Physical Sciences and Mathematics Commons^™

Three Bosons In One Dimension With Short-Range Interactions: Zero-Range Potentials, Nirav Mehta, James Shepard

Nirav P Mehta

We consider the three-boson problem with δ-function interactions in one spatial dimension. Three different approaches are used to calculate the phase shifts, which we interpret in the context of the effective range expansion, for the scattering of one free particle off a bound pair. We first follow a procedure outlined by McGuire in order to obtain an analytic expression for the desired S-matrix element. This result is then compared to a variational calculation in the adiabatic hyperspherical representation, and to a numerical solution to the momentum-space Faddeev equations. We find excellent agreement with the exact phase shifts, and comment on …