| # | Date | Read | Topic |
|---|---|---|---|
| 1. | Tue, Jan 26 | JJS 3.1-3.2 | The theory of angular momentum. Translations. Rotations in three spatial dimensions. Generators of rotations. SU(2) algebra. Unitary transformations of a Hilbert space corresponding to rotations. Operators of angular momentum components. The simplest case of spin 1/2 system. Spintors, algebra of Pauli matrices, and transformations of linear operators under rotations. |
| 2. | Thu, Jan 28 | JJS 3.6 | Groups, Lie groups, Lie algebras, representation theory (some terminology). Infinitely dimensional case: orbital angular momentum. |
| 3. | Tue, Feb 2 | JJS 3.5-3.6 | Homework 12 is given. Eigenvalue problem for angular momenta. Ladder operators. (2j+1) dimensional representation. Matrix elements of angular momentum operators. Representations of rotation operator. |
| 4. | Thu, Feb 4 | JJS 3.6-3.7 | Orbital angular momentum and spherical harmonics. Angular momentum in coordinate representation. Eigenfunctions of L^2 are spherical harmonics. Legendre polynomials and associated Legendre functions. Addition of angular momenta. Example of two spin-1/2 systems. |
| 5. | Tue, Feb 9 | JJS 3.7, 3.10 | Homework 13 is given. Example of two spin-1/2 systems. Example of spin and orbital angular momenta. Formal theory of angular momentum addition. Clebsh-Gordan coefficients and their properties. |
| 6. | Thu, Feb 11 | CLASS WAS CANCELLED BECAUSE OF SNOW STORM | |
| 7. | Tue, Feb 16 | JJS 3.10 | Homework 14 is given. Properties of Clebsh-Gordan coefficients. Tensor operators. Cartesian and spherical tensors. |
| 8. | Thu, Feb 18 | JJS 3.10, 3.4 | Matrix elements of tensor operators. Wigner-Eckart theorem. Density operator. Density matrix. |
| 9. | Tue, Feb 23 | JJS 3.4 | Homework 15 is given. Density operator. Time evolution of density operator. Density operator in statistical mechanics. Entanglement. |
| 10. | Thu, Feb 25 | JJS 4.1-3 | Symmetries in Quantum Mechanics. Discrete symmetries. Parity. Polar and axial vectors, scalar and pseudoscalars. Even and odd wave functions. Parity of rotational states. Theorem of parity of eigenstates of H. |
| 11. | Tue, Mar 2 | JJS 4.3-4.4 | Homework 16 is given. Symmetric double-well potential. Parity selection rule. Other discrete symmetries (point groups, lattice translations). Time-reversal symmetry. Time-reversal symmetry in classical physics. Antiunitary operators. Construction of time-reversal (anti)symmetry operator. |
| 12. | Thu, Mar 4 | JJS 4.4, 5.1 | Time-reversal symmetry and reality of wave functions. Time-reversal for spin 1/2. Perturbation theory I. Time-independent case. Time-independent perturbation theory. Non-degenerate case. Example of two-level system. |
| 13. | Tue, Mar 9 | JJS 5.1 | Homework 17 is given. Perturbation theory expansion for non-degenerate case. Normalization of the wave function. Example: quadratic Stark effect. |
| 14. | Thu, Mar 11 | JJS 5.2 | Degenerate case. Secular equation. Example: linear Stark effect. Hydrogen atom. Estimate of the energy of the graound state. Bohr radius and Rydberg. Laguerre equation. |
| 15. | Tue, Mar 16 | Midterm - one-hour exam (closed book). Three problems: 1) Angular momentum, 2) Discrete symmetries, 3) Time-independent perturbation theory. | |
| 16. | Thu, Mar 18 | JJS 5.3 | Fine structure of atomic terms Relativistic corrections to the Hamiltonian of a hydrogenlike atom. Application of perturbation theory. Fine structure of atomic terms. |
| 17. | Tue, Mar 23 | JJS 5.3 | Zeeman effect. Lande and Paschen-Back cases. Perturbation theory II. Time-dependent case. Interaction representation. |
| 18. | Thu, Mar 25 | JJS 5.5, 5.6 | Homework 18 is given. Interaction representation. Example of a two-level system. Dyson series. Transition probabilities. |
| Tue, Mar 30 | No classes, Spring Break. | ||
| Thu, Apr 1 | No classes, Spring Break. | ||
| 19. | Tue, Apr 6 | Measurements in quantum mechanics. Entanglement, quantum computing, etc. | |
| 20. | Thu, Apr 8 | JJS 5.6 | Homework 19 is given. Time-dependent perturbation theory. Constant and harmonic perturbations. Fermi's Golden Rule. |
| 21. | Tue, Apr 13 | JJS 5.8 EM Ch.7 |
Energy shift and decay width. Semiclassical (WKB) approximation. Quasiclassical approximation. Expansion in Planck's constant. Wave function and classical action. Criterion of quasiclassicity. |
| 22. | Thu, Apr 15 | EM Ch.7 | Homework 20 is given. Connection formulas. Bound states. Bohr-Sommerfeld quantization condition. |
| 23. | Tue, Apr 20 | EM Ch.7 | Double-well potential. Transmission through the barrier. Resonant transmission. |
| 24. | Thu, Apr 22 | LL 52-53 DJG Ch.10 |
Homework 21 is given. Reflection above the barrier. The method of complex classical paths. Adiabatic approximation. Adiabatic theorem. Dynamic and Berry's phases. |
| 25. | Tue, Apr 27 | DJG Ch.10 JJS 2.5 |
Berry's (geometrical) phase. Landau-Zener transitions. Path integrals. Path integral representation of transition amplitudes. Path integral for phase space trajectories. Feynmann path integral. |
| 26. | Thu, Apr 29 | JJS 6.1-6.2 | Homework 22 is given. Identical particles and spin. The permutation symmetry. Symmetrization postulate. Bosons and fermions. Spin-statistics theorem. Two-electron system. Spin triplet and spin singlet: orbital and spin functions. Exchange density and exchange interaction. |
| 27. | Tue, May 4 | JJS 7.1-7.2 | Introduction to scattering theory. Scattering problem. Differential and total scattering cross sections in classical mechanics. Scattering amplitude. The Lippmann-Schwinger equation. Green's function. |
| 28. | Thu, May 6 | JJS 7.2-7.3 7.3, 7.5-7.6 |
The Born approximation. Example of Yukawa potential. Coulomb limit. Optical theorem. Scattering of slow particles. Method of partial waves and phase shifts. |
| Thu, May 13 | FINAL EXAM: Room P-128, 11:15am-1:45pm The final is "closed books and notes". |
