22:56

L1.1 General problem. Non-degenerate perturbation theory

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16:09

L1.2 Setting up the perturbative equations

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6:27

L1.3 Calculating the energy corrections

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13:45

L1.4 First order correction to the state. Second order correction to energy

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22:28

L2.1 Remarks and validity of the perturbation series

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20:56

L2.2 Anharmonic Oscillator via a quartic perturbation

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25:21

L2.3 Degenerate Perturbation theory: Example and setup

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6:52

L2.4 Degenerate Perturbation Theory: Leading energy corrections

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17:39

L3.1 Remarks on a 'good basis'

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29:12

L3.2 Degeneracy resolved to first order; state and energy corrections

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18:28

L3.3 Degeneracy resolved to second order

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11:36

L3.4 Degeneracy resolved to second order (continued)

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25:51

L4.1 Scales and zeroth-order spectrum

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17:12

L4.2 The uncoupled and coupled basis states for the spectrum

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18:12

L4.3 The Pauli equation for the electron in an electromagnetic field

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15:01

L4.4 Dirac equation for the electron and hydrogen Hamiltonian

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12:51

L5.1 Evaluating the Darwin correction

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21:47

L5.2 Interpretation of the Darwin correction from nonlocality

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19:16

L5.3 The relativistic correction

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8:32

L5.4 Spin-orbit correction

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15:23

L5.5 Assembling the fine-structure corrections

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13:07

L6.1 Zeeman effect and fine structure

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10:09

L6.2 Weak-field Zeeman effect; general structure

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19:10

L6.3 Weak-field Zeeman effect; the projection lemma

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9:50

L6.4 Strong-field Zeeman

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23:30

L6.5 Semiclassical approximation and local de Broglie wavelength

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22:51

L7.1 The WKB approximation scheme

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19:02

L7.2 Approximate WKB solutions

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17:01

L7.3 Validity of the WKB approximation

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21:10

L7.4 Connection formula stated and example

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17:55

L8.1 Airy functions as integrals in the complex plane

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19:38

L8.2 Asymptotic expansions of Airy functions

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22:32

L8.3 Deriving the connection formulae

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14:45

L8.4 Deriving the connection formulae (continued) logical arrows

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26:34

L9.1 The interaction picture and time evolution

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15:07

L9.2 The interaction picture equation in an orthonormal basis

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29:25

L9.3 Example: Instantaneous transitions in a two-level system

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6:36

L9.4 Setting up perturbation theory

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20:32

L10.1 Box regularization: density of states for the continuum

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19:02

L10.2 Transitions with a constant perturbation

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19:38

L10.3 Integrating over the continuum to find Fermi's Golden Rule

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11:31

L10.4 Autoionization transitions

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15:13

L11.1 Harmonic transitions between discrete states

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17:13

L11.2 Transition rates for stimulated emission and absorption processes

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20:55

L11.3 Ionization of hydrogen: conditions of validity, initial and final states

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22:21

L11.4 Ionization of hydrogen: matrix element for transition

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16:24

L12.1 Ionization rate for hydrogen: final result

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14:32

L12.2 Light and atoms with two levels, qualitative analysis

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19:32

L12.3 Einstein's argument: the need for spontaneous emission

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9:43

L12.4 Einstein's argument: B and A coefficients

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11:11

L12.5 Atom-light interactions: dipole operator

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17:51

L13.1 Transition rates induced by thermal radiation

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16:36

L13.2 Transition rates induced by thermal radiation (continued)

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13:55

L13.3 Einstein's B and A coefficients determined. Lifetimes and selection rules

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21:51

L13.4 Charged particles in EM fields: potentials and gauge invariance

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8:39

L13.5 Charged particles in EM fields: Schrodinger equation

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21:09

L14.1 Gauge invariance of the Schrödinger Equation

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25:15

L14.2 Quantization of the magnetic field on a torus

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18:20

L14.3 Particle in a constant magnetic field: Landau levels

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9:08

L14.4 Landau levels (continued). Finite sample

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16:35

L15.1 Classical analog: oscillator with slowly varying frequency

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15:08

L15.2 Classical adiabatic invariant

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16:24

L15.3 Phase space and intuition for quantum adiabatic invariants

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26:47

L15.4 Instantaneous energy eigenstates and Schrodinger equation

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13:03

L16.1 Quantum adiabatic theorem stated

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14:32

L16.2 Analysis with an orthonormal basis of instantaneous energy eigenstates

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14:22

L16.3 Error in the adiabatic approximation

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19:31

L16.4 Landau-Zener transitions

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14:19

L16.5 Landau-Zener transitions (continued)

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15:28

L17.1 Configuration space for Hamiltonians

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25:05

L17.2 Berry's phase and Berry's connection

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11:13

L17.3 Properties of Berry's phase

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17:58

L17.4 Molecules and energy scales

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24:49

L18.1 Born-Oppenheimer approximation: Hamiltonian and electronic states

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20:03

L18.2 Effective nuclear Hamiltonian. Electronic Berry connection

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27:02

L18.3 Example: The hydrogen molecule ion

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15:36

L19.1 Elastic scattering defined and assumptions

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25:03

L19.2 Energy eigenstates: incident and outgoing waves. Scattering amplitude

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20:21

L19.3 Differential and total cross section

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17:47

L19.4 Differential as a sum of partial waves

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9:03

L20.1 Review of scattering concepts developed so far

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16:58

L20.2 The one-dimensional analogy for phase shifts

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15:00

L20.3 Scattering amplitude in terms of phase shifts

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13:14

L20.4 Cross section in terms of partial cross sections. Optical theorem

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18:02

L20.5 Identification of phase shifts. Example: hard sphere

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18:15

L21.1 General computation of the phase shifts

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27:39

L21.2 Phase shifts and impact parameter

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30:27

L21.3 Integral equation for scattering and Green's function

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21:08

L22.1 Setting up the Born Series

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13:03

L22.2 First Born Approximation. Calculation of the scattering amplitude

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21:42

L22.3 Diagrammatic representation of the Born series. Scattering amplitude for spherically symm...

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19:42

L22.4 Identical particles and exchange degeneracy

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22:23

L23.1 Permutation operators and projectors for two particles

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11:45

L23.2 Permutation operators acting on operators

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29:40

L23.3 Permutation operators on N particles and transpositions

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11:35

L23.4 Symmetric and Antisymmetric states of N particles

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16:50

L24.1 Symmetrizer and antisymmetrizer for N particles

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24:55

L24.2 Symmetrizer and antisymmetrizer for N particles (continued)

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11:39

L24.3 The symmetrization postulate

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20:51

L24.4 The symmetrization postulate (continued)

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