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Analysis of a Toy Model of Electron "Splitting"

B. Altschul·C. Rebbi
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Abstract

We examine Maris' recent suggestion that the fission of electron-inhabited bubbles in liquid helium may give rise to a new form of electron fractionization. We introduce a one-dimensional toy-model--a simplified analogue of the helium system--which may be analyzed using the Born-Oppenheimer approximation. We find that none of the model's low-lying energy eigenstates have the form suggested by Maris' computations, in which the bubbles were treated completely classically. Instead, the eigenstates are quantum-mechanically entangled superposition states, which the classical treatment overlooks.

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B. Altschul, C. Rebbi. 2002-11-05. Analysis of a Toy Model of Electron "Splitting". https://doi.org/10.1103/physreva.69.032111

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