Video Lectures

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)

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