Thanks for the reply and I'm sorry for the messy question. Is there a reason why we can assume that wave function go to 0 faster than 1/x ? or do we just assume for convenience?
The book on quantum mechanics that I was reading says:
d<x>/dt = d/dt ∫∞-∞ |ψ(x,t)|2 dx
=iħ/2m ∫∞-∞ x∂/∂x [ψ∂ψ*/∂x+ψ*∂ψ/∂x]dx (1)
=-∫∞-∞ [ψ∂ψ*/∂x+ψ*∂ψ/∂x]dx (2)
I want to know how to get from (1) to (2)
The book says you use integration by part:
∫abfdg/dx dx = [fg]ab - ∫abdf/df dg dx
I chose f...