My interpretation: When we have no angular momentum, the potential well looks like this, my question is: How do you find the point where the wavefunction penetrates its classical forbidden region, i.e. quantum tunnelling effect? The answer is $r>2a_0$ where $a_0$ is the Bohr's radius.
My answer: It seems you have to equate the Coulomb potential with the energy of the ground state of the hydrogen atom.
And what would the wavefunction intersect? Does it pass through $(0,0)$? Can we view the infinite deep well, as a infinite barrier, by imagining we shift the zero reference level down to infinity?
I'm quite confused by the idea of having negative energy. Does it mean I need infinite energy to get out of the well? Just like an infinite square well?
Best Answer
only from the point of view of r=0, but the electron is not there in the classical model; and even in the Schrodinger model r=0 is only one infinitesimal point, you would have to considered the expectation value of the energy.
the s-orbitals do have a non-zero probability density at (0,0), but again that is only one point.
No, the electron does not need infinite energy to get out of the well because it does not start at the bottom of the well in the classical model, and has zero probability of starting at the bottom of the well in the Schrodinger because it is only a single point.
You need to consider potential energy, kinetic energy and total energy. If you look at the following question and answer you should have a solution to the problem: Hydrogen atom: potential well and orbit radii