On the Non-Orthonormality of Lippmann-Schwinger-Low States

Abstract

It is pointed out that for a general short-ranged potential the Lippmann-Schwinger-Low scattering state $|{\psi }_k^L>$ does not strictly satisfy the Schrodinger eigen equation, and the pair $|{\psi }_n^L>$, $|{\psi }_k^L>$ is mutually nonorthogonal if $E_n=E_k$. For this purpose, we carefully use an infinitesimal adiabatic parameter $\epsilon$, a nonlinear relation among transition amplitudes, and a separable interaction as illustration.

9 pages (modified version)