Abstract
A complete analytical approach is used to study the problem of two electrons in aharmonic potential. The effective potential of the combined system is described as thesum of the harmonic and anharmonic potentials. For large separation distancesbetween two electrons, it is possible to ignore the anharmonic contribution andhence the combined system behaves as a harmonic oscillator. The frequency of themodified oscillator depends on the separation distance between the two electrons andon the angular quantum momentum. When there is a small separation distancebetween the two electrons, the anharmonic contributions become significant andthe system does not have an exact solution. The anharmonic constant, however,does not have explicit dependence on the frequency of the harmonic potentialresponsible for the confinement. We give a rough estimate of the contribution ofanharmonic potentials. As the angular momentum increases, we observe that thecontribution of the anharmonic constant becomes negligibly small. The presentapproximate analytical solution is critically compared with other, existing solutions.
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