The Role of Vacuum Fluctuations and Symmetry in the Hydrogen Atom in Quantum Mechanics and Stochastic Electrodynamics

G Maclay

doi:10.3390/atoms7020039

Abstract

Stochastic Electrodynamics (SED) has had success modeling black body radiation, the harmonic oscillator, the Casimir effect, van der Waals forces, diamagnetism, and uniform acceleration of electrodynamic systems using the stochastic zero-point fluctuations of the electromagnetic field with classical mechanics. However the hydrogen atom, with its 1/r potential remains a critical challenge. Numerical calculations have shown that the SED field prevents the electron orbit from collapsing into the proton, but, eventually the atom becames ionized. We look at the issues of the H atom and SED from the perspective of symmetry of the quantum mechanical Hamiltonian, used to obtain the quantum mechanical results, and the Abraham-Lorentz equation, which is a force equation that includes the effects of radiation reaction, and is used to obtain the SED simulations. We contrast the physical computed effects of the quantized electromagnetic vacuum fluctuations with the role of the real stochastic electromagnetic field.

Highlights

The hydrogen atom has been the testing ground for theoretical atomic physics for over a hundred years
Precision measurements of hydrogen energy levels by Willis Lamb in 1947 disagreed with the theory, which stimulated the development of Quantum Electrodynamics (QED), which included the effects of the vacuum fluctuations of the quantized electromagnetic field
In the quantum mechanical H atom there is no radiation from the electron due to the standing wave nature of the electron orbitals when the atom is in a stationary state

Summary

Introduction

The hydrogen atom has been the testing ground for theoretical atomic physics for over a hundred years. Precision measurements of hydrogen energy levels by Willis Lamb in 1947 disagreed with the theory, which stimulated the development of Quantum Electrodynamics (QED), which included the effects of the vacuum fluctuations of the quantized electromagnetic field. Stochastic electrodynamics (SED) represents an effort to explain quantum phenomena through classical physics done in the presence of a real stochastic electromagnetic field which is the sum of a portion for T = 0 with spectral energy density ρ(ω ) = hω 3 /2π 2 c3 , identical to that of the virtual zero-point vacuum fluctuations of the quantized electromagnetic field in QED, plus a Planckian spectrum for a finite temperature T > 0. We will contrast the approach of quantum mechanics with that of SED, discussing the role of vacuum fluctuations in both theories. We discuss the most recent SED calculations which have shown stability for a limited number of orbits, but ionization for longer times [3,4]

Role of Vacuum Fluctuations in Quantum Mechanics and SED

The Hydrogen Atom in Quantum Mechanics and Classical Mechanics with No

The Hydrogen Atom in SED

SED Simulations of the Ground State of the H Atom

Discussion