Can an electron be inside a proton?

This article has an image showing the 2S and 2P states of a hydrogen atom. The caption makes the following claim:

The 2S and 2P states of hydrogen show where the electron could be found at any given time. These images show the possible locations of the electron in each state; the proton, unmarked, is at the center of each image. In the 2S state, the electron overlaps the proton, and for a non-zero amount of time, the electron is inside of the proton itself. In the 2P state, the electron and the proton never overlap.

My question is about the statement

for a non-zero amount of time, the electron is inside of the proton itself

It doesn't make sense to me that the electron could be inside the proton. Does that actually happen, or is this a simplification?

• The 1s (and 2s, ...) electron wavefunction is non-zero where the proton is. However, I prefer to not think of the electron as a tiny ball zooming around where the wavefunction suggests it might be, so I disagree with how the article is worded. But, yes, electron capture processes rely on the overlap... – Jon Custer Sep 11 at 16:59
• Why do you think it can’t happen? A proton is just a bound state of quarks held together by gluons. It isn’t impenetrable. – G. Smith Sep 11 at 17:20
• – Qmechanic Sep 11 at 17:36

Electrons are quantum mechanical entities, elementary point particles in the Standard model of particle physics, thus obey quantum mechanical laws.They are described by a probability distribution for their location, given by $$Ψ^*Ψ$$, where $$Ψ$$ is the wavefunction, a solution of the quantum mechanical wave equation describing the particular atom. ( I suppose it is hydrogen)