An new kind of experiment is performed, where now the edges of the box
are partially opened, forming the Finite Square Well shown in
Figure 1, where 
.
In what fraction of such experiments can we
expect the particles to remain in the box?
Hints: You may assume that the box is opened so quickly that,
during the opening process, the particle does not have time to change
its state appreciably. There is only one bound state in this finite
square well, and the energy of that state 
may be found exactly.
Finally, because there is only one bound state, observing the particle
remaining in the box is equivalent to measuring its energy as 
.
Figure 1: ``Box'' (Infinite Square Well) partially opening into a
Finite Square Well