Simulation Aspects of the Classical Hydrogen Atom Problem


Several examples are shown below of simulation work involving a nonrelativistic classical electron particle orbiting an infinitely massive classical proton, under a variety of conditions. The underlying physics is briefly described here, but for a full understanding of what is happening, please see the recent article that has been submitted for publication in the "Journal of Scientific Computing. (This material was also presented by Prof. Dan Cole and Yi Zou at a special international workshop on stochastic electrodynamics, at Boston University, on June 4, 2001. To view the actual report,
Click Here or go to Prof. Dan Cole's publications page.

All the orbits shown here start with the electron in a circular orbit with radius 0.5 Angstroms.

All of the following simulations are currently being drafted and will be availible in the near future.

View Orbit: Case 1

Case 1: Here, one sees a particle following a circular motion around a center. This simulation contains no radiation reaction. Consequently, the circular motion continues indefinitely.

View Orbit: Case 2

Case 2: The only force acting is the Coulombic interaction between the proton and electron. However, as opposed to Case 1, here classical radiation reaction is assumed to exist. As the electron orbits the proton, electromagnetic radiation is radiated off, resulting in the electron's orbit decaying as shown. This example exhibits the classical problem recognized around 1900 of the collapse that must occur if atoms were composed of classical electrons and classical protons, and no other effects existed to compensate the radiation that must be emitted.

View Orbit: Case 3

Case 3: In this example, in addition to the conditions in Case 2, circularly polarized plane waves act on the electron, with an angular frequency equal to the nonperturbed circular orbit of 0.5 Angstroms. As can be seen, the orbit still decays, but is retarded in its decay somewhat.

View Orbit: Case 4

Case 4: Now the amplitude of the circularly polarized plane wave is made equal and opposite to the reaction reaction force. Now, the orbit does not decrease. The applied circularly polarized plane waves exactly compensates the effect of the radiation reaction.

View Orbit: Case 5

Cases 5 through 7: Here, the amplitude of the applied circularly polarized plane waves are increased in amplitude, by a factor of about 3 from case 4 to case 5, then by a factor of 10 beyond that in case 6, and by another factor of 10 beyond that in case 7. As can be seen, the electron spirals in and out, but still, the overall orbit does not decay. What is exhibited here is a very interesting example of a highly nonlinear electrodynamic problem. For more details on this behavior, please contact the authors for the preprints mentioned earlier.


View Orbit: Case 6

View Orbit: Case 7

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