Lecture 1: Time Independent Perturbation Theory

L1.1

L1.1 General problem. Nondegenerate 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 zerothorder 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 Spinorbit correction (8:30)

L5.5

L5.5 Assembling the finestructure 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 Weakfield Zeeman effect; general structure (10:08)

L6.3

L6.3 Weakfield Zeeman effect; the projection lemma (19:09)

L6.4

L6.4 Strongfield 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 twolevel system (29:23)

L9.4

L9.4 Setting up perturbation theory (6:35)
