Reanalysis of an open problem associated with the fractional Schrödinger equation

Reanalysis of an open problem associated with the fractional Schrödinger equation It was recently shown that there are some difficulties in the solution method proposed by Laskin for obtaining the eigenvalues and eigenfunctions of the one-dimensional time-independent fractional Schrödinger equation with an infinite potential well encountered in quantum mechanics. In fact, this problem is still open. We propose a new fractional approach that allows overcoming the limitations of some previously introduced strategies. In deriving the solution, we use a method based on the eigenfunction of the Weyl fractional derivative. We obtain a solution suitable for computations in a closed form in terms of Mittag–Leffler functions and fractional trigonometric functions. It is a simple extension of the results previously obtained by Laskin et al. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Theoretical and Mathematical Physics Springer Journals

Reanalysis of an open problem associated with the fractional Schrödinger equation

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Publisher
Pleiades Publishing
Copyright
Copyright © 2017 by Pleiades Publishing, Ltd.
Subject
Physics; Theoretical, Mathematical and Computational Physics; Applications of Mathematics
ISSN
0040-5779
eISSN
1573-9333
D.O.I.
10.1134/S0040577917070078
Publisher site
See Article on Publisher Site

Abstract

It was recently shown that there are some difficulties in the solution method proposed by Laskin for obtaining the eigenvalues and eigenfunctions of the one-dimensional time-independent fractional Schrödinger equation with an infinite potential well encountered in quantum mechanics. In fact, this problem is still open. We propose a new fractional approach that allows overcoming the limitations of some previously introduced strategies. In deriving the solution, we use a method based on the eigenfunction of the Weyl fractional derivative. We obtain a solution suitable for computations in a closed form in terms of Mittag–Leffler functions and fractional trigonometric functions. It is a simple extension of the results previously obtained by Laskin et al.

Journal

Theoretical and Mathematical PhysicsSpringer Journals

Published: Aug 15, 2017

References

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