These are some examples to illustrate the uncertainty principle. I also include a proof of the uncertainty principle, although we will be doing a more general proof when we cover the formalism of quantum mechanics in chapter 3. There is also an accompanying matlab file which can be used to generate the plots below as well as others. Although it is not easy to read someone else's code, the code is well documented. For those familiar with Matlab, I would encourage that you look at it. I strongly recommend that all of you learn some Matlab. uncertainty.m The wave functions considered are Gaussian psi(x) = C exp(ikx) exp(-(x/width))^2) "quartic" psi(x) = C exp(ikx) exp(-(x/width))^4) where C in each case is a constant that gives normalization to 1. To place this on a computer I have set hbar equal to 1 so the uncertainty principle is sigmax sigmap greater than or equal to 1/2 . The Gaussian wave function above is the minimum uncertainty wave packet, where sigmax sigmap = 1/2 . Uncertainty PrincipleResults:function width k sigmax sigmap (sigmax sigmap) ---------------------------------------------------------------- Gaussian 1 6 0.5 1 0.5 graph Gaussian 1 6 0.125 4 0.5 graph "quartic" 0.25 6 0.489 1.195 0.584 graph "quartic" 0.25 6 0.122 4.77 0.583 graph ---------------------------------------------------------------- The computer code does not give exactly 0.5 for (sigmax sigmap), but something like 0.499 . This difference is due to discretizing the integrals for the expectation values.