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Search Results (3)

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Keywords = the Abraham–Lorentz equation

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13 pages, 271 KB  
Review
Classicalization of Quantum Mechanics: Classical Radiation Damping Without the Runaway Solution
by Tomio Petrosky, Yuki Goto and Savannah Garmon
Physics 2024, 6(4), 1191-1203; https://doi.org/10.3390/physics6040073 - 22 Oct 2024
Cited by 2 | Viewed by 3780
Abstract
In this paper, we review a new treatment of classical radiation damping, which resolves a known contradiction in the Abraham–Lorentz equation that has long been a concern. This radiation damping problem has already been solved in quantum mechanics by the method introduced by [...] Read more.
In this paper, we review a new treatment of classical radiation damping, which resolves a known contradiction in the Abraham–Lorentz equation that has long been a concern. This radiation damping problem has already been solved in quantum mechanics by the method introduced by Friedrichs. Based on Friedrichs’ treatment, we solved this long-standing problem by classicalizing quantum mechanics by replacing the canonical commutation relation from quantum mechanics with the Poisson bracket relation in classical mechanics. Full article
(This article belongs to the Special Issue Matter-Radiation Interactions—In Memory of Professor Francesco Saverio Persico)
8 pages, 350 KB  
Article
On the Schott Term in the Lorentz-Abraham-Dirac Equation
by Tatsufumi Nakamura
Quantum Beam Sci. 2020, 4(4), 34; https://doi.org/10.3390/qubs4040034 - 28 Sep 2020
Cited by 4 | Viewed by 6249
Abstract
The equation of motion for a radiating charged particle is known as the Lorentz–Abraham–Dirac (LAD) equation. The radiation reaction force in the LAD equation contains a third time-derivative term, called the Schott term, which leads to a runaway solution and a pre-acceleration solution. [...] Read more.
The equation of motion for a radiating charged particle is known as the Lorentz–Abraham–Dirac (LAD) equation. The radiation reaction force in the LAD equation contains a third time-derivative term, called the Schott term, which leads to a runaway solution and a pre-acceleration solution. Since the Schott energy is the field energy confined to an area close to the particle and reversibly exchanged between particle and fields, the question of how it affects particle motion is of interest. In here we have obtained solutions for the LAD equation with and without the Schott term, and have compared them quantitatively. We have shown that the relative difference between the two solutions is quite small in the classical radiation reaction dominated regime. Full article
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12 pages, 696 KB  
Article
The Role of Vacuum Fluctuations and Symmetry in the Hydrogen Atom in Quantum Mechanics and Stochastic Electrodynamics
by G. Jordan Maclay
Atoms 2019, 7(2), 39; https://doi.org/10.3390/atoms7020039 - 31 Mar 2019
Cited by 2 | Viewed by 5207
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, [...] Read more.
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. Full article
(This article belongs to the Special Issue Stochastic Electrodynamics)
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