Double finite square well. Tunneling from one well to another.

Here is a reference in case anyone would like to delve more deeply into double square well wave-functions:
Double finite square well
With reference to the above link: why does \(\psi_3\) have a lower energy than \(\psi_4\)?
(You can address this question in the comments here if you like.)

Here is a possibly interesting problem that provides a sense of how quantum mechanics can work:
1. a) Can you use the wave-functions \(\psi_1\) and \(\psi_2\), as shown in the link above, to construct a state in which an electron is initially in the left hand well?
 b) How long does it take for the electron to tunnel from one well to the other? What does that depend on?

(These are the same wave functions that we called \(\psi_{1,1}\) and \(\psi_{1,2}\) in class. Assume that these are energy eigenstate wave-functions with energies \(E_{1,1}\) and \(E_{1,2}\) respectively.