On the ambiguous treatment of the Schrödinger equation for the infinite potential well and an alternative via flat solutions: the one-dimensional case
Summary: An ambiguity in the mathematical treatment of the study of bound state solutions of the Schrödinger equation for infinite well type potentials (studied for the first time in a pioneering article of 1928 by \textit{G. Gamow} [Z. Phys. 51, 204--212 (1928; JFM 54.0969.04)]) is pointed out. An alternative to prove a similar ``localizing effect'' is here offered ``in terms Hardy type potentials'' with the distance to the boundary as a variable. The existence of flat solutions (with zero normal derivative at the boundary) and solutions with compact support is here obtained by first time in the literature for elliptic problems for this kind of linear equations.
scientific article; zbMATH DE number 6524744