A system at initial time t=0 with wave function (x,0) propagates freely (no forces). The wave function for this system at all times is Ψ(x,t) = Ψ(x-Pot) e^(iht/2m) Ψ(x,t=0).
a. (15 points) Determine Ψ(x,t) (which is a function of t).
b. (15 points) Determine Ψ(x,t=0) (not a function of t).
c. (15 points) Determine Ψ(x^2,t) (which is a function of t).
d. (15 points) Determine Ψ(p^2,t) (not a function of t).
e. (15 points) Determine Ψ(x,t) and Ψ(p,t).