Perturbation Solution for Two Trapped Particles in an Effective Field Theory Framework

Abstract

Particles interacting with sufficiently low energies have dynamics independent of the details of the interaction. This problem is generalized and extended within the context of an effective field theory (EFT). We investigate the case of two such particles in an harmonic trap and construct the inter-particle potential using an EFT expansion. In position space the effective interaction consists of a series of delta-functions and their derivatives. We approximate the energy spectrum in perturbation theory, compare to the results of analytical solutions and discuss the ordering of terms from the potential within the perturbation expansion.