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.
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Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 192, No. 1, pp. 103–114, July, 2017.
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Sayevand, K., Pichaghchi, K. Reanalysis of an open problem associated with the fractional Schrödinger equation. Theor Math Phys 192, 1028–1038 (2017). https://doi.org/10.1134/S0040577917070078
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DOI: https://doi.org/10.1134/S0040577917070078