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Section 11.1: Finite Potential Energy Wells: Qualitative
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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) = −|V0| which is controlled by the slider. In addition, ħ = 2m = 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 |V0| gets smaller, the energy eigenfunction 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 |V0|, but you are now not limited to the ground-state energy eigenfunction. 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 |V0| 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 |V0| 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.