A new approach to solve the Schrodinger equation with an anharmonic sextic potential

2021 ◽  
Author(s):  
Luca Nanni
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
New Approach

A new approach to the Schrödinger equation with rational potentials

1984 ◽  
Vol 101 (9) ◽  
pp. 473-478 ◽  
Author(s):  
Ming-de Dong ◽  
Jue-Hui Chu
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
New Approach

scholarly journals Radiation reduction of optical solitons resulting from higher order dispersion terms in the nonlinear Schrödinger equation

2005 ◽  
Vol 23 (4) ◽  
pp. 483-502 ◽  
Author(s):  
ROBERT BEECH ◽  
FREDERICK OSMAN
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Optical Solitons ◽  
Higher Order ◽  
Nonlinear Schrodinger Equation ◽  
New Approach ◽  
Nonlinear Schrödinger ◽  
Clear Idea ◽  
Higher Order Dispersion

This paper will present the nonlinearity and dispersion effects involved in propagation of optical solitons, which can be understood by using a numerical routine to solve the nonlinear Schrödinger equation (NLSE). Here, Mathematica v5© (Wolfram, 2003) is used to explore in depth several features of optical solitons formation and propagation. These numerical routines were implemented through the use of Mathematica v5© and the results give a very clear idea of this interesting and important practical phenomenon. It is hoped that this work will open up an important new approach to the cause, effect, and correction of interference from secondary radiation found in the uses of soliton waves in lasers and in optical fiber telecommunication. It is believed that these results will be of considerable use in any work or research in this field and in self-focusing properties of the soliton (Osman et al., 2004a, 2004b; Hora, 1991). In a previous paper on this topic (Beech & Osman, 2004), it was shown that solitons of NLSE radiate. This paper goes on from there to show that these radiations only occur in solitons derived from cubic, or odd-numbered higher orders of NLSE, and that there are no such radiations from solitons of quadratic, or even-numbered higher order of NLSE. It is anticipated that this will stimulate research into practical means to control or eliminate such radiations.

SIMPLE AND ACCURATE EXPLICIT BESSEL AND NEUMANN FITTED METHODS FOR THE NUMERICAL SOLUTION OF THE SCHRÖDINGER EQUATION

2000 ◽  
Vol 11 (01) ◽  
pp. 79-89 ◽  
Author(s):  
T. E. SIMOS
Keyword(s):  
Schrödinger Equation ◽  
Numerical Solution ◽  
Schrodinger Equation ◽  
New Approach ◽  
New Methods ◽  
Radial Schrödinger Equation ◽  
Variable Step ◽  
Algebraic Order ◽  
Free Parameters ◽  
Step Algorithm

Explicit second and fourth algebraic order methods for the numerical solution of the Schrödinger equation are developed in this paper. The new methods have free parameters defined so that the methods are fitted to spherical Bessel and Neumann functions. Based on these new methods we obtained a variable-step algorithm. The results produced based on the numerical solution of the radial Schrödinger equation and the coupled differential equations arising from the Schrödinger equation indicate that this new approach is more efficient than other well known ones.

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