Ionizing solutions to the hydrogen atom

[mordechai9]

Are there any ionizing solutions for the hydrogen atom problem, where the electron breaks away from the proton?

[alxm]

Of course. For E > 0 you have a continuum of unbound states. Same as for when E > V for a particle in a finite-barrier box.

[mordechai9]

I mean a solution where the electron transitions from being bound to breaking away... like in a collision.

[alxm]

And the answer is still "of course".

Why would a transition to an unbound state be fundamentally different than transitions between bound states? It isn't.

[mordechai9]

Could you help point me to one of these solutions then? I don't recall ever seeing the time-dependent Schrodinger equation solved for transitions or ionization and I'm not sure where to look...

[DrDu]

The book by Landau and Lifshetz "Quantum Mechanics" has a fairly complete discussion of the continuum eigenstates of the hydrogen atom.