Correction to: Scientific Reports https://doi.org/10.1038/s41598-020-76512-5, published online 10 November 2020
The original version of this Article contained errors in the Formalism section, where Equation 1 and the subsequent formula were incorrect and Equations 2–4 were omitted.
“The wavepacket propagation in the two-dimensional fractional Schrodinger equation formalism can be studied by using:
where \({\alpha }\), \(\beta\), and \({\gamma }\) are the fractional derivative order, Laplacian coefficient, and nonlinear interaction strength, respectively. We also have \(\Delta = \partial^{2} /\partial x^{2} + \partial^{2} /\partial y^{2}\).”
now reads:
“The wavepacket propagation in the two-dimensional fractional Schrodinger equation formalism can be studied by using:
where \({\alpha }\), \({\upbeta}\), and \({\gamma }\) are the fractional derivative order, Laplacian coefficient, and nonlinear interaction strength, respectively. We also have \(\Delta^{2} = \partial^{2} /\partial x^{2} + \partial^{2} /\partial y^{2}\). Also \({\text{Q}}_{{\text{R}}}\), and M are real and complex functions, respectively. Let us assume that
where the geometrical potential \({\text{V}}\left( {x,y} \right)\) is defined for the double slit problem, and \({\upbeta }{\text{Q}}_{{\text{I}}} \left( {{\text{x}},{\text{y}},t,\alpha } \right)\) is a real function that determines amplitude of imaginary part of the potential. By substituting Eq. (2) in Eq. (1), we have
where \({\text{Q}}\left( {{\text{x}},{\text{y}},t,\alpha } \right) = {\text{Q}}_{R} \left( {{\text{x}},{\text{y}},t,\alpha } \right) + {\text{ iQ}}_{{\text{I}}} \left( {{\text{x}},{\text{y}},t,\alpha } \right)\).
Note that when \({\text{Q}}\left( {{\text{x}},{\text{y}},t,\alpha } \right) = {\text{exp}}\left( {2\pi i} \right) = 1\), we obtain the usual NFSE. In this paper however, we investigated a more general case of \({\text{Q}}\left( {{\text{x}},{\text{y}},t,\alpha } \right)\) as follows
where \(g\left( {{\text{x}},{\text{y}},t} \right) = - i\frac{{\Delta \psi \left( {x,y,t} \right)}}{{\psi \left( {x,y,t} \right)}}\) is a real function.”
As a result, Equations 5–8 were originally listed as Equations 2–5.
The original Article has been corrected.
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Ghalandari, M., Solaimani, M. Author Correction: Fractional Young double-slit numerical experiment with Gaussian wavepackets. Sci Rep 11, 10120 (2021). https://doi.org/10.1038/s41598-021-88754-y
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DOI: https://doi.org/10.1038/s41598-021-88754-y
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