خسرو سایوند

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 Schr¨odinger 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 the Mittag–Leffler functions and fractional trigonometric functions. It is a simple extension of the results previously obtained by Laskin et al.