Superimposition of Waves

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I am reading a very good book on physics/mathematics currently. While it ends up branching off into some really interesting stuff, the first couple chapters introduce the (assumed) unprepared reader to foundations of modern quantum physics, with one chapter focusing on the uncertainty principle.

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?
 

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Your second paragraph seems contradictory....a single wave function with definite position IS localized....thats where it is located.

For example the probability density function (wave) of a free electron extends everywhere, but a bound electron...in a box or attached to a local nucleus...has a localized wave function.....
 
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