Chapter 2
Semiclassical Conceptual Models

Part I: Classical Position Probability Densities

Announcement
Källén Prize

Molecule in a room

Microscopic origin of pressure
Probability formulation
Classical and BSW
Quantization
Energy levels
Experimental testing
The median isn't the message

Harmonic oscillator

Generalized formulation
Classical and BSW
SHO average values
Anharmonic well
Perturbation expansion
Exact solution

Semiclassical Quantization

BSW Quantization
EKB Quantization
EKB References
Sommerfeld and Caustics
Caustic animation
Feynman and least action

Part II: The Kepler-Coulomb Potential

The probabilistic Kepler problem

Kepler's laws
Kepler in Probabilities
The radial derivative
Kepler distribution
Box, SHO, Kepler
Kepler average values
Azimuthal alternative
Laplace integral
Legendre polynomials
Avg for powers of r
Classical values for rk
Quantum values for rk
Atomic perturbations

The EKB Kepler problem

Generalized momenta
Action formulation
Nonrel angle-action
  • Cauchy's integral theorem
  • Poles of the Kepler problem
  • The Balmer energy
  • Turning points
  • The angular libration integral
    EKB elliptic orbits
    Periapsis and apoapsis
    nd orbitals
    Classical and QM k operators
    Classical and QM observables

    • EBK and QM radial wave functions

    Y(1s), Y(2s),Y(2p)
    Y(3s), Y(3p),Y(3d)
    Y(n=40,l=20)
    QM Distributions
    QM Distributions
    Orbital Distributions
    Morphologies
    Eta Carina
    Morphologies (continued)
    More Morphologies

    Part III: Applications to Atoms and Planets

    Perturbed energy and Precession

    Relativistic corrections

    Special Relativity Corrections
    Force between a moving charge and a current
    Zur Elektrodynamik bewegter Körper
    Woldemar Voigt's 1887 discovery
    Voigt bio
    Torque on a current loop
    Magnetic moment of an orbiting charge
    Magnetic moment of a Dirac electron
    Spin-orbit fine structure
    Spin-orbit fs (continued)
    Combining relativistic mass and spin-orbit
    Rel. mass and spin-orbit (continued)
    Explicit calculations for spin 1/2
    Gen.Rel. and Spin-Orbit

    Core polarization model

    Multipole expansion
    Dipole moments
    Quadrupole moments
    Expectation value expansion
    Hydrogenic expectation values
    Non-penetrating orbits

    Planetary perturbations

    The two-center problem
    Expansion for a smeared ring of mass
    Perturbations of the Planets
    Effects on the period of Mercury

    Part IV: Self-Consistent Fields for Many-Electron Atoms

    Semiclassical Self-Consistent Field Calculations

    Generalized Momenta
    EBK for the Many Body Problem
    Potential energy with screening
    Internal and external screening
    Iterate effective potential
    Newton-Raphson method
    Comparison with HF for Na seq
    Y(QM) and Y(EBK)
    Artifact in Cu seq

    Relativistic Semiempirical Formulation

    Perihelions and Aphelions
    Lorentz potential
    Relativistic Hamiltonian
    Relativistic generalized momenta
    Relativistic formulation
    Perihelion and aphelion
    Collapse of the Maslov Perihelion
    Relativistic angle-action

    Part V: Time-Dependent Processes

    Semiempirical formulation of the decay meanlife

    Maxwell Radiation
    Classical vs QM
    Wien's paper
    Wien's paper (cont)
    Wien model
    Compare to QM
    Large n limit
    Worst case value
    Classical vs QM
    Noble employment
    Orbital Ages

    Chapt. 1
    Chapt. 3
    Chapt. 4
    Chapt. 5
    Chapt. 6
    Chapt. 7
    Chapt. 8
    Chapt. 9
    Chapt. 10
    Chapt. 11
    Chapt. 12
    Chapt. 13

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