On the consistency of the solutions of the space fractional Schrodinger equation

Download
2012-04-01
Bayin, Selcuk S.
Recently, it was pointed out that the solutions found in the literature for the space fractional Schrodinger equation in a piecewise manner are wrong, except the case with the delta potential. We re-analyze this problem and show that an exact and a proper treatment of the relevant integral prove otherwise. We also discuss effective potential approach and present a free particle solution for the space and time fractional Schrodinger equation in general coordinates in terms of Fox's H-functions. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4705268]
JOURNAL OF MATHEMATICAL PHYSICS

Suggestions

On the consistency of the solutions of the space fractional Schroumldinger equation (vol 53, 042105, 2012)
Bayin, Selcuk S. (2012-08-01)
Recently we have reanalyzed the consistency of the solutions of the space fractional Schroumldinger equation found in a piecewise manner, and showed that an exact and a proper treatment of the relevant integrals prove that they are consistent. In this comment, for clarity, we present additional information about the critical integrals and describe how their analytic continuation is accomplished.
An Application of the rayleigh-ritz method to the integral-equation representation of the one-dimensional schrödinger equation
Kaya, Ruşen; Taşeli, Hasan; Department of Mathematics (2019)
In this thesis, the theory of the relations between differential and integral equations is analyzed and is illustrated by the reformulation of the one-dimensional Schrödinger equation in terms of an integral equation employing the Green’s function. The Rayleigh- Ritz method is applied to the integral-equation formulation of the one-dimensional Schrödinger equation in order to approximate the eigenvalues of the corresponding singular problem within the desired accuracy. The outcomes are compared with those r...
On the accuracy of MFIE and CFIE in the solution of large electromagnetic scattering problems
Ergül, Özgür Salih (null; 2006-11-10)
We present the linear-linear (LL) basis functions to improve the accuracy of the magnetic-field integral equation (MFIE) and the combined-field integral equation (CFIE) for three-dimensional electromagnetic scattering problems involving large scatterers. MFIE and CFIE with the conventional Rao-Wilton-Glisson (RWG) basis functions are significantly inaccurate even for large and smooth geometries, such as a sphere, compared to the solutions by the electric-field integral equation (EFIE). By using the LL funct...
On solutions of the Schrodinger equation for some molecular potentials: wave function ansatz
IKHDAİR, SAMEER; Sever, Ramazan (2008-09-01)
Making an ansatz to the wave function, the exact solutions of the D-dimensional radial Schrodinger equation with some molecular potentials, such as pseudoharmonic and modified Kratzer, are obtained. Restrictions on the parameters of the given potential, delta and nu are also given, where eta depends on a linear combination of the angular momentum quantum number l and the spatial dimensions D and delta is a parameter in the ansatz to the wave function. On inserting D = 3, we find that the bound state eigenso...
On the stability at all times of linearly extrapolated BDF2 timestepping for multiphysics incompressible flow problems
AKBAŞ, MERAL; Kaya, Serap; Kaya Merdan, Songül (2017-07-01)
We prove long-time stability of linearly extrapolated BDF2 (BDF2LE) timestepping methods, together with finite element spatial discretizations, for incompressible Navier-Stokes equations (NSE) and related multiphysics problems. For the NSE, Boussinesq, and magnetohydrodynamics schemes, we prove unconditional long time L-2 stability, provided external forces (and sources) are uniformly bounded in time. We also provide numerical experiments to compare stability of BDF2LE to linearly extrapolated Crank-Nicolso...
Citation Formats
S. S. Bayin, “On the consistency of the solutions of the space fractional Schrodinger equation,” JOURNAL OF MATHEMATICAL PHYSICS, pp. 0–0, 2012, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/63875.