Källén Prize

continued

van der Waals equation

Multipoles by differentiation

Dipole-dipole interaction

Force or energy?

Exclusion principle

EBK box quantization

Classical and BSW

Mean position

Mean square position

Variance and standard deviation

Electron in a cell

Energy levels

Measurements

SHO average values

Summary

Action quantization

Classical and BSW

Anharmonic well

Perturbation expansion

Accepted QM solution

Chaos

Einstein, Deutsche Physikalische Gesellschaft 19,(1917) (translation)

EBK Quantization

EBK References

J.B. Keller, Ann.Phys. (NY) 4, 180 (1958).

Sommerfeld and Caustics

Caustic animation

Kepler's laws

Kepler applet

perimeter

Kepler in probabilities

Conservation laws

The radial derivative

Kepler distribution

Azimuthal alternative

Laplace integral

Legendre polynomials

Classical values for

Symmetry about k=-3/2

Expansion of Rydberg's formula

Quantum values for

Atomic perturbations

Generalized momenta

Action formulation

Nonrel angle-action

Classical vs QM results

EKB orbits, n=4

EKB orbits, n=1,2,3

Periapsis and apoapsis

nd orbitals

Y(3s), Y(3p),Y(3d)

Y(n=40,

QM distributions

Classical vs QM

continued

Woldemar Voigt's 1887 discovery

Voigt bio

Einstein, Ann. Phys, Chim

English translation

Length contraction and time dilation

Model for a current in a wire

Force between a moving charge and a current

Reverse direction

Average value of KE-squared

EBK values

Magnetic moment of an orbiting charge

Magnetic moment of a Dirac electron

Speed of an electron of finite radius

Zitterbewegung of a point charge

Gen.Rel. and spin-orbit

EKB and QM formulations

Classical and QM

Strengths of internal fields

Thomas precession g-1, not g/2

Explicit calculations for spin 1/2

Expansion of the Dirac equation

The two-center problem

Multipole expansion

Multipole energy corrections

Classical formulation

EBK expectation values

Na-like P IV example

Polarization plot

Potential due to a ring of charge

Perturbations of the Planets

Masses and orbital data

Effects on the period of Mercury

Test of relativity

1-D radial probability distribution

Newton-Raphson method

Schematic

EBK for the Many Body Problem

Y(QM) and Y(EBK)

Comparison with HF for Na seq

Artifact in Cu seq

In terms of alpha

Repeat SCSCF

Collapse of the Maslov Perihelion

Calculated examples of turning points

Redistribution

Relativistic angle-action

Classical vs QM

Wien model

Compare with experiment

Expelling two action quanta

Compare to QM

Large

Worst case value

Blending

Noble employment

Review

Express as oscillators

Relationships between absorption and emission

Chapt. 1

Chapt. 3

Chapt. 4

Chapt. 5

Chapt. 6

Chapt. 7

Chapt. 8

Chapt. 9

Chapt. 10

Chapt. 11

Chapt. 12

Chapt. 13

Homepage

Trojan asteroids (still)

Wave packets of high Rydberg states

Animation

Whole number of heartbeats per cycle

Box, SHO, Kepler

Wavelengths of light emitted