Chapter 6 - Time-Independent Perturbation Theory
Semiclassical applications to atoms and planets

Perturbation theory (Griffiths pp. 249-266)

  • 1st order perturbation theory
  • 2nd order
  • Kepler-Coulomb in zeroth order
  • Orbital precession
  • Power law perturbations
  • Moments of r

    • Dwell time of falling objects

  • Formulation
  • Average values
  • Perturbation with altitude

    • Harmonic oscillator

  • Unperturbed solution
  • Anharmonic well
  • Perturbation expansion
  • Accepted QM solution
  • 2nd order corrections

    • Mechanics and electrodynamics of moving bodies

  • Maxwell's equations
  • Woldemar Voigt's 1887 discovery
  • Voigt bio
  • Invariance of the speed of light
  • Apparent length contraction applet
  • Apparent time dilation applet
  • Why does length contract and time dilate?
  • Do we get small?

    Is it about rocket ships?

  • Einstein, Ann. Phys. Chim. 17, 890-921 (1905).
  • English translation
  • Model for magnetism
  • Force between a moving charge and a current
  • Reverse direction

    • Nature is symmetric in space and time

  • The Lumière brothers
  • The dawn of time reversal
  • Slow-motion photography
  • Stop action
  • Time-lapse photography
  • Reverse-action photography
  • Time reversal

    • Relativistic corrections to the kinetic energy (Griffiths pp. 266-270)

  • Mass-energy: just a units conversion
  • Rotations among four-vectors
  • Space-time transformations of momentum and energy
  • Special Relativity Corrections
  • With quantization
  • Agrees with QM

    • Relativistic corrections to the potential energy (Griffiths pp. 271-274)

  • Magnetic moment of a Dirac electron
  • Spin-orbit fine structure
  • EBK and QM formulations
  • Darwin correction, Zitterbewegung, and EBK

    Compare gravitational and electromagnetic

  • Kepler & Coulomb corrections
  • Gen.Rel. and Spin-Orbit
  • The Triplets of Belleville and Einstein
  • Gravitation spin-orbit coupling?

    • Combining relativistic corrections (Griffiths pp. 274-276)

  • Combining relativistic mass and spin-orbit
  • Explicit calculations for spin 1/2

  • Expansion of the Dirac equation
  • Nested binomial expressions
  • Collecting terms and shifting sums
  • Formulation
  • Coefficients

  • Thomas precession g-1, not g/2
  • Griffith
  • Lamb shift

    • The Landé interval rule

  • Landé interval rule
  • Examples: Boron
  • continued

    • External magnetic fields (Griffiths pp. 277-283)

  • The earth and moon
  • Spin-orbit vector sums
  • Landé g-factor
  • Anomalous Zeeman effect
  • Anom. Zeeman (continued)
  • Grotrian diagram
  • Zeeman splitting
  • Sunspots
  • Sigma and pi radiation
  • Dipole radiation pattern

  • Strong field decoupling of L and S
  • Paschen-Back effect
  • Splitting with increasing field
  • Level crossing
  • Very strong fields

    • The quantum defect parametrization

  • Hydrogen, hydrogenlike, and Rydberg atoms
  • Rydberg's seminar
  • Expansion of Rydberg's formula
  • n-dependence of powers of r
  • Phase shift
  • Parametrization
  • Non-Coulombic EBK formulation
  • Large r limit
  • Ritz expansion

  • Quantum defect on both sides?
  • Iteration example
  • Iteration example 2


  • Data parametrization
  • Slope
  • Polarization slope
  • Penetration and polarization
  • continued

    • Midterm Exam - Wednesday 19 March 2008

    Core polarization model

  • Nonpenetrating orbits
  • EBK formulation of polarization
  • Multipole expansion
  • The two-center problem
  • Legendre polynomials
  • Dipole moments
  • Multipoles in external fields
  • Quadrupole moments
  • EKB expectation values
  • Schrödinger expectation values
  • Na-like P IV example

    • Second order perturbation theory (Griffiths pp. 255-256, 289-292)

  • Linear Stark effect
  • Quadratic Stark effect
  • Mg II

    • Planetary perturbations

  • Potential due to a ring
  • Legendre polynomials
  • Perturbations of the Planets
  • Average powers of r
  • Moments
  • Masses and orbital data
  • Effects on the period of Mercury
  • Precession
  • Lowest order
  • Test of relativity

    • Hyperfine structure (Griffiths pp. 283-285)

  • Overview
  • Summary of contributions
  • Michelson's Ryerson speech
  • Michelson's Nobel lecture
  • Structure of the nucleon

  • Finite size of the nucleus
  • Perturbative correction
  • H wave function
  • 1s level (exact to 1st order)
  • Approximate solution
  • Isotope shifts

    • Defer until later, if time permits

    Magnetic dipole contribution (Griffiths pp. 283-285)

  • Link to background material
  • Magnetic dipole interaction
  • Magnetic field
  • Vector algebra
  • Pauli spin matrices
  • Commutation rules
  • Energy
  • Stretch and jacknife

    • Fermi contact term

  • QM and EBK
  • Darwin term
  • Magnetized sphere

    • Baryon mass formulae

  • Isospin and hypercharge
  • Baryon terms
  • Perturbation
  • Intermediate coupling
  • J=1/2 octet
  • Model
  • J=3/2 decuplet
  • Gell-Mann Okuba formula
  • Three spectroscopies

    • Schmidt model for nucleon magnetic dipole moments

  • Independent particle model
  • Spin-orbit coupling
  • Stretch and jacknife states
  • Dirac moment g-factors
  • Data plot for odd-even
  • Data plot for even-odd
  • Plots of odd-even and even-odd isotopes