Non-orthogonality of Lippmann-Schwinger-Low states

Abstract

For the general short-ranged potential the Lippmann-Schwinger-Low (LSL) scattering formalism by taking the limit ε → +0 at the end of the analysis, with ε being an infinitesimal adiabatic parameter has been re-examined. It is found that the LSL state |ψ k L〉 does not strictly satisfy the Schrodinger eigen equation, and the pair |ψ n L〉,|ψ k L〉 is mutually non-orthogonal if E n = E k, n ≠ k. For this purpose a new type of projection operator η k o, a non-linear relation among transition amplitudes, and a separable interaction as illustration have been used.