The following equation (5.122) is the minimum-uncertainty wave function, which is a Gaussian wave packet. Since it is Gaussian in ##x##, we may get ##\Delta x## directly from the ##\sigma## of the Gaussian distribution: ##(\Delta x)^2=\frac{\hbar^2}{2(\Delta p_x)^2}##. We have ##\Delta x\Delta p_x=\frac{\hbar}{\sqrt2}##, which contradicts the fact that the wave function has minimum uncertainty, ie., ##\Delta x\Delta p_x=\frac{\hbar}{2}##.(adsbygoogle = window.adsbygoogle || []).push({});

Derivation of (5.122):

Gaussian distribution:

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# Minimum-uncertainty wave function -- contradiction?

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