Considering how Heisenberg's uncertainty principle is applied to a top-hat wave function: This hyperphysics page shows how you can go about estimating the minimum kinetic energy of a particle in a 1,2,3-D box: http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/uncer2.html You can also investigate a particle in a box via the following treatment: http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/schr.html#c2 I'm having difficulty reconciling these two things? The first I would think of as applying the uncertainty principle to a top hat function, yet in the second link (the same scenario I think) we clearly have sinusoidal (i.e. non top hat) wavefunctions. How can you bring these two things together? Can you in general apply the uncertainty principle to a top hat function?