MIT 8.04 Quantum Physics I, Spring 2016
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What you'll learn
This course includes
- 28.3 hours of video
- Certificate of completion
- Access on mobile and TV
Course content
1 modules • 115 lessons • 28.3 hours of video
MIT 8.04 Quantum Physics I, Spring 2016
115 lessons
• 28.3 hours
MIT 8.04 Quantum Physics I, Spring 2016
115 lessons
• 28.3 hours
- Quantum mechanics as a framework. Defining linearity17:49
- Linearity and nonlinear theories. Schrödinger's equation10:03
- Necessity of complex numbers07:39
- Photons and the loss of determinism17:21
- The nature of superposition. Mach-Zehnder interferometer14:31
- More on superposition. General state of a photon and spin states17:11
- Entanglement13:08
- Mach-Zehnder interferometers and beam splitters15:32
- Interferometer and interference12:25
- Elitzur-Vaidman bombs10:30
- The photoelectric effect22:55
- Units of h and Compton wavelength of particles12:41
- Compton Scattering22:37
- de Broglie’s proposal10:37
- de Broglie wavelength in different frames14:53
- Galilean transformation of ordinary waves12:16
- The frequency of a matter wave10:23
- Group velocity and stationary phase approximation10:32
- Motion of a wave-packet08:59
- The wave for a free particle14:33
- Momentum operator, energy operator, and a differential equation20:32
- Free Schrödinger equation09:56
- The general Schrödinger equation. x, p commutator17:58
- Commutators, matrices, and 3-dimensional Schrödinger equation16:13
- Interpretation of the wavefunction07:57
- Normalizable wavefunctions and the question of time evolution16:49
- Is probability conserved? Hermiticity of the Hamiltonian20:40
- Probability current and current conservation15:20
- Three dimensional current and conservation18:11
- Wavepackets and Fourier representation11:14
- Reality condition in Fourier transforms09:09
- Widths and uncertainties19:12
- Shape changes in a wave16:56
- Time evolution of a free particle wavepacket09:44
- Fourier transforms and delta functions13:57
- Parseval identity15:49
- Three-dimensional Fourier transforms06:04
- Expectation values of operators28:15
- Time dependence of expectation values07:38
- Expectation value of Hermitian operators16:40
- Eigenfunctions of a Hermitian operator13:06
- Completeness of eigenvectors and measurement postulate16:56
- Consistency condition. Particle on a circle17:45
- Defining uncertainty10:31
- Uncertainty and eigenstates15:52
- Stationary states: key equations18:42
- Expectation values on stationary states09:00
- Comments on the spectrum and continuity conditions13:10
- Solving particle on a circle11:05
- Energy eigenstates for particle on a circle16:12
- Infinite square well energy eigenstates13:13
- Nodes and symmetries of the infinite square well eigenstates09:43
- Finite square well. Setting up the problem22:30
- Finite square well energy eigenstates10:39
- Nondegeneracy of bound states in 1D. Real solutions12:35
- Potentials that satisfy V(-x) = V(x)14:18
- Qualitative insights: Local de Broglie wavelength15:51
- Correspondence principle: amplitude as a function of position05:54
- Local picture of the wavefunction12:52
- Energy eigenstates on a generic symmetric potential. Shooting method15:26
- Delta function potential I: Preliminaries16:04
- Delta function potential I: Solving for the bound state15:21
- Node Theorem13:01
- Harmonic oscillator: Differential equation16:42
- Behavior of the differential equation10:31
- Recursion relation for the solution12:26
- Quantization of the energy23:19
- Algebraic solution of the harmonic oscillator16:50
- Ground state wavefunction15:57
- Number operator and commutators15:49
- Excited states of the harmonic oscillator18:19
- Creation and annihilation operators acting on energy eigenstates21:04
- Scattering states and the step potential10:35
- Step potential probability current15:00
- Reflection and transmission coefficients08:12
- Energy below the barrier and phase shift18:41
- Wavepackets20:52
- Wavepackets with energy below the barrier05:55
- Particle on the forbidden region06:50
- Waves on the finite square well15:45
- Resonant transmission17:50
- Ramsauer-Townsend phenomenology10:16
- Scattering in 1D. Incoming and outgoing waves18:06
- Scattered wave and phase shift08:41
- Incident packet and delay for reflection18:52
- Phase shift for a potential well09:13
- Excursion of the phase shift15:17
- Levinson's theorem, part 114:46
- Levinson's theorem, part 209:30
- Time delay and resonances18:19
- Effects of resonance on phase shifts, wave amplitude and time delay14:54
- Modelling a resonance15:38
- Half-width and time delay08:18
- Resonances in the complex k plane15:15
- Translation operator. Central potentials19:14
- Angular momentum operators and their algebra14:28
- Commuting observables for angular momentum17:17
- Simultaneous eigenstates and quantization of angular momentum24:36
- Associated Legendre functions and spherical harmonics18:52
- Orthonormality of spherical harmonics17:57
- Effective potential and boundary conditions at r=014:29
- Hydrogen atom two-body problem25:05
- Center of mass and relative motion wavefunctions14:23
- Scales of the hydrogen atom09:57
- Schrödinger equation for hydrogen20:59
- Series solution and quantization of the energy14:22
- Energy eigenstates of hydrogen12:25
- Energy levels and diagram for hydrogen13:42
- Degeneracy in the spectrum and features of the solution14:21
- Rydberg atoms26:23
- Orbits in the hydrogen atom10:45
- More on the hydrogen atom degeneracies and orbits23:22
- The simplest quantum system13:55
- Hamiltonian and emerging spin angular momentum15:43
- Eigenstates of the Hamiltonian14:04
