Bound states for two dimensional Schrödinger equation with anisotropic interactions localized on a circle

2015 ◽  
Vol 56 (2) ◽  
pp. 022103 ◽  
Author(s):  
E. de Prunelé
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Bound States ◽  
Two Dimensional ◽  
Anisotropic Interactions

A Dynamic Adaptive Wavelet Method for Solution of the Schrodinger Equation

2015 ◽  
Vol 06 (01) ◽  
pp. 1450001 ◽  
Author(s):  
Ratikanta Behera ◽  
Mani Mehra
Keyword(s):  
Schrödinger Equation ◽  
Computational Efficiency ◽  
Schrodinger Equation ◽  
Computational Cost ◽  
Two Dimensional ◽  
Wavelet Method ◽  
Adaptive Wavelet ◽  
One Dimensional ◽  
Grid Adaptation ◽  
Adaptive Wavelet Method

In this paper, we present a dynamically adaptive wavelet method for solving Schrodinger equation on one-dimensional, two-dimensional and on the sphere. Solving one-dimensional and two-dimensional Schrodinger equations are based on Daubechies wavelet with finite difference method on an arbitrary grid, and for spherical Schrodinger equation is based on spherical wavelet over an optimal spherical geodesic grid. The method is applied to the solution of Schrodinger equation for computational efficiency and achieve accuracy with controlling spatial grid adaptation — high resolution computations are performed only in regions where a solution varies greatly (i.e., near steep gradients, or near-singularities) and a much coarser grid where the solution varies slowly. Thereupon the dynamic adaptive wavelet method is useful to analyze local structure of solution with very less number of computational cost than any other methods. The prowess and computational efficiency of the adaptive wavelet method is demonstrated for the solution of Schrodinger equation on one-dimensional, two-dimensional and on the sphere.

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