Scattering state of the multiparameter potential with an improved approximation for the centrifugal term inD-dimensions

2015 ◽  
Vol 116 (2) ◽  
pp. 81-87 ◽  
Author(s):  
Akpan N. Ikot ◽  
Eno J. Ibanga ◽  
Hassan Hassanabadi
Keyword(s):  
Centrifugal Term ◽  
Scattering State

Bound and scattering state solutions of a hyperbolic-type potential

2013 ◽  
Vol 91 (2) ◽  
pp. 120-125 ◽  
Author(s):  
Ali Ghoumaid ◽  
Farid Benamira ◽  
Larbi Guechi
Keyword(s):  
Hyperbolic Type ◽  
Wave Functions ◽  
Integral Approach ◽  
Centrifugal Term ◽  
Scattering Function ◽  
S Waves ◽  
Barrier Potential ◽  
Scattering States ◽  
Scattering State ◽  
Type Potential

A hyperbolic-type potential with a centrifugal term is solved approximately using the path integral approach. The radial Green's function is expressed in closed form, from which the energy spectrum and the suitably normalized wave functions of bound and scattering states are extracted for (1/2) − [Formula: see text] < σ < (1/2) + [Formula: see text]. Besides, the phase shift and the scattering function Sl for each angular momentum l are deduced. The particular cases corresponding to the s-waves (l = 0) and the barrier potential (σ = 1) are also analyzed.

THE RELATIVISTIC BOUND AND SCATTERING STATES OF THE ECKART POTENTIAL WITH A PROPER NEW APPROXIMATE SCHEME FOR THE CENTRIFUGAL TERM

2009 ◽  
Vol 24 (01) ◽  
pp. 161-172 ◽  
Author(s):  
GAO-FENG WEI ◽  
SHI-HAI DONG ◽  
V. B. BEZERRA
Keyword(s):  
Bound States ◽  
Gordon Equation ◽  
Scattering Amplitude ◽  
Centrifugal Term ◽  
Radial Wave ◽  
Scattering States ◽  
Special Cases ◽  
Scattering State ◽  
Klein Gordon ◽  
Klein Gordon Equation

The approximately analytical bound and scattering state solutions of the arbitrary l wave Klein–Gordon equation for mixed Eckart potentials are obtained through a proper new approximation to the centrifugal term. The normalized analytical radial wave functions of the l wave Klein–Gordon equation with the mixed Eckart potentials are presented and the corresponding energy equations for bound states and phase shifts for scattering states are derived. It is shown that the energy levels of the continuum states reduce to those of the bound states at the poles of the scattering amplitude. Two special cases — for the s wave and for l = 0 and β = 0 — are also studied, briefly.

The relativistic bound and scattering states of the Manning-Rosen potential with an improved new approximate scheme to the centrifugal term

Open Physics ◽  
2009 ◽  
Vol 7 (1) ◽  
Author(s):  
Gao-Feng Wei ◽  
Zhi-Zhong Zhen ◽  
Shi-Hai Dong
Keyword(s):  
Bound States ◽  
Gordon Equation ◽  
Scattering Amplitude ◽  
Energy Levels ◽  
Centrifugal Term ◽  
Radial Wave ◽  
Scattering States ◽  
Scattering State ◽  
Klein Gordon ◽  
Klein Gordon Equation

AbstractThe approximately analytical bound and scattering state solutions of the arbitrary l-wave Klein-Gordon equation for the mixed Manning-Rosen potentials are carried out by an improved new approximation to the centrifugal term. The normalized analytical radial wave functions of the l-wave Klein-Gordon equation with the mixed Manning-Rosen potentials are presented and the corresponding energy equations for bound states and phase shifts for scattering states are derived. It is shown that the energy levels of the continuum states, reduce to the bound states of those at the poles of the scattering amplitude. Some useful figures are plotted to show the improved accuracy of our results and the special case for wave is studied briefly.

Scattering State of Coupled Hulthen–Woods–Saxon Potentials for the Duffin–Kemmer–Petiau Equation with Pekeris Approximation for the Centrifugal Term

2015 ◽  
Vol 70 (3) ◽  
pp. 185-191 ◽  
Author(s):  
Akpan N. Ikot ◽  
Hillary P. Obong ◽  
Joy D. Olisa ◽  
Hassan Hassanabadi
Keyword(s):  
Energy Spectrum ◽  
Wave Functions ◽  
Centrifugal Term ◽  
Saxon Potential ◽  
Radial Wave ◽  
Dkp Equation ◽  
Scattering States ◽  
Special Cases ◽  
Scattering State ◽  
Pekeris Approximation

AbstractWe studied the approximate analytical scattering state of the Duffin–Kemmer–Petiau (DKP) equation for arbitrary l-state for couple Hulthen–Woods–Saxon potential using the Pekeris approximation for the centrifugal term. We obtained an energy spectrum, normalised radial wave functions of the scattering states, and the corresponding formula for the phase shifts, which is derived in detail. Special cases of Hulthen and Woods–Saxon potentials were also studied.

DEVELOPMENT AND ANALYSIS OF A NOVEL KIND OF SMART THERMOTROPIC MATERIAL

2010 ◽  
Vol 03 (02) ◽  
pp. 135-139 ◽  
Author(s):  
JIAN YAO ◽  
CHENG-WEN YAN
Keyword(s):  
Energy Efficient ◽  
High Performance ◽  
Pure Water ◽  
Methyl Cellulose ◽  
Spectral Transmittance ◽  
Thermally Induced ◽  
Scattering State ◽  
Turbid State ◽  
Mixing Proportion ◽  
Switching Temperature

Thermally induced switching temperature and spectral transmittance of a novel kind of smart thermotropic material developed by a different mixing proportion of hydroxypropyl methyl cellulose (HPMC), sodium chloride ( NaCl ) and pure water was measured. Radiation transmittance measurements were carried out on a thermotropic double glazing window sample, a double glazing window and a low-E double glazing window. Results show that the thermotropic double-glazed window with optimum mixing proportion of HPMC, NaCl and pure water of 2:10:100 by mass-reduces radiation transmittance at fully turbid state by up to 72% and 32% respectively, compared to the ordinary double-glazed window and low-E double-glazed window which do not have adjustable radiation transmittance; its radiation transmittance changed from transparent state to light scattering state up to 60%, indicating a high performance on switching solar radiation and a great potential for energy efficient windows.

scholarly journals The Nonrelativistic Scattering States of the Deng-Fan Potential

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Bentol Hoda Yazarloo ◽  
Liangliang Lu ◽  
Guanghui Liu ◽  
Saber Zarrinkamar ◽  
Hassan Hassanabadi
Keyword(s):  
Approximation Scheme ◽  
Wave Functions ◽  
Energy Eigenvalues ◽  
Scattering States ◽  
Special Cases ◽  
Scattering State ◽  
Term Energy ◽  
Scattering Phase ◽  
Scattering Phase Shifts ◽  
Nonrelativistic Scattering

The approximately analytical scattering state solution of the Schrodinger equation is obtained for the Deng-Fan potential by using an approximation scheme to the centrifugal term. Energy eigenvalues, normalized wave functions, and scattering phase shifts are calculated. We consider and verify two special cases: thel=0and thes-wave Hulthén potential.

Strichartz Estimates for Wave Equations with Charge Transfer Hamiltonians

2021 ◽  
Vol 273 (1339) ◽  
Author(s):  
Gong Chen
Keyword(s):  
Wave Equation ◽  
Charge Transfer ◽  
Wave Equations ◽  
Linear Models ◽  
Energy Estimate ◽  
Strichartz Estimates ◽  
Content Type ◽  
Scattering States ◽  
Scattering State ◽  
A Charge

We prove Strichartz estimates (both regular and reversed) for a scattering state to the wave equation with a charge transfer Hamiltonian in R 3 \mathbb {R}^{3} : \[ ∂ t t u − Δ u + ∑ j = 1 m V j ( x − v → j t ) u = 0. \partial _{tt}u-\Delta u+\sum _{j=1}^{m}V_{j}\left (x-\vec {v}_{j}t\right )u=0. \] The energy estimate and the local energy decay of a scattering state are also established. In order to study nonlinear multisoltion systems, we will present the inhomogeneous generalizations of Strichartz estimates and local decay estimates. As an application of our results, we show that scattering states indeed scatter to solutions to the free wave equation. These estimates for this linear models are also of crucial importance for problems related to interactions of potentials and solitons, for example, in [Comm. Math. Phys. 364 (2018), no. 1, pp. 45–82].

scholarly journals Breakdown of Regularity of Scattering for Mass-Subcritical NLS

2020 ◽  
Author(s):  
Gyu Eun Lee
Keyword(s):  
Initial Data ◽  
Wave Operator ◽  
Schrodinger Equation ◽  
Scattering Problem ◽  
Asymptotic Completeness ◽  
Nonlinear Schrodinger Equation ◽  
Mild Form ◽  
Scattering State ◽  
Subcritical Nonlinearity ◽  
Class C

Abstract We study the scattering problem for the nonlinear Schrödinger equation $i\partial _t u + \Delta u = |u|^p u$ on $\mathbb{R}^d$, $d\geq 1$, with a mass-subcritical nonlinearity above the Strauss exponent. For this equation, it is known that asymptotic completeness in $L^2$ with initial data in $\Sigma$ holds and the wave operator is well defined on $\Sigma$. We show that there exists $0&lt;\beta &lt;p$ such that the wave operator and the data-to-scattering-state map do not admit extensions to maps $L^2\to L^2$ of class $C^{1+\beta }$ near the origin. This constitutes a mild form of ill-posedness for the scattering problem in the $L^2$ topology.

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