I think this speed is quantified but is it a constant in all the jumps of the electron?
In the absence of an external field, it's zero, because these are eigenstates 9f the Hamiltonian, so, if the electron is in any state of definite n at t=0, it will remain in that state forever.
When the electron jump between orbits in hydrogen atom, its velocity is never constant because either it is accelerating or decelerating. This jump involves change in its energy which is either ejected as photon or absorbed by electron.
Look at the wavefunctions psi of the electron in state n=1 and n=2 with energy difference Delta E.
The transition lasts according to the Heisenberg uncertainty:
Delta t ~ 1/Delta E
A kind of "velocity" may be calculated as
v = ( - ) / Delta t
However:
( - ) = 0
Hence it is not the same for other transitions.
The classical mechanical picture of a point like electron is not very useful here as you can see.
Rather think of resonant waves behaving differently as particles
Cheers, Claus
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