The Schrödinger equation for the eigenvalues of the infinitely deep square well potential is solved within the class of generalised functions. It is found that the ground state consists of a step function like eigenfunction with the eigenvalue zero.
"Application of a generalised function method to the infinitely deep square well problem,"
Turkish Journal of Mathematics: Vol. 41:
3, Article 12.
Available at: https://journals.tubitak.gov.tr/math/vol41/iss3/12