For stationary Schrödinger equation in with the finite potential the singular pseudopotential is constructed in the form allowing us to find wave functions. The method does not require the knowledge of the explicit form of a potential and assumes only knowledge of the scattering amplitude for fixed level of energy.
"On the method of pseudopotential for Schrödinger equation with nonlocal boundary conditions." Abstr. Appl. Anal. 6 (6) 329 - 338, 10 December 2001. https://doi.org/10.1155/S1085337501000689