Use of wavelets in potential scattering problems

Application of the Daubechies compact support wavelets to problems of nonrelativistic potential scattering described by integral Lippmann-Schwinger equation is discussed. Structure of wavelet representation of various physical operators is investigated. It is shown that for a special class of potentials wavelets enable sparse approximation of the kernel of the Lippmann-Schwinger equation. Constraints for such potentials are derived. This paper is dedicated to Prof. J. Bičák on the occasion of his 60th birthday.