Plane-wave approximation in theS-matrix and the construction of bound-state wave functions

1974 ◽  
Vol 24 (2) ◽  
pp. 125-145 ◽  
Author(s):  
J. Weiss
Keyword(s):  
Plane Wave ◽  
Bound State ◽  
Wave Functions ◽  
Wave Approximation ◽  
State Wave ◽  
Thes Matrix ◽  
Plane Wave Approximation

scholarly journals Hydrodynamic Interactions in Multiple Body Array: A Simple and Fast Approach Coupling Boundary Element Method and Plane Wave Approximation

2013 ◽  
Author(s):  
Jitendra Singh ◽  
Aurélien Babarit
Keyword(s):  
Boundary Element Method ◽  
Plane Wave ◽  
Boundary Element ◽  
Hydrodynamic Interaction ◽  
Computational Time ◽  
Linear Potential ◽  
Wave Approximation ◽  
Interaction Problem ◽  
Plane Wave Approximation ◽  
Element Method

The hydrodynamic forces acting on an isolated body could be considerably different than those when it is considered in an array of multiple bodies, due to wave interactions among them. In this context, we present in this paper a numerical approach based on the linear potential flow theory to solve full hydrodynamic interaction problem in a multiple body array. In contrast to the previous approaches that considered all bodies in an array as a single unit, the present approach relies on solving for an isolated body. The interactions among the bodies are then taken into account via plane wave approximation in an iterative manner. The boundary value problem corresponding to a isolated body is solved by the Boundary Element Method (BEM). The approach is useful when the bodies are sufficiently distant from each other, at-least greater than five times the characteristic dimensions of the body. This is a valid assumption for wave energy converter devices array of point absorber type, which is our target application at a later stage. The main advantage of the proposed approach is that the computational time requirement is significantly less than the commonly used direct BEM. The time savings can be realized for even small arrays consisting of four bodies. Another advantage is that the computer memory requirements are also significantly smaller compared to the direct BEM, allowing us to consider large arrays. The numerical results for hydrodynamic interaction problem in two arrays consisting of 25 cylinders and same number of rectangular flaps are presented to validate the proposed approach.

RETARDATION EFFECTS IN COVARIANT THREE-DIMENSIONAL BOUND STATE WAVE FUNCTIONS

2005 ◽  
Vol 14 (06) ◽  
pp. 931-947 ◽  
Author(s):  
F. PILOTTO ◽  
M. DILLIG
Keyword(s):  
Bound States ◽  
Three Dimensional ◽  
Bound State ◽  
Relative Energy ◽  
Wave Functions ◽  
Three Dimensions ◽  
State Wave ◽  
Scalar Diquark ◽  
Bound State Wave Function ◽  
Retardation Effects

We investigate the influence of retardation effects on covariant 3-dimensional wave functions for bound hadrons. Within a quark-(scalar) diquark representation of a baryon, the four-dimensional Bethe–Salpeter equation is solved for a 1-rank separable kernel which simulates Coulombic attraction and confinement. We project the manifestly covariant bound state wave function into three dimensions upon integrating out the non-static energy dependence and compare it with solutions of three-dimensional quasi-potential equations obtained from different kinematical projections on the relative energy variable. We find that for long-range interactions, as characteristic in QCD, retardation effects in bound states are of crucial importance.

scholarly journals Exponential decay of bound state wave functions

1973 ◽  
Vol 32 (4) ◽  
pp. 319-340 ◽  
Author(s):  
A. J. O'Connor
Keyword(s):  
Exponential Decay ◽  
Bound State ◽  
Wave Functions ◽  
State Wave

Nuclear bound state wave functions subroutine

1984 ◽  
Vol 35 ◽  
pp. C-10
Author(s):  
William R. Smith
Keyword(s):  
Bound State ◽  
Wave Functions ◽  
State Wave

scholarly journals Post-processing of the plane-wave approximation of Schrödinger equations. Part II: Kohn–Sham models

2020 ◽  
Author(s):  
Geneviève Dusson
Keyword(s):  
Plane Wave ◽  
Ground State ◽  
A Priori ◽  
Processing Method ◽  
Linear Operators ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Post Processing ◽  
Wave Approximation ◽  
Plane Wave Approximation

Abstract In this article, we provide a priori estimates for a perturbation-based post-processing method of the plane-wave approximation of nonlinear Kohn–Sham local density approximation (LDA) models with pseudopotentials, relying on Cancès et al. (2020, Post-processing of the plane-wave approximation of Schrödinger equations. Part I: linear operators. IMA Journal of Numerical Analysis, draa044) for the proofs of such estimates in the case of linear Schrödinger equations. As in Cancès et al. (2016, A perturbation-method-based post-processing for the plane-wave discretization of Kohn–Sham models. J. Comput. Phys., 307, 446–459), where these a priori results were announced and tested numerically, we use a periodic setting and the problem is discretized with plane waves (Fourier series). This post-processing method consists of performing a full computation in a coarse plane-wave basis and then to compute corrections based on the first-order perturbation theory in a fine basis, which numerically only requires the computation of the residuals of the ground-state orbitals in the fine basis. We show that this procedure asymptotically improves the accuracy of two quantities of interest: the ground-state density matrix, i.e. the orthogonal projector on the lowest $N$ eigenvectors, and the ground-state energy.

scholarly journals Limits of the Plane Wave Approximation in the Measurement of Molecular Properties†

2008 ◽  
Vol 112 (39) ◽  
pp. 9439-9447 ◽  
Author(s):  
Zachary B. Walters ◽  
Stefano Tonzani ◽  
Chris H. Greene
Keyword(s):  
Plane Wave ◽  
Molecular Properties ◽  
Wave Approximation ◽  
Plane Wave Approximation

‘‘Exact’’ relativistic theory of two-body bound-state wave functions

1986 ◽  
Vol 34 (5) ◽  
pp. 1920-1934 ◽  
Author(s):  
R. S. Bhalerao ◽  
C. S. Warke
Keyword(s):  
Relativistic Theory ◽  
Bound State ◽  
Wave Functions ◽  
State Wave
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