Quantum Mechanics - Gaussian Wave Packet

A Gaussian wave packet travels through free space. Which of the following statement about the wave packet are correct for all such wave packets?

1. The average momentum of the wave packet is zero
2. The width of the wave packet increases with time, as t → ∞.
3. The amplitude of the wave packet remains constant with time.
4. The narrower the wave packet is in momentum space, the wider it is in coordinate space.

A. I and III only
B. II and IV only
C. I, II, and IV only
D. II,III, and IV only
E. I, II,III, and IV only

(GR9677 #76)

Solution:

The Gaussian wave packet satisfies the Heisenberg uncertainty principle: ΔxΔp ≥ ħ/2

→ Statement IV is TRUE.
→ Statement I is FALSE, Δp cannot be 0
→ Answer A, C, E are FALSE.

Answer D suggests that both II and III are true.
If II and III are true, the area of gaussian wave packet can go to ∞
This is not allowed by the Heisenberg uncertainty principle.
→ D is FALSE

Answer: B