1 L1.1 General problem. Non-degenerate perturbation theory 2 L1.2 Setting up the perturbative equations 3 L1.3 Calculating the energy corrections 4 L1.4 First order correction to the state. Second order correction to energy 5 L2.1 Remarks and validity of the perturbation series 6 L2.2 Anharmonic Oscillator via a quartic perturbation 7 L2.3 Degenerate Perturbation theory: Example and setup 8 L2.4 Degenerate Perturbation Theory: Leading energy corrections 9 L3.1 Remarks on a 'good basis' 10 L3.2 Degeneracy resolved to first order; state and energy corrections 11 L3.3 Degeneracy resolved to second order 12 L3.4 Degeneracy resolved to second order (continued) 13 L4.1 Scales and zeroth-order spectrum 14 L4.2 The uncoupled and coupled basis states for the spectrum 15 L4.3 The Pauli equation for the electron in an electromagnetic field 16 L4.4 Dirac equation for the electron and hydrogen Hamiltonian 17 L5.1 Evaluating the Darwin correction 18 L5.2 Interpretation of the Darwin correction from nonlocality 19 L5.3 The relativistic correction 20 L5.4 Spin-orbit correction 21 L5.5 Assembling the fine-structure corrections 22 L6.1 Zeeman effect and fine structure 23 L6.2 Weak-field Zeeman effect; general structure 24 L6.3 Weak-field Zeeman effect; the projection lemma 25 L6.4 Strong-field Zeeman 26 L6.5 Semiclassical approximation and local de Broglie wavelength 27 L7.1 The WKB approximation scheme 28 L7.2 Approximate WKB solutions 29 L7.3 Validity of the WKB approximation 30 L7.4 Connection formula stated and example 31 L8.1 Airy functions as integrals in the complex plane 32 L8.2 Asymptotic expansions of Airy functions 33 L8.3 Deriving the connection formulae 34 L8.4 Deriving the connection formulae (continued) logical arrows 35 L9.1 The interaction picture and time evolution 36 L9.2 The interaction picture equation in an orthonormal basis 37 L9.3 Example: Instantaneous transitions in a two-level system 38 L9.4 Setting up perturbation theory 39 L10.1 Box regularization: density of states for the continuum 40 L10.2 Transitions with a constant perturbation 41 L10.3 Integrating over the continuum to find Fermi's Golden Rule 42 L10.4 Autoionization transitions 43 L11.1 Harmonic transitions between discrete states 44 L11.2 Transition rates for stimulated emission and absorption processes 45 L11.3 Ionization of hydrogen: conditions of validity, initial and final states 46 L11.4 Ionization of hydrogen: matrix element for transition 47 L12.1 Ionization rate for hydrogen: final result 48 L12.2 Light and atoms with two levels, qualitative analysis 49 L12.3 Einstein's argument: the need for spontaneous emission 50 L12.4 Einstein's argument: B and A coefficients 51 L12.5 Atom-light interactions: dipole operator 52 L13.1 Transition rates induced by thermal radiation 53 L13.2 Transition rates induced by thermal radiation (continued) 54 L13.3 Einstein's B and A coefficients determined. Lifetimes and selection rules 55 L13.4 Charged particles in EM fields: potentials and gauge invariance 56 L13.5 Charged particles in EM fields: Schrodinger equation 57 L14.1 Gauge invariance of the Schrödinger Equation 58 L14.2 Quantization of the magnetic field on a torus 59 L14.3 Particle in a constant magnetic field: Landau levels 60 L14.4 Landau levels (continued). Finite sample 61 L15.1 Classical analog: oscillator with slowly varying frequency 62 L15.2 Classical adiabatic invariant 63 L15.3 Phase space and intuition for quantum adiabatic invariants 64 L15.4 Instantaneous energy eigenstates and Schrodinger equation 65 L16.1 Quantum adiabatic theorem stated 66 L16.2 Analysis with an orthonormal basis of instantaneous energy eigenstates 67 L16.3 Error in the adiabatic approximation 68 L16.4 Landau-Zener transitions 69 L16.5 Landau-Zener transitions (continued) 70 L17.1 Configuration space for Hamiltonians 71 L17.2 Berry's phase and Berry's connection 72 L17.3 Properties of Berry's phase 73 L17.4 Molecules and energy scales 74 L18.1 Born-Oppenheimer approximation: Hamiltonian and electronic states 75 L18.2 Effective nuclear Hamiltonian. Electronic Berry connection 76 L18.3 Example: The hydrogen molecule ion 77 L19.1 Elastic scattering defined and assumptions 78 L19.2 Energy eigenstates: incident and outgoing waves. Scattering amplitude 79 L19.3 Differential and total cross section 80 L19.4 Differential as a sum of partial waves 81 L20.1 Review of scattering concepts developed so far 82 L20.2 The one-dimensional analogy for phase shifts 83 L20.3 Scattering amplitude in terms of phase shifts 84 L20.4 Cross section in terms of partial cross sections. Optical theorem 85 L20.5 Identification of phase shifts. Example: hard sphere 86 L21.1 General computation of the phase shifts 87 L21.2 Phase shifts and impact parameter 88 L21.3 Integral equation for scattering and Green's function 89 L22.1 Setting up the Born Series 90 L22.2 First Born Approximation. Calculation of the scattering amplitude 91 L22.3 Diagrammatic representation of the Born series. Scattering amplitude for spherically symm... 92 L22.4 Identical particles and exchange degeneracy 93 L23.1 Permutation operators and projectors for two particles 94 L23.2 Permutation operators acting on operators 95 L23.3 Permutation operators on N particles and transpositions 96 L23.4 Symmetric and Antisymmetric states of N particles 97 L24.1 Symmetrizer and antisymmetrizer for N particles 98 L24.2 Symmetrizer and antisymmetrizer for N particles (continued) 99 L24.3 The symmetrization postulate 100 L24.4 The symmetrization postulate (continued)