Reflectionless potentials for difference Schrödinger equations
نویسندگان
چکیده
منابع مشابه
Generating potentials via difference equations
The condition for pressure isotropy, for spherically symmetric gravitational fields with charged and uncharged matter, is reduced to a recurrence equation with variable, rational coefficients. This difference equation is solved in general using mathematical induction leading to an exact solution to the Einstein field equations which extends the isotropic model of John and Maharaj. The metric fu...
متن کاملReflectionless Sturm-Liouville Equations
We consider compactly supported perturbations of periodic Sturm-Liouville equations. In this context, one can use the Floquet solutions of the periodic background to define scattering coefficients. We prove that if the reflection coefficient is identically zero, then the operators corresponding to the periodic and perturbed equations, respectively, are unitarily equivalent. In some appendices, ...
متن کاملCharacteristics of regionally reflectionless potentials
This paper considers potentials that are reflectionless for a range of energies and not reflectionless elsewhere. The focus of this paper is to see if reflection coefficients of this type have characteristics that would make it possible to solve for the associated potentials using known methods. Using the Gelfand-Levitan equation it is shown that the spectral measure function has several limits...
متن کاملRealization of reflectionless potentials in photonic lattices.
We realize experimentally a true reflectionless potential, which facilitates nonresonant unity transmission for all incident waves and at the same time supports localized modes. We utilize arrays of evanescently coupled optical waveguides, where a particular modulation of the transverse waveguide separations provides a physical realization of reflectionless Ablowitz-Ladik soliton potentials.
متن کاملNonstandard finite difference schemes for differential equations
In this paper, the reorganization of the denominator of the discrete derivative and nonlocal approximation of nonlinear terms are used in the design of nonstandard finite difference schemes (NSFDs). Numerical examples confirming then efficiency of schemes, for some differential equations are provided. In order to illustrate the accuracy of the new NSFDs, the numerical results are compared with ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and Theoretical
سال: 2015
ISSN: 1751-8113,1751-8121
DOI: 10.1088/1751-8113/48/11/115204