Schrödinger cat state
A Schrödinger cat state is a superposition of two very distinct or nearly orthogonal states. Here the wave packet at t=0 describes the simultaneous localization of a single particle in two disjoint regions.
This movie combines the time evolution in position space (upper part) with the time evolution in momentum space (lower part). The state at time t=0 is a superposition of two Gaussian functions. At later times the wave function in position space shows a nice interference pattern. The probability distribution in momentum space remains stationary because for the free motion the momentum observable is a conserved quantity.
Although the initial wave packet in position space consists of two separated peaks, this is the state of a single particle (which, in fact, can be realized experimentally). The initial state is a superposition of two very distinct wave functions. Thus the particle has two properties at the same time (the property of being localized at x, and of being localized at x+dx).
"Visual Quantum Mechanics - Book One" explains why states of this type are often called Schrödinger cat states.
You will also learn that the asymptotic shape of a wave packet in position space can be obtained by scaling the initial wave packet in momentum space (i.e., the Fourier transform).