Our study of one-dimensional quantum mechanics begins with what you may think is a simple problem: that of a free particle. The Schrödinger equation for this system is as simple as it gets, after all, V(x) = 0. However, it is not so simple to construct a particle-like solution should we wish to compare quantum mechanics to classical mechanics. In order to do this we must add together an infinite number of individual solutions to the free Schrödinger equation to get a (Gaussian) wave packet that in many ways behaves like a classical free particle.