Phase-function method from the Riccati form of the Schrodinger equation

Jana, A K; Bera, Pulakesh; Das, U.; Talukdar, B.

doi:10.1088/0305-4470/23/2/012

Cited by 2 publications

(1 citation statement)

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“…If the division interval length is decreased to zero, then the recurrent relations in the limit transform into the Riccati equation, which is analogous to (3). Other authors [16] combined the radial Schrödinger equation and the expression for the logarithmic derivative of the wave function, obtaining the Riccati equation. Then, using the method of a variation of constants, they derived the phase equation, which was analogous to (3).…”

Section: Theory Of the Methodsmentioning

confidence: 99%

Application of the Method of Phase-Amplitude Functions in X-Ray and Neutron Reflectometries

Salamatov

Кравцов²

2021

J. Synch. Investig.

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The application of a method of phase-amplitude functions for the calculation of reflectograms obtained during the reflection of neutrons and X-rays from planar nanostructures is considered. Several approximations and substitutions that can be useful for different problems are described. It is shown that this method can be used to calculate reflectivity curves with lower computational expenditures than in the case of other approaches. A comparison between model numerical results for different algorithms is given. The Levenberg-Marquardt algorithm is used to solve the inverse problem and reconstruct the scattering potential of a metal film using the experimental reflection intensity. Experimental results for two systems, namely, the Al 2 O 3 //Cr(200 Å) film and the Al 2 O 3 //Cr(100 Å)/[Gd(50 Å)/Cr(11 Å)] 6 /Cr(100 Å) metal superlattice are presented. The obtained scattering potentials make it possible to draw conclusions about the layered structures of the samples and determine their dependence on the growth conditions.

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Section: Theory Of the Methodsmentioning

confidence: 99%