Low-energy expansion of theS(k) matrix for the Schrödinger equation with a certain type of spherically symmetric potentials

1968 ◽  
Vol 55 (1) ◽  
pp. 125-142 ◽  
Author(s):  
H. Almström
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Low Energy ◽  
Spherically Symmetric ◽  
K Matrix ◽  
Energy Expansion

EXACT SOLUTIONS OF THE SCHRÖDINGER EQUATION WITH SPHERICALLY SYMMETRIC OCTIC POTENTIAL

2012 ◽  
Vol 27 (20) ◽  
pp. 1250112 ◽  
Author(s):  
DAVIDS AGBOOLA ◽  
YAO-ZHONG ZHANG
Keyword(s):  
Schrödinger Equation ◽  
Exact Solutions ◽  
Closed Form ◽  
Schrodinger Equation ◽  
Wave Functions ◽  
Spherically Symmetric ◽  
Algebraic Equations ◽  
Potential Parameters

We present exact solutions of the Schrödinger equation with spherically symmetric octic potential. We give closed-form expressions for the energies and the wave functions as well as the allowed values of the potential parameters in terms of a set of algebraic equations.

scholarly journals Numerical Investigation of a Class of Nonlinear Schrödinger Equations

2004 ◽  
Vol 3 (2) ◽  
Author(s):  
Christopher Ventura
Keyword(s):  
Schrödinger Equation ◽  
Numerical Investigation ◽  
Schrodinger Equation ◽  
Stationary Solutions ◽  
Step Function ◽  
Nonlinear Schrodinger Equation ◽  
Spherically Symmetric ◽  
Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations

This paper numerically investigates the space-localized spherically symmetric, stationary, and singularity-free solutions of the Nonlinear Schrödinger equation when the nonlinearity is a step function. Previously no-node solutions have been obtained analytically. Here, it is shown that localized stationary solutions with one node and two nodes also exist.

scholarly journals NONCOMMUTATIVE SPACE AND THE LOW-ENERGY PHYSICS OF QUASICRYSTALS

2008 ◽  
Vol 23 (13) ◽  
pp. 2037-2045 ◽  
Author(s):  
L. MONREAL ◽  
P. FERNÁNDEZ DE CÓRDOBA ◽  
A. FERRANDO ◽  
J. M. ISIDRO
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Low Energy ◽  
Noncommutative Space ◽  
Nonlinear Schrödinger ◽  
Quasiperiodic Potential ◽  
Space Noncommutativity ◽  
Energy Physics

We prove that the effective low-energy, nonlinear Schrödinger equation for a particle in the presence of a quasiperiodic potential is the potential-free, nonlinear Schrödinger equation on noncommutative space. Thus quasiperiodicity of the potential can be traded for space noncommutativity when describing the envelope wave of the initial quasiperiodic wave.

scholarly journals Axially and spherically symmetric solitons in warm plasma

2011 ◽  
Vol 77 (6) ◽  
pp. 749-764 ◽  
Author(s):  
MAXIM DVORNIKOV
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Numerical Solutions ◽  
Theoretical Description ◽  
Nonlinear Schrodinger Equation ◽  
Spherically Symmetric ◽  
Local Electron ◽  
Non Local ◽  
Warm Plasma

AbstractWe study the existence of stable axially and spherically symmetric plasma structures on the basis of the new nonlinear Schrödinger equation (NLSE) accounting for non-local electron nonlinearities. The numerical solutions of NLSE having the form of spatial solitions are obtained and their stability is analyzed. We discuss the possible application of the obtained results to the theoretical description of natural plasmoids in the atmosphere.

scholarly journals SOLVING THE SCHRÖDINGER EQUATION FOR BOUND STATES WITH MATHEMATICA 3.0

1999 ◽  
Vol 10 (04) ◽  
pp. 607-619 ◽  
Author(s):  
WOLFGANG LUCHA ◽  
FRANZ F. SCHÖBERL
Keyword(s):  
Wave Function ◽  
Schrödinger Equation ◽  
Interaction Potential ◽  
Schrodinger Equation ◽  
Bound States ◽  
Energy Eigenvalue ◽  
Wave Functions ◽  
Spherically Symmetric ◽  
Method Of Solution ◽  
Numerical Integration Procedure

Using Mathematica 3.0, the Schrödinger equation for bound states is solved. The method of solution is based on a numerical integration procedure together with convexity arguments and the nodal theorem for wave functions. The interaction potential has to be spherically symmetric. The solving procedure is simply defined as some Mathematica function. The output is the energy eigenvalue and the reduced wave function, which is provided as an interpolated function (and can thus be used for the calculation of, e.g., moments by using any Mathematica built-in function) as well as plotted automatically. The corresponding program schroedinger.nb can be obtained from [email protected].

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