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Probability densities are illustrated in text books and on Wikipedia as static pictures. Is the probability density of an electron within an isolated Hydrogen atom static or does it oscillate in some way?

Probability densities

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  • $\begingroup$ It depends on initial conditions. $\endgroup$ – Gabriel Golfetti Sep 5 '18 at 12:58
  • $\begingroup$ Interesting. I have in mind mainly what I assume is the simplest case of a single electron in the lowest available energy state. $\endgroup$ – David B Sep 5 '18 at 13:06
  • $\begingroup$ Static in that case. $\endgroup$ – Lewis Miller Sep 5 '18 at 13:10
  • $\begingroup$ It wouldn't necessarily have to oscillate, if you bring another hydrogen atom in (say on a stick) and held it close, the orbitals would change to a new shape (distort) and be static as long as you held it very still. Also it's the electron that's oscillating within this probability density distribution. $\endgroup$ – PhysicsDave Sep 5 '18 at 13:15
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In this link, one can see how the plots you show are derived from the solution of the Schrodinger equation for the hydrogen atom. There are checkable options.

There is no time dependence in the wavefunctions, or the corresponding probability distributions for the given eigenvalues (seen by checking next to the solutions).

Emilio Pisanti has given here the case of the time dependent hydrogen atom solutions:

and it will then show oscillations in both the position-space and momentum-space probability distributions.

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