Lecture 43 of 100Time Dependent Perturbation Theory and Adiabatic Approximation16 min
L11.1 Harmonic transitions between discrete states
Prof. Barton Zwiebach · Massachusetts Institute of Technology
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- Quantum Physics III, Massachusetts Institute of Technology (at MIT OpenCourseWare)
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- CC BY-NC-SA 4.0, as MIT OpenCourseWare states it. Non-commercial use only.
- Attribution
- Prof. Barton Zwiebach. Quantum Physics III. Spring 2018. Massachusetts Institute of Technology: MIT OpenCourseWare, https://ocw.mit.edu/. License: Creative Commons BY-NC-SA.
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All the lectures
- L1.1 General problem. Non-degenerate perturbation theory
- L1.2 Setting up the perturbative equations
- L1.3 Calculating the energy corrections
- L1.4 First order correction to the state. Second order correction to energy
- L2.1 Remarks and validity of the perturbation series
- L2.2 Anharmonic Oscillator via a quartic perturbation
- L2.3 Degenerate Perturbation theory: Example and setup
- L2.4 Degenerate Perturbation Theory: Leading energy corrections
- L3.1 Remarks on a "good basis"
- L3.2 Degeneracy resolved to first order; state and energy corrections
- L3.3 Degeneracy resolved to second order
- L3.4 Degeneracy resolved to second order (continued)
- L4.1 Scales and zeroth-order spectrum
- L4.2 The uncoupled and coupled basis states for the spectrum
- L4.3 The Pauli equation for the electron in an electromagnetic field
- L4.4 Dirac equation for the electron and hydrogen Hamiltonian
- L5.1 Evaluating the Darwin correction
- L5.2 Interpretation of the Darwin correction from nonlocality
- L5.3 The relativistic correction
- L5.4 Spin-orbit correction
- L5.5 Assembling the fine-structure corrections
- L6.1 Zeeman effect and fine structure
- L6.2 Weak-field Zeeman effect; general structure
- L6.3 Weak-field Zeeman effect; the projection lemma
- L6.4 Strong-field Zeeman
- L6.5 Semiclassical approximation and local de Broglie wavelength
- L7.1 The WKB approximation scheme
- L7.2 Approximate WKB solutions
- L7.3 Validity of the WKB approximation
- L7.4 Connection formula stated and example
- L8.1 Airy functions as integrals in the complex plane
- L8.2 Asymptotic expansions of Airy functions
- L8.3 Deriving the connection formulae
- L8.4 Deriving the connection formulae (continued) logical arrows
- L9.1 The interaction picture and time evolution
- L9.2 The interaction picture equation in an orthonormal basis
- L9.3 Example: Instantaneous transitions in a two-level system
- L9.4 Setting up perturbation theory
- L10.1 Box regularization: density of states for the continuum
- L10.2 Transitions with a constant perturbation
- L10.3 Integrating over the continuum to find Fermi's Golden Rule
- L10.4 Autoionization transitions
- L11.1 Harmonic transitions between discrete states
- L11.2 Transition rates for stimulated emission and absorption processes
- L11.3 Ionization of hydrogen: conditions of validity, initial and final states
- L11.4 Ionization of Hydrogen: Matrix Element for Transition
- L12.1 Ionization Rate for Hydrogen: Final Result
- L12.2 Light and Atoms with Two Levels, Qualitative Analysis
- L12.3 Einstein's Argument: the Need for Spontaneous Emission
- L12.4 Einstein's argument: B and A coefficients
- L12.5 Atom-light interactions: dipole operator
- L13.1 Transition rates induced by thermal radiation
- L13.2 Transition rates induced by thermal radiation (continued)
- L13.3 Einstein's B and A coefficients determined. Lifetimes and selection rules
- L13.4 Charged particles in EM fields: potentials and gauge invariance
- L13.5 Charged particles in EM fields: Schrodinger equation
- L14.1 Gauge invariance of the Schrodinger Equation
- L14.2 Quantization of the magnetic field on a torus
- L14.3 Particle in a constant magnetic field: Landau levels
- L14.4 Landau levels (continued). Finite sample
- L15.1 Classical analog: oscillator with slowly varying frequency
- L15.2 Classical adiabatic invariant
- L15.3 Phase space and intuition for quantum adiabatic invariants
- L15.4 Instantaneous energy eigenstates and Schrodinger equation
- L16.1 Quantum adiabatic theorem stated
- L16.2 Analysis with an orthonormal basis of instantaneous energy eigenstates
- L16.3 Error in the adiabatic approximation
- L16.4 Landau-Zener transitions
- L16.5 Landau-Zener transitions (continued)
- L17.1 Configuration space for Hamiltonians
- L17.2 Berry's phase and Berry's connection
- L17.3 Properties of Berry's phase
- L17.4 Molecules and energy scales
- L18.1 Born-Oppenheimer approximation: Hamiltonian and electronic states
- L18.2 Effective nuclear Hamiltonian. Electronic Berry connection
- L18.3 Example: The hydrogen molecule ion
- L19.1 Elastic scattering defined and assumptions
- L19.2 Energy eigenstates: incident and outgoing waves. Scattering amplitude
- L19.3 Differential and total cross section
- L19.4 Differential as a Sum of Partial Waves
- L20.1 Review of Scattering Concepts Developed So Far
- L20.2 The One-Dimensional Analogy for Phase Shifts
- L20.3 Scattering Amplitude in Terms of Phase Shifts
- L20.4 Cross Section in Terms of Partial Cross Sections. Optical Theorem
- L20.5 Identification of Phase Shifts. Example: Hard Sphere
- L21.1 General Computation of the Phase Shifts
- L21.2 Phase Shifts and Impact Parameter
- L21.3 Integral Equation for Scattering and Green's Function
- L22.1 Setting Up the Born Series
- L22.2 First Born Approximation. Calculation of the Scattering Amplitude
- L22.3 Diagrammatic Representation of the Born series. Scattering Amplitude for Spherically Symmetric Potentials
- L22.4 Identical Particles and Exchange Degeneracy
- L23.1 Permutation Operators and Projectors for Two Particles
- L23.2 Permutation Operators Acting on Operators
- L23.3 Permutation Operators on N Particles and Transpositions
- L23.4 Symmetric and Antisymmetric States of N Particles
- L24.1 Symmetrizer and Antisymmetrizer for N Particles
- L24.2 Symmetrizer and Antisymmetrizer for N Particles (continued)
- L24.3 The Symmetrization Postulate
- L24.4 The Symmetrization Postulate (continued)