that the result of second-order degenerate PT for Sakurai's problem 5.12 is as was claimed in class. |
| 9.1 | 3/3 |
The "real" hydrogen atom: fine structure, hyperfine structure, and a passing mention of the Zeeman effect Sakurai 5.3 has a patchy discussion---other texts have more |
You should read about the Zeeman effect in 5.3, and also the example of the Van de Waals effect. I will not discuss Variational methods in this class |
| 9.2 | 3/5 |
Start discussion of time independent PT (5.5) Interaction picture and Dyson series for time evolution operator Solving 2 state problem with oscillating off diagonal perturbation |
Read Sakurai's discussion of two-state problems (in 5.5), both to see the generality of this example, and a different method of solution. |
| 9.3 | 3/7 | Finish discussion of 2 state exact solution. | |
| 10.1 | 3/10 |
Time independent perturbation theory: Fermi's Golden rule for constant and harmonic potentials (Sakurai 5.6) |
|
| 10.2 | 3/12 |
Example of use of Fermi's Golden rule: photoelectric effect. Evaluations |
Read Sakurai 5.8---relation of time dependent and time independent PT |
| 10.3 | 3/14 | Review for final exam | |
| 11 | 3/19 | FINAL EXAM (8:30-10:20) |