[tex]\psi (x)= \frac{1}{(\pi\Delta^2)^\frac{1}{4}} e^(\frac{i<p>(x-<x>)}{\hbar})e^(\frac{-(x-<x>)^2}{2\Delta^2})[/tex] as [tex]\Delta\rightarrow\infty[/tex] should approach the plane wave [tex]\frac{1}{(2\pi\hbar)^\frac{1}{2}} e^(\frac{i<p>x}{\hbar}) [/tex] up to a phase factor. I guess this happens by setting the [tex]e^(\frac{-(x-<x>)^2}{2\Delta^2})[/tex] term equal to 1. However, ignoring phase factor differences, the normalization factor out front still seems to be different. One is [tex]\frac{1}{(\pi\Delta^2)^\frac{1}{4}} [/tex] while the other is [tex]\frac{1}{(2\pi\hbar)^\frac{1}{2}} [/tex]. Am I not seeing something?(adsbygoogle = window.adsbygoogle || []).push({});

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# Plane wave limit of Gaussian packet

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