This page lists what was covered in lectures, reading assignments, and also archives notes, handouts and pretests.
To bottom (most recent lectures)| Lecture | Date | Covered in lecture | Further Reading |
| 1.1 | 3/28 |
Class organization. Identical particles in QM, permutation operator and the spin-statistics connection. Notes. |
Sakurai 6.1-6.3 and GY 6.1. |
| 1.2 | 3/30 |
Application to Helium atom. Using variational estimates for Helium How to define probability densities. Notes. |
Read Sakurai 6.4 and GY 6.2, and also the last 4 pages
of today's notes, which I didn't have time to cover.
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 | 4/1 | Intro to elastic scattering. Notes. | Read GY 8.1 |
| 2.1 | 4/4 |
Derive partial wave form for scattering amplitude f Relate f to differential cross section. Notes. Qual problem |
|
| 2.2 | 4/6 |
Derive the optical theorem (following GY 8.1) Partial wave expansion and the Argand diagram. Notes. Complete qual problem. |
Read Sakurai 7.6, pp. 405-6. |
| 2.3 | 4/8 |
Phase-shifts for hard-sphere potential, both
for kR <<1 and kR >> 1
Notes. |
Sakurai 7.6, pp. 407-410. |
| 3.1 | 4/11 |
Finish hard sphere for kR>>1 Low energy scattering for a general potential: scattering length, effective range, their meaning and implications for bound states. Notes. |
Sakurai 7.7 |
| 3.2 | 4/13 |
Phase-shifts for all energies and Levinson's theorem. Bound state energies from poles in scattering amplitude. Notes. Qual problem (determining relative phase shifts from differential cross section). |
See main web page for references on Levinson's theorem. |
| 3.3 | 4/15 | Resonances. Notebook used in class (and pdf version). Notes. | Resonances are discussed in Sakurai 7.8 |
| 4.1 | 4/18 |
Wavepacket treatment of scattering (see GY 8.1)
"Black sphere" scattering (old qual problem) Notes. |
The only discussion of the black sphere case in a text that I could find is in Landau and Lifshitz. |
| 4.2 | 4/20 | Lippmann-Schwinger eq. and its derivation (GY 8.2 and Sak 7.1) Notes. | You should make sure you understand how to calculate the overall constant in the free Schrodinger eq. Green functions |
| 4.3 | 4/22 |
Scattering (or "T") operator.
Born series (Sak 7.2, GY 8.3(a)). General features of Born approx and example of Yukawa potential. Notes. |
Read in Sakurai 7.3 or lecture notes about optical theorem from Born Series. |
| 5.1 | 4/25 |
Validity of Born expansion (GY 8.3(b)) Application of Born approximation to spherical well Eikonal approximation (GY 8.3(c), Sakurai 7.4) Notes. Mathematica notebook (and PDF ) used in class. |
Please read Sakurai 7.9 and 7.10: identical particle scattering
and symmetry considerations in scattering. Interesting topics not covered in this course are inelastic scattering (Sak 7.12, GY Ch 9) and Coulomb scattering (Sak 7.13, GY 8.4). |
| 5.2 | 4/27 |
Quantizing the free EM field (GY 10.1): recap of classical field theory, Maxwell's equations in covariant form, gauge fixing, begin quantization. Notes. |
Read GY 10.1(a) for a nice historical introduction |
| 5.3 | 4/29 | Complete the quantization of EM field, and begin interpretation of results. 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. |
| 6.1 | 5/2 | Photons as bosons, Uncertainty relations, causality, vacuum fluctuations, linear momentum and angular momentum. Notes. | GY have a nice discussion of helicity in general in sec. 7.5(b). |
| 6.2 | 5/4 |
Complete discussion of helicity of photons Begin radiative transistions (GY 10.4): derive Hamiltonian for charged particles and EM field ( Notes ) |
For further reading on the derivation of the Coulomb interaction see Sakurai's "Advanced QM" |
| 6.3 | 5/6 | Review for midterm (run by Max) | |
| 7.1 | 5/9 |
MIDTERM Solution |
|
| 7.2 | 5/11 | Calculation of radiative transition rates, dipole approx. ( Notes ) |
Read GY 10.4 for discussion of relative sizes of
contributions of different terms in our Hamiltonian Sakurai's discussion in 5.7 is useful although EM field is not quantized (but beware different units than GY) |
| 7.3 | 5/13 | Finish dipole approximation. Selection rules for E1 transitions. ( Notes ) | |
| 8.1 | 5/16 |
Higher order multipole radiative transitions Thomas-Reiche-Kuhn sum rule for absorption (Sak 5.7) ( Notes ) |
|
| 8.2 | 5/18 | Introduction to second quantization, mainly for bosons [GY 11.1 and 11.2(a)]. Fock space, simple 1-body operators, field operators. ( Notes ) | Read GY 11.1 for an overview, and a discussion of permutations in more detail than covered in class. |
| 8.3 | 5/20 | Density operator, position-space symmetrized basis states. ( Notes ) | |
| 9.1 | 5/23 |
General one-body and two-body operators for bosons Second quantization for fermions Begin application to Bose-Einstein condensates. ( Notes ) |
For more background on the BEC application, see Baym and Pethick, Phys. Rev. Lett. 76 (1996) 6. |
| 9.2 | 5/25 |
Complete Bose-Einstein condensation including
interactions using
2nd-quantized formalism (GY 11.4a), leading
to Gross-Pitaevsky equation. ( Notes ) |
In HW8 you work out details skipped in class. |
| 9.3 | 5/27 |
BEC without trap---simple example of use of chemical potential
(
Notes )
Begin introduction to Dirac equation (GY 13.2a) ( Notes for this and next lecture) |
Read GY 13.1 for nice historical introduction |
| 10.1 | 5/30 | HOLIDAY! | |
| 10.2 | 6/1 |
Run by Max. Finish introduction to Dirac eq. (GY 13.2) Evaluations |
|
| 10.3 | 6/3 |
Review for final |
|
| 11 | 6/7 | FINAL EXAM (10:30-12:20) |