Consider a free particle of mass m in 1D that is initially very strongly localized at the origin (x = 0) and has the following wave function:
ψ(x,t=0) = Ce^(-ax^2/2e^(ikox))
where C, a, and ko are some positive constants, and ψ has a very large value.
(a) Find C.
(b) Show that the initial probability density approaches the delta function when x → -∞.
(c) Keeping a finite, determine the evolved wave function ψ(x,t) at t > 0.
