| Lecture 1: Time Independent Perturbation Theory |
| L1.1 |
General problem. Non-degenerate perturbation theory (22:55) |
| L1.2 |
Setting up the perturbative equations (16:07) |
| L1.3 |
Calculating the energy corrections (6:25) |
| L1.4 |
First order correction to the state. Second order correction to energy (13:43) |
| Lecture 2: Time Independent Perturbation Theory (continued) |
| L2.1 |
Remarks and validity of the perturbation series (22:26) |
| L2.2 |
Anharmonic Oscillator via a quartic perturbation (20:54) |
| L2.3 |
Degenerate Perturbation theory: Example and setup (25:19) |
| L2.4 |
Degenerate Perturbation Theory: Leading energy corrections (6:50) |
| Lecture 3: Degenerate Perturbation Theory |
| L3.1 |
Remarks on a "good basis" (17:37) |
| L3.2 |
Degeneracy resolved to first order; state and energy corrections (29:10) |
| L3.3 |
Degeneracy resolved to second order (18:27) |
| L3.4 |
Degeneracy resolved to second order (continued) (11:34) |
| Lecture 4: Hydrogen Atom Fine Structure |
| L4.1 |
Scales and zeroth-order spectrum (25:49) |
| L4.2 |
The uncoupled and coupled basis states for the spectrum (17:10) |
| L4.3 |
The Pauli equation for the electron in an electromagnetic field (18:10) |
| L4.4 |
Dirac equation for the electron and hydrogen Hamiltonian (14:59) |
| Lecture 5: Hydrogen Atom Fine Structure (continued) |
| L5.1 |
Evaluating the Darwin correction (12:49) |
| L5.2 |
Interpretation of the Darwin correction from nonlocality (21:46) |
| L5.3 |
The relativistic correction (19:15) |
| L5.4 |
Spin-orbit correction (8:30) |
| L5.5 |
Assembling the fine-structure correction (15:21) |
| Lecture 6: Zeeman Effect and Introduction to the Semiclassical Approximation |
| L6.1 |
Zeeman effect and fine structure (13:06) |
| L6.2 |
Weak-field Zeeman effect; general structure (10:08) |
| L6.3 |
Weak-field Zeeman effect; the projection lemma (19:09) |
| L6.4 |
Strong-field Zeeman (9:49) |
| L6.5 |
Semiclassical approximation and local de Broglie wavelength (23:29) |
| Lecture 7: The Semiclassical WKB Approximation |
| L7.1 |
The WKB approximation scheme (22:50) |
| L7.2 |
Approximate WKB solutions (19:01) |
| L7.3 |
Validity of the WKB approximation (17:00) |
| L7.4 |
Connection formula stated and example (21:09) |
| Lecture 8: WKB (continued). Airy Functions and Connection Formulae |
| L8.1 |
Airy functions as integrals in the complex plane (17:53) |
| L8.2 |
Asymptotic expansions of Airy functions (19:36) |
| L8.3 |
Deriving the connection formulae (22:30) |
| L8.4 |
Deriving the connection formulae (continued) logical arrows (14:44) |
| Lecture 9: Time Dependent Perturbation Theory |
| L9.1 |
The interaction picture and time evolution (26:32) |
| L9.2 |
The interaction picture equation in an orthonormal basis (15:06) |
| L9.3 |
Example: Instantaneous transitions in a two-level system (29:23) |
| L9.4 |
Setting up perturbation theory (6:35) |
