In a continuation of the (unfortunately, not well cited) study [1]
of the influence of a perturbation of the point-interaction type on
the linear and quadratic potentials the authors choose now the
square-well unperturbed potential. Elementary formulae and two
pictures display the results when the perturbation is, or is not,
centered at the origin.

MR2810776 Gadella, M.; Glasser, M. L.; Nieto, L. M. The infinite
square well with a singular perturbation. Internat. J. Theoret.
Phys. 50 (2011), no. 7, 2191--2200. 81Q15