Few-body systems
Few-body systems are groups of just a few particles. They sit between simple two‑body problems and large many‑body systems. In quantum physics, examples include light nuclei with a few nucleons, small molecules, light atoms in fields, atomic collisions, and quantum dots.
A main challenge is that the equations used to describe motion (the Schrödinger equation in quantum mechanics, or classical equations) are rarely solvable exactly when more than two particles interact. This is known as the few‑body problem.
For some three‑body cases, there is a way to solve them exactly using Faddeev equations. Under certain conditions, these equations can lead to the Efimov effect, a strange quantum state that can occur in three-body systems.
In practice, most few‑body systems are solved with very accurate computer calculations that use many building blocks (basis functions) and optimize the results. The hydrogen molecular ion and the helium atom are classic examples that can be treated this way. Helium, in particular, has been solved very precisely with special mathematical functions named after Hylleraas and Frankowski‑Pekeris.
Often, physicists must use approximations to handle few‑body problems. These approximations have to be checked against real experiments, such as atomic collisions or precision laser spectroscopy.
Because the electromagnetic force is well understood, any mismatch between theory and experiment usually points to how we describe the few‑body effects, or possibly to new physics beyond the current theory.
In nuclear physics, the underlying forces are less well known, making the problems harder.
Atomic collision experiments can sometimes measure complete information about every particle, while in larger systems you usually see only averaged quantities.
In classical physics, the few‑body problem is just a part of the broader N‑body problem.
This page was last edited on 2 February 2026, at 18:09 (CET).