1 Quantum mechanics as a framework. Defining linearity 2 Linearity and nonlinear theories. Schrödinger's equation 3 Necessity of complex numbers 4 Photons and the loss of determinism 5 The nature of superposition. Mach-Zehnder interferometer 6 More on superposition. General state of a photon and spin states 7 Entanglement 8 Mach-Zehnder interferometers and beam splitters 9 Interferometer and interference 10 Elitzur-Vaidman bombs 11 The photoelectric effect 12 Units of h and Compton wavelength of particles 13 Compton Scattering 14 de Broglie’s proposal 15 de Broglie wavelength in different frames 16 Galilean transformation of ordinary waves 17 The frequency of a matter wave 18 Group velocity and stationary phase approximation 19 Motion of a wave-packet 20 The wave for a free particle 21 Momentum operator, energy operator, and a differential equation 22 Free Schrödinger equation 23 The general Schrödinger equation. x, p commutator 24 Commutators, matrices, and 3-dimensional Schrödinger equation 25 Interpretation of the wavefunction 26 Normalizable wavefunctions and the question of time evolution 27 Is probability conserved? Hermiticity of the Hamiltonian 28 Probability current and current conservation 29 Three dimensional current and conservation 30 Wavepackets and Fourier representation 31 Reality condition in Fourier transforms 32 Widths and uncertainties 33 Shape changes in a wave 34 Time evolution of a free particle wavepacket 35 Fourier transforms and delta functions 36 Parseval identity 37 Three-dimensional Fourier transforms 38 Expectation values of operators 39 Time dependence of expectation values 40 Expectation value of Hermitian operators 41 Eigenfunctions of a Hermitian operator 42 Completeness of eigenvectors and measurement postulate 43 Consistency condition. Particle on a circle 44 Defining uncertainty 45 Uncertainty and eigenstates 46 Stationary states: key equations 47 Expectation values on stationary states 48 Comments on the spectrum and continuity conditions 49 Solving particle on a circle 50 Energy eigenstates for particle on a circle 51 Infinite square well energy eigenstates 52 Nodes and symmetries of the infinite square well eigenstates 53 Finite square well. Setting up the problem 54 Finite square well energy eigenstates 55 Nondegeneracy of bound states in 1D. Real solutions 56 Potentials that satisfy V(-x) = V(x) 57 Qualitative insights: Local de Broglie wavelength 58 Correspondence principle: amplitude as a function of position 59 Local picture of the wavefunction 60 Energy eigenstates on a generic symmetric potential. Shooting method 61 Delta function potential I: Preliminaries 62 Delta function potential I: Solving for the bound state 63 Node Theorem 64 Harmonic oscillator: Differential equation 65 Behavior of the differential equation 66 Recursion relation for the solution 67 Quantization of the energy 68 Algebraic solution of the harmonic oscillator 69 Ground state wavefunction 70 Number operator and commutators 71 Excited states of the harmonic oscillator 72 Creation and annihilation operators acting on energy eigenstates 73 Scattering states and the step potential 74 Step potential probability current 75 Reflection and transmission coefficients 76 Energy below the barrier and phase shift 77 Wavepackets 78 Wavepackets with energy below the barrier 79 Particle on the forbidden region 80 Waves on the finite square well 81 Resonant transmission 82 Ramsauer-Townsend phenomenology 83 Scattering in 1D. Incoming and outgoing waves 84 Scattered wave and phase shift 85 Incident packet and delay for reflection 86 Phase shift for a potential well 87 Excursion of the phase shift 88 Levinson's theorem, part 1 89 Levinson's theorem, part 2 90 Time delay and resonances 91 Effects of resonance on phase shifts, wave amplitude and time delay 92 Modelling a resonance 93 Half-width and time delay 94 Resonances in the complex k plane 95 Translation operator. Central potentials 96 Angular momentum operators and their algebra 97 Commuting observables for angular momentum 98 Simultaneous eigenstates and quantization of angular momentum 99 Associated Legendre functions and spherical harmonics 100 Orthonormality of spherical harmonics 101 Effective potential and boundary conditions at r=0 102 Hydrogen atom two-body problem 103 Center of mass and relative motion wavefunctions 104 Scales of the hydrogen atom 105 Schrödinger equation for hydrogen 106 Series solution and quantization of the energy 107 Energy eigenstates of hydrogen 108 Energy levels and diagram for hydrogen 109 Degeneracy in the spectrum and features of the solution 110 Rydberg atoms 111 Orbits in the hydrogen atom 112 More on the hydrogen atom degeneracies and orbits 113 The simplest quantum system 114 Hamiltonian and emerging spin angular momentum 115 Eigenstates of the Hamiltonian