Quantum Physics III

Time Independent Perturbation Theory and WKB Approximation

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