1. The problem statement, all variables and given/known data I need Part B of this question http://physics.wustl.edu/classes/FL2013/217/homework/ps03.pdf [Broken] Recall that the free particle Schr¨odinger equation, i~ ∂ ∂tψ(x, t) = − ~ 2 2m ∂ 2 ∂x2 ψ(x, t) (1) has solutions of the “plane wave” form ψk(x, t) = exp[ikx − iω(k)t] , (2) where ω(k) = ~k 2/2m. (a) (10 points) Consider φ1(x, t) = cos(k0x − ω(k0)t). Show that φ1(x, t) is not a solution of the Schr¨odinger equation, i.e. when plugged into both sides of the equation, identity does not hold for all x and t as long as k0 6= 0. (b) (10 points) Find a solution φ2(x, t) to the Schr¨odingier equation that also satisﬁes φ1(x, 0) = φ2(x, 0). (Hint: Write cos(k0x) as the sum of a right moving and a left moving plane wave the way we did in class, and use the superposition principle. That is, if you know the correct time dependence for each term in the sum, see class notes, then you also know the correct time dependence of their sum.) 2. Relevant equations 3. The attempt at a solution I thought the solution may be φ(x, t)=Ae(-k1x-ω1t)+Ae(-k2x-ω2t) but I dont think it works out Anyone have any idea how to solve Part B? Thanks!