Thus we can read off the solutions. I found 7 of them by putting the mouse on the intersection points. Notice that this shows the x, y value of the mouse in the lower left corner of the window. Try it. It may not be as accurate as zooming over and over, but it's pretty good.
The solutions I find are
# State Energy 1 0.280 2 2.502 3 6.976 4 13.643 5 22.455 6 33.307 7 45.811 |
A graphical way of seeing these states is to plot them as lines at a height above "0 energy" (the bottom of the well), much like one does in Chemistry for the electron states of an atom. That looks like this:
We can see that if this Well was a quantum dot with a trapped electron, there are many excitations we could induce, which would lift the electron up to another level. When it falls back down, a photon is emitted with energy equal to the difference in energy between the two levels. For example, a transition from state 4->3 would give off a photon of energy 6.665 in the units we are using.
Using nanotechnology tools, scientists can build quantum dots to have just the right spacing between levels to act like customizable atoms.