  In this work, based on consideration of periodicity and asymptotic forms of
wave function, we propose a novel approach to the solution of finite volume
three-body problem by mapping a three-body problem into a higher dimensional
two-body problem. The idea is demonstrated by an example of two light spinless
particles and one heavy particle scattering in one spatial dimension. This 1D
three-body problem resembles a two-body problem in two spatial dimensions
mathematically, and quantization condition of 1D three-body problem is thus
derived accordingly.
