Frustating use of the Laplace transform for the quantum states of a particle in a box

Abstract

In a recent paper diffused in the literature, the quantum problem of a particle in a infinite square well potential was claimed to be solved via Laplace transform. Surprisingly, the correct solutions were found for an eigenvalue problem with variable defined on a finite range. As a matter of fact, the authors have misused the Laplace transform of the time-independent Schrödinger equation, and they have also used incorrectly the inversion process. In the present paper it is pointed out carefully and clearly those mistakes that might occur with the use of inappropriate methods for a given eigenvalue problem.