Geodesic
Reanalysis of an~open problem associated with the~fractional Schr\"odinger equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 192 (2017) no. 1, pp. 103-114

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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.
Keywords: fractional Schrödinger equation, infinite potential well, Riesz fractional derivative, Mittag–Leffler function. 
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     author = {K. Sayevand and K. Pichaghchi},
     title = {Reanalysis of an~open problem associated with the~fractional {Schr\"odinger} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {103--114},
     publisher = {mathdoc},
     volume = {192},
     number = {1},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2017_192_1_a6/}
}
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K. Sayevand; K. Pichaghchi. Reanalysis of an~open problem associated with the~fractional Schr\"odinger equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 192 (2017) no. 1, pp. 103-114. http://geodesic.mathdoc.fr/item/TMF_2017_192_1_a6/