Infinite Square Well

Marshall A. Bowen, Joseph Coster

Yuchuan Wei

There has been a continuous argument on the correctness of the Laskins solution for the infinite square well problem in the fractional quantum mechanics. In this paper, we prove that the Laskins functions are not amathematical solution to the fractional Schrodinger equation and the equation does not have any nonzero solutions at all in the sense of mathematics. As in the standard quantum mechanics, we view the infinite square well problem as the limit of the finite well problem, and define the solution for the infinite square well problem as the limit of the solution for the finite square well problem. Using the simple property of the infinite operators, we show that Laskins function can be the limit solution for the infinite square well problem. The single-sided well problem and the 3 dimensional well problem are included. This operator method works for the same problems in the relativistic quantum mechanicsas well.

Pieter Naaijkens

Ryoichi Seki

A well-known problem of an infinite square-well potential in quantum mechanics furnishes an interesting boundary condition. We investigate this in detail by considering the infinite square-well potential as a limiting case of an finite square-well potential.

David M. Rosenbaum

Discrete time eigenvalues are found for the Infinite Square Well.

Barry R. Parker