MIT 8.06 Quantum Physics III, Spring 2018
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What you'll learn
This course includes
- 29.5 hours of video
- Certificate of completion
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Course content
1 modules • 100 lessons • 29.5 hours of video
MIT 8.06 Quantum Physics III, Spring 2018
100 lessons
• 29.5 hours
MIT 8.06 Quantum Physics III, Spring 2018
100 lessons
• 29.5 hours
- L1.1 General problem. Non-degenerate perturbation theory 22:56
- L1.2 Setting up the perturbative equations 16:09
- L1.3 Calculating the energy corrections 06:27
- L1.4 First order correction to the state. Second order correction to energy 13:45
- L2.1 Remarks and validity of the perturbation series 22:28
- L2.2 Anharmonic Oscillator via a quartic perturbation 20:56
- L2.3 Degenerate Perturbation theory: Example and setup 25:21
- L2.4 Degenerate Perturbation Theory: Leading energy corrections 06:52
- L3.1 Remarks on a 'good basis' 17:39
- L3.2 Degeneracy resolved to first order; state and energy corrections 29:12
- L3.3 Degeneracy resolved to second order 18:28
- L3.4 Degeneracy resolved to second order (continued) 11:36
- L4.1 Scales and zeroth-order spectrum 25:51
- L4.2 The uncoupled and coupled basis states for the spectrum 17:12
- L4.3 The Pauli equation for the electron in an electromagnetic field 18:12
- L4.4 Dirac equation for the electron and hydrogen Hamiltonian 15:01
- L5.1 Evaluating the Darwin correction 12:51
- L5.2 Interpretation of the Darwin correction from nonlocality 21:47
- L5.3 The relativistic correction 19:16
- L5.4 Spin-orbit correction 08:32
- L5.5 Assembling the fine-structure corrections 15:23
- L6.1 Zeeman effect and fine structure 13:07
- L6.2 Weak-field Zeeman effect; general structure 10:09
- L6.3 Weak-field Zeeman effect; the projection lemma 19:10
- L6.4 Strong-field Zeeman 09:50
- L6.5 Semiclassical approximation and local de Broglie wavelength 23:30
- L7.1 The WKB approximation scheme 22:51
- L7.2 Approximate WKB solutions 19:02
- L7.3 Validity of the WKB approximation 17:01
- L7.4 Connection formula stated and example 21:10
- L8.1 Airy functions as integrals in the complex plane 17:55
- L8.2 Asymptotic expansions of Airy functions 19:38
- L8.3 Deriving the connection formulae 22:32
- L8.4 Deriving the connection formulae (continued) logical arrows 14:45
- L9.1 The interaction picture and time evolution 26:34
- L9.2 The interaction picture equation in an orthonormal basis 15:07
- L9.3 Example: Instantaneous transitions in a two-level system 29:25
- L9.4 Setting up perturbation theory 06:36
- L10.1 Box regularization: density of states for the continuum 20:32
- L10.2 Transitions with a constant perturbation 19:02
- L10.3 Integrating over the continuum to find Fermi's Golden Rule 19:38
- L10.4 Autoionization transitions 11:31
- L11.1 Harmonic transitions between discrete states 15:13
- L11.2 Transition rates for stimulated emission and absorption processes 17:13
- L11.3 Ionization of hydrogen: conditions of validity, initial and final states 20:55
- L11.4 Ionization of hydrogen: matrix element for transition 22:21
- L12.1 Ionization rate for hydrogen: final result 16:24
- L12.2 Light and atoms with two levels, qualitative analysis 14:32
- L12.3 Einstein's argument: the need for spontaneous emission 19:32
- L12.4 Einstein's argument: B and A coefficients 09:43
- L12.5 Atom-light interactions: dipole operator 11:11
- L13.1 Transition rates induced by thermal radiation 17:51
- L13.2 Transition rates induced by thermal radiation (continued) 16:36
- L13.3 Einstein's B and A coefficients determined. Lifetimes and selection rules 13:55
- L13.4 Charged particles in EM fields: potentials and gauge invariance 21:51
- L13.5 Charged particles in EM fields: Schrodinger equation 08:39
- L14.1 Gauge invariance of the Schrödinger Equation 21:09
- L14.2 Quantization of the magnetic field on a torus 25:15
- L14.3 Particle in a constant magnetic field: Landau levels 18:20
- L14.4 Landau levels (continued). Finite sample 09:08
- L15.1 Classical analog: oscillator with slowly varying frequency 16:35
- L15.2 Classical adiabatic invariant 15:08
- L15.3 Phase space and intuition for quantum adiabatic invariants 16:24
- L15.4 Instantaneous energy eigenstates and Schrodinger equation 26:47
- L16.1 Quantum adiabatic theorem stated 13:03
- L16.2 Analysis with an orthonormal basis of instantaneous energy eigenstates 14:32
- L16.3 Error in the adiabatic approximation 14:22
- L16.4 Landau-Zener transitions 19:31
- L16.5 Landau-Zener transitions (continued) 14:19
- L17.1 Configuration space for Hamiltonians 15:28
- L17.2 Berry's phase and Berry's connection 25:05
- L17.3 Properties of Berry's phase 11:13
- L17.4 Molecules and energy scales 17:58
- L18.1 Born-Oppenheimer approximation: Hamiltonian and electronic states 24:49
- L18.2 Effective nuclear Hamiltonian. Electronic Berry connection 20:03
- L18.3 Example: The hydrogen molecule ion 27:02
- L19.1 Elastic scattering defined and assumptions 15:36
- L19.2 Energy eigenstates: incident and outgoing waves. Scattering amplitude 25:03
- L19.3 Differential and total cross section 20:21
- L19.4 Differential as a sum of partial waves 17:47
- L20.1 Review of scattering concepts developed so far 09:03
- L20.2 The one-dimensional analogy for phase shifts 16:58
- L20.3 Scattering amplitude in terms of phase shifts 15:00
- L20.4 Cross section in terms of partial cross sections. Optical theorem 13:14
- L20.5 Identification of phase shifts. Example: hard sphere 18:02
- L21.1 General computation of the phase shifts 18:15
- L21.2 Phase shifts and impact parameter 27:39
- L21.3 Integral equation for scattering and Green's function 30:27
- L22.1 Setting up the Born Series 21:08
- L22.2 First Born Approximation. Calculation of the scattering amplitude 13:03
- L22.3 Diagrammatic representation of the Born series. Scattering amplitude for spherically symm... 21:42
- L22.4 Identical particles and exchange degeneracy 19:42
- L23.1 Permutation operators and projectors for two particles 22:23
- L23.2 Permutation operators acting on operators 11:45
- L23.3 Permutation operators on N particles and transpositions 29:40
- L23.4 Symmetric and Antisymmetric states of N particles 11:35
- L24.1 Symmetrizer and antisymmetrizer for N particles 16:50
- L24.2 Symmetrizer and antisymmetrizer for N particles (continued) 24:55
- L24.3 The symmetrization postulate 11:39
- L24.4 The symmetrization postulate (continued) 20:51
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