 This brings us to the Heisenberg Uncertainty Principle. In our quest to understand how small things can get, we need to know if there is a measure of size below which we can't go. We see from our little thought experiment that as a wave, a particle's location is not fixed. The wave is spread out. Here we see three different wave packets for an electron. The wave packet at the top is narrow and therefore easier to locate, but it is less than one wavelength so its momentum is impossible to figure out. The bottom wave packet contains plenty of wavelength information, but it is quite spread out and its location is more uncertain. The wave packet in the middle has enough wavelength information to make its momentum less uncertain and it is less spread out than the one on the bottom, making its location less uncertain. But due to the spread out nature of matter waves, we still can't know both the location and momentum at the same time. Mathematically stated, the uncertainty in position times the uncertainty in momentum is always greater than or equal to Planck's constant divided by 4 pi. This is the Heisenberg uncertainty principle. It has nothing to do with the accuracy of our instruments and everything to do with the wave nature of matter. A good way to illustrate this is to look at an electron in an energy well too deep for it to get out. But remembering that the electron has a wave function that gives the probability of finding it at any given point, and some of those points, admittedly with very low probability, can be found outside the walls of the well, as if it had tunneled through the wall when in fact it did not.