Interfaces and Free Boundaries


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Volume 17, Issue 3, 2015, pp. 333–351
DOI: 10.4171/IFB/345

Published online: 2015-11-03

On the ambiguous treatment of the Schrödinger equation for the infinite potential well and an alternative via flat solutions: The one-dimensional case

Jesús Ildefonso Díaz[1]

(1) Universidad Complutense de Madrid, Spain

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 G. Gamow) 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

Keywords: Schrödinger equation, infinite well potential, Hardy potentials, sublinear eigenvalue type problem, flat solution, solution with compact support

Díaz Jesús Ildefonso: On the ambiguous treatment of the Schrödinger equation for the infinite potential well and an alternative via flat solutions: The one-dimensional case. Interfaces Free Bound. 17 (2015), 333-351. doi: 10.4171/IFB/345