Viruses and Quantum Mechanical Spreading

Domnu
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I was just wondering if viruses experenced quantum mechanical spreading... if we represent a virus by a wave packet, we have that (assuming that the density of a virus is, say, 300 kg/m^3)...

a = 10 nm, m = \pi * a^3 * 300 = 9.43 \cdot 10^{-22} kg

Now, after a period of time, \tau where

\tau = 2ma^2/ \hbar

, a wave packet experiences significant quantum mechanical spreading. But here, \tau = 0.001787 s! What exactly does this mean? Does this mean we have major difficulties locating viruses at a particular time and place (we can see them through electron microscopes...)? What exactly does quantum mechanical spreading refer to?
 
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where does the equation
\tau = 2ma^2/ \hbar
come from?
 
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