Quantum mechanics

Finite volume method

Algorithm

Quantization (signal processing)

Scattering theory

Statistics

Excluded volume

Nuclear magnetic resonance

Scattering

Operating system

Atomic physics

Computer science

Geology

Oceanography

Polymer

Physics

Mathematics

Particle (ecology)

Particle system

Dimer

State (computer science)

Physical review. D/Physical review. D.

Using the three-particle quantization condition recently obtained in the particle-dimer framework, the finite-volume energy shift of the two lowest three-particle scattering states is derived up to and including order ${L}^{\ensuremath{-}6}$. Furthermore, assuming that a stable dimer exists in the infinite volume, the shift for the lowest particle-dimer scattering state is obtained up to and including order ${L}^{\ensuremath{-}3}$. The result for the lowest three-particle state agrees with the results from the literature, and the result for the lowest particle-dimer state reproduces the one obtained by using the L\"uscher equation.

Energy shift of the three-particle system in a finite volume