For a local and spherical symmetric potential, the coupled momentum space Schroedinger equations given in equation (3) decouples in angular momentum, giving $$ \begin{equation} \frac{\hbar^2}{2\mu} k^2 \psi_{n l}(k) +\int_{0}^\infty dk' {k'}^2 V_{l}(k,k') \psi_{n l }(k')=E_{n l} \psi_{n l}(k) \tag{14} \end{equation} $$ Where we have written \( \psi_{n l }(k)=\psi_{nlm}(k) \), since the equation becomes independent of the projection \( m \) for spherical symmetric interactions. The momentum space wave functions \( \psi_{n l}(k) \) defines a complete orthogonal set of functions, which spans the space of functions with a positive finite Euclidean norm (also called \( l^2 \)-norm), \( \sqrt{\langle\psi_n\vert\psi_n\rangle} \), which is a Hilbert space. The corresponding normalized wave function in coordinate space is given by the Fourier-Bessel transform $$ \phi_{n l}(r) = \sqrt{\frac{2}{\pi}}\int dk k^2 j_l(kr) \psi_{n l}(k) $$