Answer Happy

A free particle has the initial wave function V(1,0) =Ae-a, where A and a are constants and a is real and positive. (a) Find the constant A. (b) Defining o(k) by (x,0) take the inverse Fourier transform to show that А (k) V2a (Hint: Integrals of the form . can be handled by completing the square, i.e. by writing vža Locks dk, dx e ax?+dos) ar? +bxa + b 2a 4a
(e) Show that exp(-12 loker) Y(X.) 1 + 2iaht/m In order to simplify the algebra, I found it helpful to introduce the complex variable () 0=+2 (d) Show that 19(x,0) AW where 1 + (2aft/m2 (e) Explain qualitatively, what happens to V as time goes on (remember the video from the lecture showing the time-evolution a Gaussian wave packet)? a