Existence of solutions and scattering theory for the non linear schrödinger equation

2008 ◽  
pp. 218-232
Author(s):  
J. Ginibre ◽  
G. Velo
Keyword(s):  
Schrödinger Equation ◽  
Scattering Theory ◽  
Schrodinger Equation ◽  
Existence Of Solutions ◽  
Non Linear

LOCAL DENSITY CALCULATIONS FOR LARGE SYSTEMS USING MULTIPLE SCATTERING THEORY

1995 ◽  
Vol 02 (01) ◽  
pp. 71-79
Author(s):  
D.M.C. NICHOLSON ◽  
G.M. STOCKS ◽  
Y. WANG ◽  
W.A. SHELTON ◽  
Z. SZOTEK ◽  
...  
Keyword(s):  
Schrödinger Equation ◽  
Multiple Scattering ◽  
Scattering Theory ◽  
Schrodinger Equation ◽  
Local Density ◽  
Basis Set ◽  
Scattering Method ◽  
Multiple Scattering Theory ◽  
Large Systems ◽  
Multiple Scattering Method

The accuracy of energy differences calculated from first principles within the local density approximation (LDA) has been demonstrated for a large number of systems. Armed with these energy differences researchers are addressing questions of phase stability and structural relaxation. However, these techniques are very computationally intensive and are therefore not being used for the simulation of large complex systems. Many of the methods for solving the Kohn-Sham equations of the LDA rely on basis set methods for solution of the Schrodinger equation. An alternative approach is multiple scattering theory (MST). We feel that the locally exact solutions of the Schrodinger equation which are at the heart of the multiple scattering method give the method an efficiency which cannot be ignored in the search for methods with which to attack large systems. Furthermore, the analytic properties of the Green function which is determined directly in MST result in computational shortcuts.

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