MIT 8.04 Quantum Physics I, Spring 2016
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This course includes
- 28.3 hours of video
- Certificate of completion
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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 linearity 17:49
- Linearity and nonlinear theories. Schrödinger's equation 10:03
- Necessity of complex numbers 07:39
- Photons and the loss of determinism 17:21
- The nature of superposition. Mach-Zehnder interferometer 14:31
- More on superposition. General state of a photon and spin states 17:11
- Entanglement 13:08
- Mach-Zehnder interferometers and beam splitters 15:32
- Interferometer and interference 12:25
- Elitzur-Vaidman bombs 10:30
- The photoelectric effect 22:55
- Units of h and Compton wavelength of particles 12:41
- Compton Scattering 22:37
- de Broglie’s proposal 10:37
- de Broglie wavelength in different frames 14:53
- Galilean transformation of ordinary waves 12:16
- The frequency of a matter wave 10:23
- Group velocity and stationary phase approximation 10:32
- Motion of a wave-packet 08:59
- The wave for a free particle 14:33
- Momentum operator, energy operator, and a differential equation 20:32
- Free Schrödinger equation 09:56
- The general Schrödinger equation. x, p commutator 17:58
- Commutators, matrices, and 3-dimensional Schrödinger equation 16:13
- Interpretation of the wavefunction 07:57
- Normalizable wavefunctions and the question of time evolution 16:49
- Is probability conserved? Hermiticity of the Hamiltonian 20:40
- Probability current and current conservation 15:20
- Three dimensional current and conservation 18:11
- Wavepackets and Fourier representation 11:14
- Reality condition in Fourier transforms 09:09
- Widths and uncertainties 19:12
- Shape changes in a wave 16:56
- Time evolution of a free particle wavepacket 09:44
- Fourier transforms and delta functions 13:57
- Parseval identity 15:49
- Three-dimensional Fourier transforms 06:04
- Expectation values of operators 28:15
- Time dependence of expectation values 07:38
- Expectation value of Hermitian operators 16:40
- Eigenfunctions of a Hermitian operator 13:06
- Completeness of eigenvectors and measurement postulate 16:56
- Consistency condition. Particle on a circle 17:45
- Defining uncertainty 10:31
- Uncertainty and eigenstates 15:52
- Stationary states: key equations 18:42
- Expectation values on stationary states 09:00
- Comments on the spectrum and continuity conditions 13:10
- Solving particle on a circle 11:05
- Energy eigenstates for particle on a circle 16:12
- Infinite square well energy eigenstates 13:13
- Nodes and symmetries of the infinite square well eigenstates 09:43
- Finite square well. Setting up the problem 22:30
- Finite square well energy eigenstates 10:39
- Nondegeneracy of bound states in 1D. Real solutions 12:35
- Potentials that satisfy V(-x) = V(x) 14:18
- Qualitative insights: Local de Broglie wavelength 15:51
- Correspondence principle: amplitude as a function of position 05:54
- Local picture of the wavefunction 12:52
- Energy eigenstates on a generic symmetric potential. Shooting method 15:26
- Delta function potential I: Preliminaries 16:04
- Delta function potential I: Solving for the bound state 15:21
- Node Theorem 13:01
- Harmonic oscillator: Differential equation 16:42
- Behavior of the differential equation 10:31
- Recursion relation for the solution 12:26
- Quantization of the energy 23:19
- Algebraic solution of the harmonic oscillator 16:50
- Ground state wavefunction 15:57
- Number operator and commutators 15:49
- Excited states of the harmonic oscillator 18:19
- Creation and annihilation operators acting on energy eigenstates 21:04
- Scattering states and the step potential 10:35
- Step potential probability current 15:00
- Reflection and transmission coefficients 08:12
- Energy below the barrier and phase shift 18:41
- Wavepackets 20:52
- Wavepackets with energy below the barrier 05:55
- Particle on the forbidden region 06:50
- Waves on the finite square well 15:45
- Resonant transmission 17:50
- Ramsauer-Townsend phenomenology 10:16
- Scattering in 1D. Incoming and outgoing waves 18:06
- Scattered wave and phase shift 08:41
- Incident packet and delay for reflection 18:52
- Phase shift for a potential well 09:13
- Excursion of the phase shift 15:17
- Levinson's theorem, part 1 14:46
- Levinson's theorem, part 2 09:30
- Time delay and resonances 18:19
- Effects of resonance on phase shifts, wave amplitude and time delay 14:54
- Modelling a resonance 15:38
- Half-width and time delay 08:18
- Resonances in the complex k plane 15:15
- Translation operator. Central potentials 19:14
- Angular momentum operators and their algebra 14:28
- Commuting observables for angular momentum 17:17
- Simultaneous eigenstates and quantization of angular momentum 24:36
- Associated Legendre functions and spherical harmonics 18:52
- Orthonormality of spherical harmonics 17:57
- Effective potential and boundary conditions at r=0 14:29
- Hydrogen atom two-body problem 25:05
- Center of mass and relative motion wavefunctions 14:23
- Scales of the hydrogen atom 09:57
- Schrödinger equation for hydrogen 20:59
- Series solution and quantization of the energy 14:22
- Energy eigenstates of hydrogen 12:25
- Energy levels and diagram for hydrogen 13:42
- Degeneracy in the spectrum and features of the solution 14:21
- Rydberg atoms 26:23
- Orbits in the hydrogen atom 10:45
- More on the hydrogen atom degeneracies and orbits 23:22
- The simplest quantum system 13:55
- Hamiltonian and emerging spin angular momentum 15:43
- Eigenstates of the Hamiltonian 14:04
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