Does this problem have any sense?
Suppose an electron in an infinite well of length $0.5nm$. The state of the system is the superposition of the ground state and the first excited state. Find the time it takes the electron to go from one wall to the other.
Strictly speaking the electron isn't even moving and $\vert \Psi \vert ^2$ is zero at the walls so it doesn't even "touch" them.
It think the only solution would be a semiclassical interpretation.