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A Study of Fractional Schrodinger Equation-composed via Jumarie fractional derivative | | Joydip Banerjee
; Uttam Ghosh
; Susmita Sarkar
; Shantanu Das
; | | Date: |
25 Feb 2016 | | Abstract: | One of the motivations for using fractional calculus in physical systems is
due to fact that many times, in the space and time variables we are dealing
which exhibit coarse-grained phenomena, meaning that infinitesimal quantities
cannot be placed arbitrarily to zero-rather they are non-zero with a minimum
length. Especially when we are dealing in microscopic to mesoscopic level of
systems. Meaning if we denote x the point in space and t as point in time; then
the differentials dx (and dt) cannot be taken to limit zero, rather it has
spread. A way to take this into account is to use infinitesimal quantities as
(Deltax)^alpha (and (Deltat)^alpha) with 0<alpha<1, which for very-very
small Deltax (and Deltat); that is trending towards zero, these ’fractional’
differentials are greater that Deltax (and Deltat). That is
(Deltax)^alpha>Deltax. This way defining the differentials-or rather
fractional differentials makes us to use fractional derivatives in the study of
dynamic systems. In fractional calculus the fractional order trigonometric
functions play important role. The Mittag-Leffler function which plays
important role in the field of fractional calculus; and the fractional order
trigonometric functions are defined using this Mittag-Leffler function. In this
paper we established the fractional order Schrodinger equation-composed via
Jumarie fractional derivative; and its solution in terms of Mittag-Leffler
function with complex arguments and derive some properties of the fractional
Schrodinger equation that are studied for the case of particle in one
dimensional infinite potential well. | | Source: | arXiv, 1603.2069 | | Services: | Forum | Review | PDF | Favorites | |
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