MIT 8.06 Quantum Physics III, Spring 2018 (English) (Part 1)

   Monday, December 09, 2024   

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Lecture 1: L1.1 General problem. Non-degenerate perturbation theory

Lecture 2: L1.2 Setting up the perturbative equations

Lecture 3: L1.3 Calculating the energy corrections

Lecture 4: L1.4 First order correction to the state. Second order correction to energy

Lecture 5: L2.1 Remarks and validity of the perturbation series

Lecture 6: L2.2 Anharmonic Oscillator via a quartic perturbation

Lecture 7: L2.3 Degenerate Perturbation theory: Example and setup

Lecture 8: L2.4 Degenerate Perturbation Theory: Leading energy corrections

Lecture 9: L3.1 Remarks on a 'good basis'

Lecture 10: L3.2 Degeneracy resolved to first order; state and energy corrections

Lecture 11: L3.3 Degeneracy resolved to second order

Lecture 12: L3.4 Degeneracy resolved to second order (continued)

Lecture 13: L4.1 Scales and zeroth-order spectrum

Lecture 14: L4.2 The uncoupled and coupled basis states for the spectrum

Lecture 15: L4.3 The Pauli equation for the electron in an electromagnetic field

Lecture 16: L4.4 Dirac equation for the electron and hydrogen Hamiltonian

Lecture 17: L5.1 Evaluating the Darwin correction

Lecture 18: L5.2 Interpretation of the Darwin correction from nonlocality

Lecture 19: L5.3 The relativistic correction

Lecture 20: L5.4 Spin-orbit correction

Lecture 21: L5.5 Assembling the fine-structure corrections

Lecture 22: L6.1 Zeeman effect and fine structure

Lecture 23: L6.2 Weak-field Zeeman effect; general structure

Lecture 24: L6.3 Weak-field Zeeman effect; the projection lemma

Lecture 25: L6.4 Strong-field Zeeman

Lecture 26: L6.5 Semiclassical approximation and local de Broglie wavelength

Lecture 27: L7.1 The WKB approximation scheme

Lecture 28: L7.2 Approximate WKB solutions

Lecture 29: L7.3 Validity of the WKB approximation

Lecture 30: L7.4 Connection formula stated and example

Lecture 31: L8.1 Airy functions as integrals in the complex plane

Lecture 32: L8.2 Asymptotic expansions of Airy functions

Lecture 33: L8.3 Deriving the connection formulae

Lecture 34: L8.4 Deriving the connection formulae (continued) logical arrows

Lecture 35: L9.1 The interaction picture and time evolution

Lecture 36: L9.2 The interaction picture equation in an orthonormal basis

Lecture 37: L9.3 Example: Instantaneous transitions in a two-level system

Lecture 38: L9.4 Setting up perturbation theory

Lecture 39: L10.1 Box regularization: density of states for the continuum

Lecture 40: L10.2 Transitions with a constant perturbation

Lecture 41: L10.3 Integrating over the continuum to find Fermi's Golden Rule

Lecture 42: L10.4 Autoionization transitions

Lecture 43: L11.1 Harmonic transitions between discrete states

Lecture 44: L11.2 Transition rates for stimulated emission and absorption processes

Lecture 45: L11.3 Ionization of hydrogen: conditions of validity, initial and final states

Lecture 46: L11.4 Ionization of hydrogen: matrix element for transition

Lecture 47: L12.1 Ionization rate for hydrogen: final result

Lecture 48: L12.2 Light and atoms with two levels, qualitative analysis

Lecture 49: L12.3 Einstein's argument: the need for spontaneous emission

Lecture 50: L12.4 Einstein's argument: B and A coefficients

Lecture 51: L12.5 Atom-light interactions: dipole operator