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

It is pointed out that for a general short-ranged potential the Lippmann-Schwinger-Low scattering state $|\psi^L_k>$ does not strictly satisfy the Schrodinger eigen equation, and the pair $|\psi^L_n>$, $|\psi^L_k>$ 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.