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As you can see from figure 4.4 from Griffiths book on QM, the radial wave function of the hydrogen atom has clear points where ## |R_{nl} (r)|^2 = 0 ##. My question is three fold:

First, how is the electron able to traverse this region? My intuition is that with the uncertainty principle, the electron will only ever be observed at ##r \pm \Delta r## for which r satisfies ## |R_{nl} (r)|^2 = 0 ## though this is not as satisfying as I would like. Surely it would be possible (even if extraordinarily unlikely) to observe an electron at this specific point.

Second, how fast does the electron move during ionization? My initial guess wascsince it is emitting/absorbing a photon, however ## v = \sqrt{\frac{2 E_k}{m_e}}=\sqrt{\frac{2 \times 13.6eV}{510eV/c^2}} \cong .008c ## which seems reasonable.

Third, is there a wave function for a transitioning electron? Perhaps ## P = \left< \psi' | Q | \psi \right>## where ##\psi'## and ##\psi## are the overall initial and final wave functions?

Thanks

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# I Ionization and Nodes in the Hydrogen Wave Function

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