What is many-body problem ?
Many-body systems are composed of particles interacting mainly via two-body interactions. Atoms are composed of 1-100 electrons, while a macroscopic piece of metal are described by 10**30 electrons. If the system is composed of 2 or 3 particles, we can solve the Schroedinger equation of the system exactly. If, however, the system contains more than 4 partcles, we cannot handle the Schroedinger equation as it is. The problem how to handle such many-body systems is called as the many-body problem.