system
Given the following post, respond as if you're commenting on Reddit:
human
When an electron in an atom is excited, does its probability distribution instantly change from one shape to another, or is there a transitionary period?

If the latter, what does the distribution look like as it is shifting and how long does it take?
gpt
The electron's probability distribution is related to it's wavefunction. The time dependence of the wavefunction is governed by the Schrodinger equation, which is a first order differential equation in time. The solutions have smooth time dependence, so the probability distribution does not change instantly.  In real systems, there can be significant changes in time scales of nanoseconds, which is very fast in human terms, but the wavefunction still changes smoothly.