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Instead of simply passing it off as something that just exists, the book explains the necessity of the Uncertainty Principle by showing that a single wave function with definite position gives oscillating values of probability over an infinite range. And that when instead of one wave function, you superimpose a plethora of similar waves with a phase varying (by h-bar/2 I think, though thats not important), you get localization of the wave function.

Now at first glance this seemed like a new and incredibly intuitive approach to the uncertainty principle, but as I thought about it more I don't understand it.

Why does a range of waves with equal wavelength/amplitude but slight variations in phase cause localization of the wave function that doesn't repeat every period, and instead centralizes around one point?