A solvable three-body model in finite volume

In this work, we propose an approach to the solution of finite volume three-body problem by considering asymptotic forms and periodicity property of wave function in configuration space. The asymptotic forms of wave function define on-shell physical transition amplitudes that are related to distinct dynamics, therefore, secular equations of finite volume problem in this approach require only physical transition amplitudes. For diffractive spherical part of wave function, it is convenient to map a three-body problem into a higher dimensional two-body problem, thus, spherical part of solutions in finite volume resembles higher spatial dimensional two-body Lüscher's formula. The idea is demonstrated by an example of two light spinless particles and one heavy particle scattering in one spatial dimension.