The gaussian wave packet. A free particle has the initial wave functionΨ(x, 0) = Ae–ax2whe...

The gaussian wave packet. A free particle has the initial wave function

Ψ(x, 0) = Ae–ax2

where A and a are constants (a is real and positive). Normalize 0).

(a) Normalize ψ(x, 0)

(b) Find ψ(x, t). Hint: Integrals of the form

(c) Find |ψ|2 Express your answer in term of quantity