For scattering states, the energy is positive, \( E>0 \). The Lippman-Schwinger equation (a rewrite of the Schroedinger equation) is an integral equation where we have to deal with the amplitude \( R(k,k') \) (reaction matrix, which is the real part of the full complex \( T \)-matrix) defined through the integral equation for one partial wave (no coupled-channels) $$ \begin{equation} R_l(k,k') = V_l(k,k') +\frac{2}{\pi}{\cal P} \int_0^{\infty}dqq^2V_l(k,q)\frac{1}{E-q^2/m}R_l(q,k'). \tag{16} \end{equation} $$ For negative energies (bound states) and intermediate states scattering states blocked by occupied states below the Fermi level.