So here is an image of the third lowest energy eigenfunction of an electron in a hydrogen atom:
Image from http://imgur.com/Lu4MocL
I understand well the eigenfunctions given by Schrodinger's equation for other types of potential energies, but the application to the atom is throwing me off, because of prior knowledge.
For an oscillating potential, or a constant potential, or some other variation, the qualities of the wavefunction make sense. The particle can be found anywhere inside the "box", and it is less likely to be found in areas of greater kinetic energy.
But isn't the pictured energy eigenfunction implying that there is a small chance for an electron with E_2 energy to be found in the first energy shell? I'm not sure how to interpret that. Isn't it also implying that the electron could be found anywhere between the wave functions maxima except for one discrete location where it equals zero?