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 | 1/4 |
Class organization. Mixed ensembles and density operator (Sakurai 3.4). |
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| 1.2 | 1/6 |
Time evolution of density operator Mixed states as subsystems of pure states Boltzman distribution Begin discussion of rotation operator in QM |
For more on infinitessimal canonical transformations see Goldstein et al, Ch. 9 sec 4 |
| 1.3 | 1/8 |
First pretest . Proper rotations and the group they form: SO(3). |
I am doing more background group theory than in Sakurai, so you may want to look at some of the group theory texts listed here . |
| 2.1 | 1/11 |
Using definition of D(R) to determine ang. mom. commutation
relations, and also those of J with x and p. Vector operators in general Rotations in Spin Hilbert space (Sakurai 3.2) |
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| 2.2 | 1/13 |
Experimental tests of spin-1/2 rotation operators Why did we end up with SU(2) and not SO(3)? SU(2) versus SO(3) Representations of angular momentum (Sakurai 3.5) |
Read about the neutron interferometry experiment
in 3.2 to fill in details that I missed SU(2) vs. SO(3) is discussed in Sakurai 3.3---for further reading see group theory texts in texts link |
| 2.3 | 1/15 |
Loose ends from representations of ang. mom Discussion of HW1 Wigner functions and Euler rotations |
Optional: read Sakurai 3.8, which describes a method to calculate Wigner functions in general |
| 3.1 | 1/18 | HOLIDAY! | |
| 3.2 | 1/20 |
Discussion of questions to ponder Orbital angular momentum and Spherical harmonics |
I skipped over many details, which you can find in Sakurai section 3.6. |
| 3.3 | 1/22 |
Loose ends of spherical harmonics Adding angular momenta---overview and begin example Last half-hour: qual problem |
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 | 1/25 |
Addition of ang. mom.--an example and sketch
of general method If time: Introduction to spherical tensor operators |
Read "Clebsch-Gordon Coefficients and Rotation Matrices"--last section of 3.7 |
| 4.2 | 1/27 | Spherical tensor operators and the Wigner-Eckart theorem (Sakurai 3.10) | I sketch 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 | 1/29 |
Complete proof of W-E theorem Examples (including "projection theorem") Qual problems |
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| 5.1 | 2/1 |
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 the 3-d Schr. eqn. |
| 5.2 | 2/3 | 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 | 2/5 |
Runge-Lenz vector Recap of parity operator Qual problem |
Gottfried and Yan discuss the Runge-Lenz vector in sec. 5.2 Read Sakurai 4.2 for parity |
| 6.1 | 2/8 |
Time reversal invariance (Sakurai 4.4) Motion reversal operator, need for antiunitary operator, form for spinless particle |
Read sakurai 4.3: discrete translation symmetry (will not be discussed in lectures). |
| 6.2 | 2/10 |
Finish time reversal invariance: transformation of spin and angular momentum, Kramers degeneracy. |
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| 6.3 | 2/12 |
Review for midterm/qual problem. Pretest on time independent perturbation theory |
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| 7.1 | 2/15 | HOLIDAY! | |
| 7.2 | 2/17 | MIDTERM | |
| 7.3 | 2/19 | Discussion of qual problems run by Sichun Sun | |
| 8.1 | 2/22 | Time independent perturbation theory (non-degenerate case) | Read those parts of Sakurai 5.1 which I do not discuss in class: the 2x2 case and wavefunction renormalization. |
| 8.2 | 2/24 |
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 | 2/26 |
Formalism of degenerate PT including second order
term (Sakurai 5.2) 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 | 3/1 |
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 (we mentioned them in 517) |
| 9.2 | 3/3 |
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 | 3/5 |
Finish discussion of 2-state exact solution. End early due to visiting weekend. |
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| 10.1 | 3/8 |
Using time independent perturbation theory: Comparing first order PT to exact solution for 2-state problem Fermi's Golden rule for constant and harmonic potentials (Sakurai 5.6) |
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| 10.2 | 3/10 |
Application Fermi's Golden rule: photoelectric effect (Sakurai 5.7) Adiabatic theorem |
We will cover radiative transitions in 519, when we
treat the photon quantum mechanically. Read Sakurai 5.8---relation of time dependent and time independent PT |
| 10.3 | 3/12 |
Review for final exam Evaluations |
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| 11 | 3/16 | FINAL EXAM (10:30-12:20) |