Radiation pressure of a string on a ring: A solution in terms of the scattering theory

Abstract

The possibility of reducing the 1D problem of calculating the radiation pressure on a ring to a linear scattering problem solved in terms of partial scattering amplitudes is demonstrated. The latter approach is analogous to that previously applied to the 3D case—in particular, to the case of a spherically symmetric inclusion in an ideal liquid. The ring is represented as an inclusion with a monopole scattering amplitude. To achieve full qualitative coincidence of the expressions obtained for the 1D and 3D cases, the corresponding scattering amplitudes are considered as factors multiplying the fundamental solutions to the 1D and 3D Helmholtz equations. The results of the study enable a unified approach to the two aforementioned problems differing in dimension.