Chapter 2 - Atomic Structure and Lifetimes
Semiclassical Conceptual Models

  • Discover Magazine - Lee Smolin

    • Part I: Classical Position Probability Densities (Sect.2.1.1)

  • Announcement
  • Källén Prize

    • Gas laws

  • Microscopic origin of pressure
  • End-on dipole
  • Induced dipole
  • 6-12 potential
  • Not really 12
  • van der Waals equation
  • Is pressure a force or an energy?
  • Animation I
  • Animation II

    • Molecule in a room (Sect. 2.1.2)

  • Probability formulation
  • EBK box quantization
  • Energy levels
  • Classical and BSW
  • Mean position
  • Mean square position
  • Measurements
  • Variance and standard deviation
  • Variance of distributions
  • Experimental testing

    • Harmonic oscillator (Sect. 2.3.3)

  • Generalized formulation
  • SHO average values
  • Action quantization
  • Classical and BSW
  • Summary
  • Anharmonic well
  • Perturbation expansion
  • Accepted QM solution
  • Animation
  • Comparison with box and Kepler

    Generalize to numerical solution of arbitrary potentials

  • Formulation
  • Exercise
  • Solution

    Semiclassical Quantization (Sect. 2.3)

  • BSW Quantization
  • EKB Quantization
  • EKB References
  • Sommerfeld and Caustics
  • Caustic animation
  • In original language
  • A.Einstein, Deutsche Physikalische Gesellschaft 19 (1917).
  • Stone essay
  • J.B. Keller, Ann. Phys. (NY) 4, 180 (1958).
  • Semiclassical self-consistent fields

    • Part II: The Kepler-Coulomb Potential (Sect. 2.4)

    The probabilistic Kepler problem

  • Kepler's laws
  • 3rd law from circular case
  • Virial theorem
  • Radial probabilities
  • Conservation laws
  • The radial derivative

    • Average values of powers of r (Sect. 2.4.3)

  • Kepler average values from radial distribution
  • Kepler average values from SHO solution
  • Kepler average values from azimuthal distribution
  • Laplace integral
  • Legendre polynomials
  • Classical values for rk
  • Classical values for rk
  • Quantum values for rk
  • Avg for powers of r
  • Atomic perturbations

    • The EKB Kepler problem (Sect. 2.4.4)

  • Spherical polar coordinates
  • Generalized momenta
  • Action formulation
  • Nonrel angle-action
  • Classical and QM observables
  • EBK ellipses and probabilities
  • EBK orbits, n=1,2,3
  • EBK orbits, n=4
  • Emission spectrum
  • Balmer series

    • EBK and QM radial wave functions (Sect. 2.4.5)

  • EBK Summary
  • Y(1s), Y(2s),Y(2p)
  • Y(3s), Y(3p),Y(3d)
  • Y(n=40,l=20)
  • Orbital distributions
  • Electron configurations
  • QM and classical
  • More QM Distributions
  • Morphologies
  • Eta Carina
  • More morphologies
  • High res
  • Yet another morphology

    • Trojan asteroids

  • Lagrange points
  • 2.7 degree BBrad
  • WMAP
  • Trojan asteroids (animation)
  • Wave packets of high Rydberg states
  • Whole number of heartbeats per cycle

    Three recent publications

  • Curtis & Ellis, Use of the EBK action quantization, Am.J.Phys. 72 1521 (2004)
  • Curtis & Ellis, Probabilities as a Bridge between Classical & QM Treatments, Eur.J.Phys. (in press)
  • Larkoski, Ellis, & Curtis, Numerical implementation of the EBK quantization for arbitrary potentials, Am.J.Phys. (submitted)

    • Part III: Applications to atoms and planets (Sect. 2.4.7)

  • Perturbations
  • Orbital precession

    • Mechanics and electrodynamics of moving bodies

  • Maxwell's equations
  • Invariance of the speed of light
  • Apparent length contraction applet
  • Apparent time dilation applet
  • Why does length contract and time dilate?
  • Model for magnetism
  • Force between a moving charge and a current
  • Reverse direction
    Priority
  • Einstein, Ann. Phys. Chim. 17, 890-921 (1905).
  • English translation
  • Woldemar Voigt's 1887 discovery
  • Voigt bio

    • Relativistic corrections to the kinetic energy (Sect. 2.4.8)

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

    • Magnetic moments

  • Torque on a current loop
  • Magnetic moment of an orbiting charge
  • Magnetic moment of a Dirac electron
  • Speed of an electron of finite radius
  • Zitterbewegung of a point charge
  • Zitterbewegung animation

    • Relativistic corrections to the potential energy (Sect. 2.4.9)

  • Spin-orbit fine structure
  • EBK and QM formulations
  • Foldy-Wouthuysen transformation
  • Gen.Rel. and Spin-Orbit
  • The Triplets of Belleville and Einstein

    • Combining relativistic corrections

  • Combining relativistic mass and spin-orbit
  • Explicit calculations for spin 1/2
  • Expansion of the Dirac equation
  • Strengths of internal fields
  • Thomas precession g-1, not g/2

    • Core polarization model (Sect. 2.4.10)

  • Hydrogen, hydrogenlike, and Rydberg atoms
  • Nonpenetrating orbits
  • EBK formulation of polarization
  • Multipole expansion
  • The two-center problem
  • Dipole moments
  • Multipoles in external fields
  • Quadrupole moments
  • EKB expectation values
  • Na-like P IV example
  • Schrödinger expectation values

    • The quantum defect parametrization

  • Expansion of Rydberg's formula
  • n-dependence of powers of r

    • Planetary perturbations (Sect. 2.4.11)

  • Potential due to a ring
  • Perturbations of the Planets
  • Masses and orbital data
  • Average powers of r
  • Effects on the period of Mercury
  • Test of relativity

    • Part IV: Self-Consistent Fields for Many-Electron Atoms (Sect. 2.4.12)

    Point nucleus with homogeneous electron cloud

  • Potential energy with screening
  • Internal and external screening
  • 1-D radial probability distribution
  • Semimajor axes from energies

    • Semiclassical Self Consistent Field Calculations

  • EBK for the Many-Body Problem
  • Newton-Raphson method
  • Y(QM) and Y(EBK)
  • Comparison with HF for Na seq

    • Relativistic Semiempirical Formulation (Sect. 2.4.13)

  • Artifact in Cu seq
  • Relativistic radial momentum
  • Convert to atomic units
  • Turning points
  • Relativistic EBK quantization
  • Expansion of relativistic energy
  • Collapse of the Maslov Perihelion
  • Calculated examples of turning points

    • Part V: Time Dependent Processes (Sect. 2.5)

    Larmor's formula

  • Maxwell Radiation
  • Classical vs QM

    Wien's model (Sect. 2.5.1)

  • Wien model
  • Correspondence limit
  • Compare to QM
  • Large n limit
  • Worst case value
  • Wien's paper (1)
  • Wien's paper (2)
  • Wien's paper (3)
  • Comparison
  • Blending
  • Branched decay

    • Oscillator strength (Sect. 2.5.2)

  • Merzbacher's QM book
  • Blade article
  • Physics Letters article
  • Lorentz-Drude model
  • Express as oscillators
  • Oscillator strength
  • Relationships between absorption and emission
  • Kleppner essay

    • Chapter 1
    Bridge A
    Chapter 3
    Chapter 4
    Bridge B
    Chapter 5
    Chapter 6

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