## Transition to Finite Potential Energy Wells

*Please wait for the animation to completely load.*

We begin by looking at the ground state of a very deep, but not
quite infinite, square well. Here the potential energy function
is zero everywhere except between −0.5 <* x *< 0.5 where it is V(*x*) = −|*V*_{0}| which is controlled by the slider.
** In addition, ***ħ* = 2*m* = 1. Notice that this energy eigenfunction, here shown in
position-space, resembles that of the infinite square well in shape. Drag the slider from left to right and see
what happens. You should notice that as |*V*_{0}| gets smaller, the wave function now *
leaks* into the two classically-forbidden
regions.

Now consider a shallow well by selecting the link Show the shallow well instead.
In this animation you may again drag the slider to change |*V*_{0}|, but you are now not limited to the
ground-state wave function. To see the other bound states, simply
click-drag in the energy level diagram on the left to select a level. The
selected level will turn red. Again drag the slider from left to
right and see what happens. You should notice that as |*V*_{0}| gets
smaller, the wave function now *leaks* even more into the classically-forbidden regions than before. You
should also note that the number of bound states has been reduced as |*V*_{0}|
gets smaller. Also note that the higher *n* states have a larger
amount of leakage than the smaller *n* states for the same well
depth.