Lectures
Quantum mechanics as a framework. Defining linearity Video lecture Linearity and nonlinear theories. Schrödinger's equation Video lecture Necessity of complex numbers Video lecture Photons and the loss of determinism Video lecture The nature of superposition. Mach-Zehnder interferometer Video lecture More on superposition. General state of a photon and spin states Video lecture Entanglement Video lecture Mach-Zehnder interferometers and beam splitters Video lecture Interferometer and interference Video lecture Elitzur-Vaidman bombs Video lecture The photoelectric effect Video lecture Units of h and Compton wavelength of particles Video lecture Compton Scattering Video lecture de Broglie’s proposal Video lecture de Broglie wavelength in different frames Video lecture Galilean transformation of ordinary waves Video lecture The frequency of a matter wave Video lecture Group velocity and stationary phase approximation Video lecture Motion of a wave-packet Video lecture The wave for a free particle Video lecture Momentum operator, energy operator, and a differential equation Video lecture Free Schrödinger equation Video lecture The general Schrödinger equation. x, p commutator Video lecture Commutators, matrices, and 3-dimensional Schrödinger equation Video lecture Interpretation of the wavefunction Video lecture Normalizable wavefunctions and the question of time evolution Video lecture Is probability conserved? Hermiticity of the Hamiltonian Video lecture Probability current and current conservation Video lecture Three dimensional current and conservation Video lecture Wavepackets and Fourier representation Video lecture Reality condition in Fourier transforms Video lecture Widths and uncertainties Video lecture Shape changes in a wave Video lecture Time evolution of a free particle wavepacket Video lecture Fourier transforms and delta functions Video lecture Parseval identity Video lecture Three-dimensional Fourier transforms Video lecture Expectation values of operators Video lecture Time dependence of expectation values Video lecture Expectation value of Hermitian operators Video lecture Eigenfunctions of a Hermitian operator Video lecture Completeness of eigenvectors and measurement postulate Video lecture Consistency condition. Particle on a circle Video lecture Defining uncertainty Video lecture Uncertainty and eigenstates Video lecture Stationary states: key equations Video lecture Expectation values on stationary states Video lecture Comments on the spectrum and continuity conditions Video lecture Solving particle on a circle Video lecture Energy eigenstates for particle on a circle Video lecture Infinite square well energy eigenstates Video lecture Nodes and symmetries of the infinite square well eigenstates Video lecture Finite square well. Setting up the problem Video lecture Finite square well energy eigenstates Video lecture Nondegeneracy of bound states in 1D. Real solutions Video lecture Potentials that satisfy V(-x) = V(x) Video lecture Qualitative insights: Local de Broglie wavelength Video lecture Correspondence principle: amplitude as a function of position Video lecture Local picture of the wavefunction Video lecture Energy eigenstates on a generic symmetric potential. Shooting method Video lecture Delta function potential I: Preliminaries Video lecture Delta function potential I: Solving for the bound state Video lecture Node Theorem Video lecture Harmonic oscillator: Differential equation Video lecture Behavior of the differential equation Video lecture Recursion relation for the solution Video lecture Quantization of the energy Video lecture Algebraic solution of the harmonic oscillator Video lecture Ground state wavefunction Video lecture Number operator and commutators Video lecture Excited states of the harmonic oscillator Video lecture Creation and annihilation operators acting on energy eigenstates Video lecture Scattering states and the step potential Video lecture Step potential probability current Video lecture Reflection and transmission coefficients Video lecture Energy below the barrier and phase shift Video lecture Wavepackets Video lecture Wavepackets with energy below the barrier Video lecture Particle on the forbidden region Video lecture Waves on the finite square well Video lecture Resonant transmission Video lecture Ramsauer-Townsend phenomenology Video lecture Scattering in 1D. Incoming and outgoing waves Video lecture Scattered wave and phase shift Video lecture Incident packet and delay for reflection Video lecture Phase shift for a potential well Video lecture Excursion of the phase shift Video lecture Levinson's theorem, part 1 Video lecture Levinson's theorem, part 2 Video lecture Time delay and resonances Video lecture Effects of resonance on phase shifts, wave amplitude and time delay Video lecture Modelling a resonance Video lecture Half-width and time delay Video lecture Resonances in the complex k plane Video lecture Translation operator. Central potentials Video lecture Angular momentum operators and their algebra Video lecture Commuting observables for angular momentum Video lecture Simultaneous eigenstates and quantization of angular momentum Video lecture Associated Legendre functions and spherical harmonics Video lecture Orthonormality of spherical harmonics Video lecture Effective potential and boundary conditions at r=0 Video lecture Hydrogen atom two-body problem Video lecture Center of mass and relative motion wavefunctions Video lecture Scales of the hydrogen atom Video lecture Schrödinger equation for hydrogen Video lecture Series solution and quantization of the energy Video lecture Energy eigenstates of hydrogen Video lecture Energy levels and diagram for hydrogen Video lecture Degeneracy in the spectrum and features of the solution Video lecture Rydberg atoms Video lecture Orbits in the hydrogen atom Video lecture More on the hydrogen atom degeneracies and orbits Video lecture The simplest quantum system Video lecture Hamiltonian and emerging spin angular momentum Video lecture Eigenstates of the Hamiltonian Video lecture