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On The Space-Time Fractional Schr\"{o}dinger Equation with time independent potentials

Mathematical Physics 2017-09-20 v1 math.MP

Abstract

This paper is about the fractional Schr\"{o}dinger equation (FSE) expressed in terms of the quantum Riesz-Feller space fractional and the Caputo time fractional derivatives. The main focus is on the case of time independent potential fields as a Dirac-delta potential and a linear potential. For such type of potential fields the separation of variables method allows to split the FSE into space fractional equation and time fractional one. The results obtained in this paper contain as particular cases already known results for FSE in terms of the quantum Riesz space fractional derivative and standard Laplace operator.

Keywords

Cite

@article{arxiv.1709.06198,
  title  = {On The Space-Time Fractional Schr\"{o}dinger Equation with time independent potentials},
  author = {Saleh Baqer and Lyubomir Boyadjiev},
  journal= {arXiv preprint arXiv:1709.06198},
  year   = {2017}
}

Comments

9 pages. The corresponding author thanks Haidar Khajah, Ram Saxena and Hans Haubold for the valuable discussions and comments