Analysis of a toy model of electron splitting

摘要

We examine Maris' [ J. Low. Temp. Phys. 120, 173 (2000) ] 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 analog 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.