Chapter 3 - Formalism

Commutator relations

  • Commutation
  • Commutator algebra
  • Hermiticity
  • Dirac bra-ket
  • Length and velocity
  • Acceleration
  • Classical analogy
  • Thomas-Reiche-Kuhn
  • Sum rule
  • Applied to Na
  • Applied to H
  • H continuum contribution
  • Oscillator strength applications

    • Spinors

  • Spin 1/2
  • Other spins
  • Eigenvalues
  • Eigenvectors
  • Transformation
  • Pauli matrices
  • Commutation
  • Operation
  • Summary
  • Relationship to Dirac equation

    • The uncertainty principle

  • Example 3.7
  • Lifetime measurement
  • Energy spectrum
  • Measured value

    • Scalars, vectors and tensors

  • Index notation





































    Apply to the dipole polarizability (Sect. 6.4)

    Quadratic Stark effect
    Applied to Na I and Mg II
    ad isoelectronically
    Mg II extended
    Ca II
    Hydrogen continuum states
    Continuum states and confidence limits
    Invert for lifetimes

    Application of sums to other parameters

    Generalized f and E sums
    Index of refraction of gases
    continued

  • Adiabatic and nonadiabatic polarizabilities
  • Quadrupole polarizability
  • b and aq isoelectronically
  • Generalized f-sums
  • Values for H and inert gases
  • Computations of index
  • Hydrogenic f-sums