Lamb Shift and Sub-Compton Electron Dynamics: Dirac Hydrogen Wavefunctions without Singularities
51Google Tech Talk
October 16, 2015
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Presented by Lloyd Watts
ABSTRACT
The Schrodinger Hydrogen Atom does not explain spin or fine structure, and has wavefunctions with cusps at the origin. The Dirac Hydrogen Atom explains spin and fine structure, but does not explain Lamb Shift, and has wavefunctions that are singular at the origin. Quantum Electrodynamics (QED) explains Lamb Shift but appears to be silent on how the wavefunctions are affected and whether the wavefunction singularities are removed. In this work, we use perturbation analysis to show that the Lamb Shift is consistent with electron charge spreading inside the half-reduced Compton Wavelength, and we develop a novel numerical technique for solving the Dirac Hydrogen problem with a modified Coulomb potential, and use it to find the form of the modified Dirac Hydrogen wavefunctions. We show that the singularity at the origin of the Dirac Hydrogen wavefunction is eliminated, with a small amount of charge density near the origin displaced radially outward. The near-constant behavior of the Bethe Logarithm out to its asymptotic limit leads to a novel suggestion that this charge spreading for a bound electron in a Hydrogen Atom may also occur for a free electron. We also show novel 3D visualizations of numerical Dirac equation simulations. And finally, we show a novel physical demonstration of Spin ½ that illustrates the four Dirac Bi-spinor basis functions.
SPEAKER INFO
Lloyd Watts, founder of Audience, Inc., Caltech C.S. Ph.D., has been doing some physics recently.