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MITOCW 8.06 - Quantum physics 3 (General problem. non-degenerate…
MITOCW 8.06 - Quantum physics 3
General problem. non-degenerate perturbation theory
Setting up the perturbative equations
Calculating the energy corrections
First order corrections to the state. second order correction to energy
Remarks and validity of the perturbation series
Anharmonic oscillator via quartic perturbation
Degenerate perturbation theory: example and setup
Degenerate perturbation theory: leading energy corrections
Remarks on a good basis
Degeneracy resolved to first order; state and energy correction
Degeneracy resolved to second order
Scales and zeroth-order spectrum
The uncoupled and coupled basis states for the spectrum
The pauli equation for the electron in an electromagnetic field
Dirac equation for the electron and hydrogen hamiltonian
Evaluating the darwin correction
Interpretation of the darwin correction from nonlocality
The relativistic correction
Spin-orbit correction
Assembling the fine-structure corrections
Zeeman effect and fine structure
Weak-field zeeman effect; general structure
Weak field zeeman effect; the projection lemma
Strong-field zeeman
Semiclassical approximation and local de broglie wavelength
the WKB approximation scheme
Approximate WKB solutions
Validity of the WKB approximation
Connection formula stated and example
Airy functions as integrals in the complex plane
Asymptotic expansions of airy functions
Deriving the connection formulae
Deriving the connection formulae (continued) logical arrows
The interaction picture and time evolution
The interaction picture equation in an orthonormal basis
Example: instantaneous transitions in a two-level system
Setting up perurbation theory
Box regulation: density of states for the continuum
Transition with a constant perturbation
Integrating over the continuum to find fermi's golden rule
Autoionization transitions
Harmonic transitions between discrete states
Trasition rates fro stimulated emission and absorption processes
Ionization of hydrogen: conditions of validity, initial and final states
Ionization of hydrogen: matrix element for transition
Ionization rate for hydrogen: final results
Light and atoms with two levels, qualitative analysis
Einstein's argument: the need for spontaneous emission
Einstein's argument: B and A coefficient
Atom-light interactions: dipole operator
Transition rates induced by thermal radiation
Transition rates induced by thermal radiation (continued)
Einstein's B and A coefficients determined. Lifetimes and selection rules
Charged particles in EM fields: potentials and gauge invariance
Charged particles in EM fields: Schrodinger equation
Gauge invariance of the schrodinger equation
Quantization of the magnetic field on a torus
Particle in a constant magnetic field: landau levels
Landau levels (continued). Finite sample
Classical analog: oscillator with slowly varying frequency
Classical adabatic invariant
Phase space and intuition for quantum adabatic invariants
Instantaneous energy eigenstates and Schrodinger equation
Quantum adiabatic theorem stated
Analysis with an orthonormal basis of instantaneous energy eigenstates
Error in the adabatic approximation
Landau-Zener transitions
Landau-Zener transitions (continued)
Configuration space for hamiltonians
Berry's phase and Berry's connection
Properties of Berry's phase
Molecules and energy scales
Born-Oppenheimer approximation: hamiltonian and electronic states
Effective nuclear hamiltonian. electronic berry connection
Example: the hydrogen molecule ion
Elastic scattering defined and assimptions
Energy eigenstates: incident and outgoing waves. scattering amplitude
Differential and total cross section
Differential as a sum of partial waves
Review of scattering concepts developed so far
The one-dimensional analogy for phase shifts
Scattering amplitude in terms of phase shifts
Cross section in terms of partial cross sections. Optical theorem
Identification of phase shifts. example: hard sphere
General computation of the phase shifts
Phase shifts and impact parameter
Integral eqation for scattering and green's function
Setting up the born series
First born approximation. Calculation of the scattering amplitude
Diagrammatic representation of the born series. scattering amplitude for spherically symm...
Identical particles and exchange degeneracy
Permutation operators and projectors for two particles
Permutation operators acting on operators
Permutation operators on N particles and transpositions
Symmetric and Antisymmetric states of N particles
Symmetrizer and antisymmetrizer for N particles
Symmetrizer and antisymmetrizer for N particles (continued)
The symmetrization postulate
The symmetrization postulate (continued)