The Woods-Saxon potential with point interactions

We have investigated bound states of the Schroedinger equation for the Woods-Saxon potential decorated with a finite number of the Dirac delta functions and presented bound state wave functions for s-wave states. By applying transfer matrices, an eigenvalue equation is obtained. We solve the eigenvalue equation numerically for some finitely many delta functions cases and obtain the ground state energy. Our results can be used to model very short range interactions for atomic and nuclear systems