In relativistic quantum field theory, a clear distinction between elementary and composite particles does not always exist, and entities that are traditionally called composite particles (like mesons) are not necessarily "made of" any well-defined number of constituent particles. This article considers a strictly nonrelativistic model that does have a clear distinction between elementary and composite particles, and its composite particles do have well-defined constituents. Understanding the composite-particle phenomenon in this easier setting is an important step toward the study of particles in relativistic quantum field theory.