Although the uncertainty principal can be written without quantum harmonic oscillators, it still happens when you consider them. Can the reason for the uncertainty principal be explained in terms of changing the equation? If I have a completely undetermined momentum, I should have something like a sine wave who's maximum probability extends evenly and infinitely through space but still totals 1. But, if I begin to constrict the momentum more precisely by adding different probable frequencies, the shape changes from something that should look relatively monotonous to something that actually has more uneven "lumps" or more visibly defined maximums and minimums due to the fact that the probability still has to total 1. I can't figure out exactly why that step happens, but can it be generally explained like this?