twoparticle

Two-particle, or twoparticle, refers to the physical description and analysis of a system consisting of two interacting particles. It is a foundational concept in classical and quantum mechanics, providing the simplest nontrivial context in which interactions, correlations, and quantum statistics can be studied.

In classical mechanics, the two-particle problem is often simplified by introducing center-of-mass and relative coordinates. The total motion separates into a free motion of the center of mass and a relative motion that depends on the interparticle potential. This decoupling reduces the problem to solving a one-body problem twice, once for each coordinate, in many common cases.

In quantum mechanics, the two-particle Schrödinger equation describes the joint wavefunction of the two particles. For central interparticle potentials that depend only on the separation, the Hamiltonian separates into a center-of-mass part and a relative-part, allowing the total wavefunction to factor into CM and relative components for bound or scattering states. When the particles are identical, quantum statistics require symmetrization or antisymmetrization of the wavefunction, leading to bosonic or fermionic behavior. The two-particle problem also introduces entanglement and correlation phenomena, which have no classical analogue.

Two-particle systems appear across disciplines: ultracold atomic gases, quantum dots, and molecular vibrations in chemistry; two-particle scattering and bound-state methods in nuclear and particle physics; and two-particle correlation techniques in experimental physics. Related formalisms include the two-particle Green’s function and, in quantum field theory, the Bethe-Salpeter equation for bound states.