This page lists what was covered in lectures, reading assignments, and also archives handouts and pretests.
To bottom (most recent lectures)| Lecture | Date | Covered in lecture | Further Reading |
| 1.1 | 3/29 |
Class organization. Identical particles in QM, permutation operator and the spin-statistics connection. |
Sakurai 6.1-6.3 and GY 6.1. |
| 1.2 | 3/31 | Application to Helium atom . |
Read Sakurai 6.4 and GY 6.2.
We will not cover the material on permutation groups in Sakurai 6.5, nor the atomic shell model discussed in GY 6.3 |
| 1.3 | 4/2 |
Intro to elastic scattering Scattering amplitude and the PW expansion |
Read GY 8.1 |
| 2.1 | 4/5 |
Complete discussion of general features of PW expansion Derive the optical theorem (following GY 8.1) |
|
| 2.2 | 4/7 |
Partial wave cross sections Optical theorem from PW expansion Solving for phase-shifts: hard sphere plus some general considerations. --> |
Read Sakurai 7.6, p.405-410. |
| 2.3 | 4/9 |
Phase-shifts for hard-sphere potential (continued):
kR >> 1 Begin discussion of low-energy scattering for a general potential |
Sakurai 7.6 and 7.7 |
| 3.1 | 4/12 |
Low energy scattering for a general potential: scattering length,
effective range, their meaning and implications for bound states. Phase-shifts for all energies and Levinson's theorem. |
Continue reading Sakurai 7.7 |
| 3.2 | 4/14 |
Complete discussion of scattering length and phase-shift for all
energies Resonances. |
Resonances are discussed in Sakurai 7.8 |
| 3.3 | 4/16 | HW/qual review session, run by TA. | |
| 4.1 | 4/19 |
Wavepacket treatment of scattering (see GY 8.1)
Notes Lippmann-Schwinger eq. and its derivation (GY 8.2 and Sak 7.1) |
You should make sure you understand how to calculate the overall constant in the free Schrodinger eq. Green functions |
| 4.2 | 4/21 |
Finish derivation of Lippmann-Schwinger Born series (Sak 7.2, GY 8.3(a)) Optical theorem from Born Series (Sak 7.3) |
|
| 4.3 | 4/23 |
Validity of Born expansion (GY 8.3(b)) Application of Born approximation to spherical well Barely started Eikonal approximation (GY 8.3(c), Sakurai 7.4) |
|
| 5.1 | 4/26 | Qual review session run by Sichun Sun. | |
| 5.2 | 4/28 |
Eikonal approximation Application to spherical well Mathematica notebook and PDF used in class |
Please read Sakurai 7.9: identical particle scattering---no time
in lecture for this. Topics that we will not have time to cover but which you should read about for the qual. are symmetry considerations & scattering (Sak. 7.10, GY 8.4), and a little on inelastic scattering (Sak 7.12---GY Ch. 9 has a lot more detail), and a little on Coulomb scattering (Sak. 7.13, GY 8.4). |
| 5.3 | 4/30 |
Brief discussion of old qual problem The free EM field--recap of classical field theory, (GY 10.1.): Maxwell's equations in covariant form, then use Coulomb gauge and mode expansion to bring to form suitable for quantization. See |
Read GY 10.1(a) for a nice historical introduction. |
| 6.1 | 5/3 | Quantization of EM field: ( notes ) | We will not cover GY 10.2 or 10.3, but you should read these sections if you want a deeper understanding of the quantum nature of the EM field. |
| 6.2 | 5/5 |
Wrapping up quantization of EM field: Uncertainty relations, causality, momentum and angular momentum. Begin radiative transistions (GY 10.4) ( Notes ) |
|
| 6.3 | 5/7 |
Recap of derivation of Coulomb term Review for midterm |
|
| 7.1 | 5/10 |
MIDTERM Solution |
|
| 7.2 | 5/12 | Calculating radiative transition rates (GY 10.4) ( Notes ) | |
| 7.3 | 5/14 | Qual question session run by Sichun. | |
| 8.1 | 5/17 |
Discussion of midterm Selection rules and sum rule in radiative transitions ( Notes ) |
|
| 8.2 | 5/19 |
Introduction to second quantization,
mainly for bosons [GY 11.2(a)] ( Notes ) |
Read GY 11.1 for an overview, and a discussion of permutations in more detail than covered in class. |
| 8.3 | 5/21 | General one-body operators. ( Notes ) | |
| 9.1 | 5/24 |
Two-body operators in second quantization Second quantization for fermions Begin application to BECs ( Notes ) |
For more background read Baym and Pethick, Phys. Rev. Lett. 76 (1996) 6. |
| 9.2 | 5/26 | Continue (and almost complete) Bose-Einstein condensation using 2nd-quantized formalism (GY 11.4a). ( Notes ) | |
| 9.3 | 5/28 |
Complete BEC Begin introduction to Dirac equation (GY 13.2a) ( Notes ) |
Read GY 13.1 for nice historical introduction |
| 10.1 | 5/31 | HOLIDAY! | |
| 10.2 | 6/2 |
Complete introduction to Dirac eq. (GY 13.2) ( Notes ) |
|
| 10.3 | 6/4 |
Review for final Evaluations |
|
| 11 | 6/8 | FINAL EXAM (10:30-12:20) Solution |