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Inverse scattering Problem for the schrodinger’s equation

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International Journal of Modern Nonlinear Theory and Application 2013年第4期2卷 244-246页

作者： Asset A.Durmagambetov Leyla s.Fazilova Buketov Karaganda state University KaragandaKazakhstan

The analytic properties of the scattering amplitude are discussed. And, the representation of the potential by the scattering amplitude is obtained.

关键词： schrodinger’s equation Potential scattering Amplitude

Convective schrodinger equation:Insights on the Potential Energy’s Role to Wave Particle Decay

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Journal of Electromagnetic Analysis and Applications 2015年第9期7卷 225-232页

作者： Altair s.de Assis Hector Torres-silva Goran T.Marklund Universidade Federal Fluminense(IM-GMA) NiteroiBrasil Universidad de Tarapaca AricaChile Kungliga Tekniska Hogskolan—KTH StockholmSweden

In this paper, we coupled the Quantum Mechanics conventional schrödinger’s equation, for the particles, with the Maxwell’s wave equation, in order to study the potential’s role on the conversion of the electromagnetic field energy to mass and vice versa. We show that the dissipation (“conductivity”) factor and the particle implicit proper frequency are both related to the potential energy. We have also derived a new expression for the schrödinger’s equation considering the potential energy into this equation not as an ad hoc term, but also as an operator (Hermitian), which has the scalar potential energy as a natural eigenvalue of this operator.

关键词： schrodinger’s equation Klein-Gordon’s equation Maxwell’s Wave equation Convection Displacement Current

GRADIENT FLOW FINITE ELEMENT DIsCRETIsATIONs WITH ENERGY-BAsED ADAPTIVITY FOR EXCITED sTATEs OF sCHRÖDINGER's equation

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Journal of Computational Mathematics 2023年第5期41卷 933-955页

作者： Pascal Heid Mathematical Institute University of OxfordWoodstock RoadOxford OX26GGUK

The purpose of this paper is to verify that the computational scheme from[Heid et al.,Gradient flow finite element discretizations with energy-based adaptivity for the Gross–Pitaevskii equation,***.436(2021)]for the numerical approximation of the ground state of the Gross–Pitaevskii equation can equally be applied for the effective approximation of excited states of schr¨odinger’s *** procedure employs an adaptive interplay of a sobolev gradient flow iteration and a novel local mesh refinement strategy,and yields a guaranteed energy decay in each step of the *** computational tests in the present work highlight that this strategy is indeed able to approximate excited states,with(almost)optimal convergence rate with respect to the number of degrees of freedom.

关键词： schrodinger’s equation Excited states Gradient flows Adaptive finite element methods

Global Estimation of the Cauchy Problem solutions’the Navier-stokes equation

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Journal of Applied Mathematics and Physics 2014年第4期2卷 17-25页

作者： A.A.Durmagambetov L.s.Fazilova Buketov Karaganda state University KaragandaKazakhstan

The analytic properties of the scattering amplitude are discussed, and a representation of the potential is obtained using the scattering amplitude. A uniform time estimation of the Cauchy problem solution for the Nav... 详细信息

关键词： schrodinger’s equation Potential scattering Amplitude Cauchy Problem Navier-stokes equations Fourier Transform

Quantum-Classical Algorithm for an Instantaneous spectral Analysis of signals:A Complement to Fourier Theory

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Journal of Quantum Information science 2018年第2期8卷 52-77页

作者： Mario Mastriani Quantum Communications Group Merx Communications LLCAventuraFLUSA

A quantum time-dependent spectrum analysis, or simply, quantum spectral analysis (QsA) is presented in this work, and it’s based on schrödinger’s equation. In the classical world, it is named frequency in time (FIT), which is used here as a complement of the traditional frequency-dependent spectral analysis based on Fourier theory. Besides, FIT is a metric which assesses the impact of the flanks of a signal on its frequency spectrum, not taken into account by Fourier theory and lets alone in real time. Even more, and unlike all derived tools from Fourier Theory (i.e., continuous, discrete, fast, short-time, fractional and quantum Fourier Transform, as well as, Gabor) FIT has the following advantages, among others: 1) compact support with excellent energy output treatment, 2) low computational cost, O(N) for signals and O(N2) for images, 3) it does not have phase uncertainties (i.e., indeterminate phase for a magnitude = 0) as in the case of Discrete and Fast Fourier Transform (DFT, FFT, respectively). Finally, we can apply QsA to a quantum signal, that is, to a qubit stream in order to analyze it spectrally.

关键词： Fourier Theory Heisenberg’s Uncertainty Principle Quantum Fourier Transform Quantum Information Processing Quantum signal Processing schrodinger’s equation spectral Analysis

Navier-stokes equations—Millennium Prize Problems

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Natural science 2015年第2期7卷 88-99页

作者： Asset A.Durmagambetov Leyla s.Fazilova system Research“Factor”Company AstanaKazakhstan

In this work, we present final solving Millennium Prize Problems formulated by Clay Math. Inst., Cambridge. A new uniform time estimation of the Cauchy problem solution for the Navier-stokes equations is provided. We ... 详细信息

关键词： schrodinger’s equation Potential scattering Amplitude Cauchy Problem Navier-stokes equations Fourier Transform The Global solvability and Uniqueness of the Cauchy Problem The Loss of smoothness The Millennium Prize Problems

A Trapezoidal-Like Integrator for the Numerical solution of One-Dimensional Time Dependent schrodinger equation

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American Journal of Computational Mathematics 2014年第4期4卷 271-279页

作者： Johnson Oladele Fatokun Department of Mathematical science and Information Technology Federal University Dutsin-Ma Nigeria

In this paper, the one-dimensional time dependent schr?dinger equation is discretized by the method of lines using a second order finite difference approximation to replace the second order spatial derivative. The evolving system of stiff Ordinary Differential equation (ODE) in time is solved numerically by an L-stable trapezoidal-like integrator. Results show accuracy of relative maximum error of order 10?4 in the interval of consideration. The performance of the method as compared to an existing scheme is considered favorable.

关键词： schrodinger’s equation Partial Differential equations Method of Lines (MOL) stiff ODE Trapezoidal-Like Integrator