Bad Qubits — Learn Quantum by Doing

Multiple choice

A Gaussian wave packet has spatial width sigma_x and momentum width sigma_p. What value does the product sigma_x * sigma_p take for this packet, and what is its significance?

sigma_x * sigma_p = hbar/2; the Gaussian is the minimum-uncertainty state, saturating sigma_x*sigma_p >= hbar/2
sigma_x * sigma_p = hbar; it is twice the minimum allowed by the uncertainty principle
sigma_x * sigma_p = 0; a Gaussian packet has perfectly definite position and momentum at once
sigma_x * sigma_p = 2*hbar; every other packet shape gives a smaller product