  Students in quantum mechanics class are taught that the wave function
contains all knowable information about an isolated system. Later in the
course, this view seems to be contradicted by the mysterious density matrix,
which introduces a new set of probabilities in addition to those that are built
into the wave function. This paper brings attention to the fact that the
density matrix can be reconciled with the underlying quantum-mechanical
description using a two-particle entangled state with a one-particle subsystem
as the simplest illustration of the basic principle. The extra-quantum
probabilities are traced to the coefficients of superposition of the quantum
state vector and the seemingly irreversible exponential population decay is
shown to be compatible with the unitary time evolution of a pure state when the
two particles interact. The two-particle universe thus provides the student
with a tool for understanding how the density operator, with all its richness,
emerges from quantum mechanics.
