Viruses and Quantum Mechanical Spreading

[Domnu]

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?

 

[malawi_glenn]

where does the equation
$$\tau = 2ma^2/ \hbar$$
come from?