Hi! I'm currently studying Griffith's fantastic book on QM, and I'm confused for a bit about the wave function for a free particle. Here's what I think so far; for a free particle, there are no stationary states, so therefore we can't solve the SE with ψ(x)=Aeikx+Be-ikx That is, we can't write a discrete sum. But We can have solutions as: ψ(x,t)=∫dkφ(k)ei(kx-ωt) I don't know if my understanding is correct, so please tell me so. Now, I assume that this understanding is correct and get to the question: If the solutions can only be the latter, then why was the solution from the book for the scattering states in the delta function potential a sum of stationary states and not the continuous sum? Also, why is it the same for the bound states if we are solving for the free particle when x<0 and x>0? Is it because it has a potential at x=0? Thanks in advanced!