Minimum Uncertainty Wavefunction

[luckymango]

Why does one refers to it as a "minimum uncertainty" wavefunction?

 

[Galileo]

The Heisenberg uncertainty principle states \sigma_x\sigma_p\geq \frac{\hbar}{2}.
This is an inequality which always holds for any wavefunction. You can make wavefunctions for which \sigma_x and \sigma_p are both pretty big, but you can't make them both arbitrarily small.
You could raise the question for what wavefunction the uncertainty is minimal, that is, when the inequality becomes an equality. This is the minimum uncertainty wavefunction (It turns out be a gaussian.)

 

[Epicurus]

It has, of course, to be a gaussian as qm is a harmoinc theory!