AN AUDIO-FREQUENCY CIRCUIT MODEL OF THE ONE-DIMENSIONAL SCHROEDINGER EQUATION AND ITS SOURCES OF ERROR

1955 ◽  
Vol 33 (8) ◽  
pp. 483-491
Author(s):  
J. H. Blackwell ◽  
D. R. Fewer ◽  
L. J. Allen ◽  
R. S. Cass
Keyword(s):  
Finite Difference ◽  
Schroedinger Equation ◽  
Circuit Model ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Audio Frequency ◽  
Previous Theory ◽  
One Dimensional ◽  
The Past ◽  
The One

An audio-frequency circuit model of the one-dimensional Schroedinger equation has been constructed, based on original suggestions by G. Kron. The previous theory of such devices has been re-examined thoroughly and errors due to the basic finite-difference approximation separated from those due to electrical causes. It is found that the former type of error is likely to be dominant in practice and that in the past discrepancies due to errors of this kind have actually been ascribed to experimental causes.

Effect of the Spatial Extent of the Control in a Bilinear Control Problem for the Schroedinger Equation

2009 ◽  
Author(s):  
Katherine A. Kime
Keyword(s):  
Differential Geometry ◽  
Finite Difference ◽  
Lie Algebras ◽  
Grid Point ◽  
Schroedinger Equation ◽  
Time Varying ◽  
One Dimensional ◽  
Bilinear Control ◽  
The One ◽  
Bilinear Control Problem

We consider control of the one-dimensional Schroedinger equation through a time-varying potential. Using a finite difference semi-discretization, we consider increasing the extent of the potential from a single central grid-point in space to two or more gridpoints. With the differential geometry package in Maple 8, we compute and compare the corresponding Control Lie Algebras, identifying a trend in the number of elements which span the Control Lie Algebras.

scholarly journals New Nonpolynomial Spline in Compression Method of for the Solution of 1D Wave Equation in Polar Coordinates

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Venu Gopal ◽  
R. K. Mohanty ◽  
Navnit Jha
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Mathematical Formulation ◽  
Finite Difference Approximation ◽  
Polar Coordinates ◽  
Difference Approximation ◽  
Compression Method ◽  
One Dimensional ◽  
Spline In Compression ◽  
The Stability

We propose a three-level implicit nine point compact finite difference formulation of order two in time and four in space direction, based on nonpolynomial spline in compression approximation in -direction and finite difference approximation in -direction for the numerical solution of one-dimensional wave equation in polar coordinates. We describe the mathematical formulation procedure in detail and also discussed the stability of the method. Numerical results are provided to justify the usefulness of the proposed method.

scholarly journals Blow Up of Quintic Power 1-D Nonlinear Schroedinger Equation

2017 ◽  
Author(s):  
Agah D. Garnadi
Keyword(s):  
Blow Up ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Heat Equations ◽  
Adaptive Grids ◽  
Time Singularity ◽  
One Dimensional ◽  
Blowing Up ◽  
Similarity Scaling ◽  
The One

This work studies an adaptive finite difference approximation to the one dimensional nonlinear Schroedinger equiation with quintic power, with special emphasis on the case when the solution blows up with finite blowing-up time $T_\infty.$ The adaptivity is utilizing similarity scaling adaptive grids studied by Berger and Kohn to study numerical solution of semilinear heat equations with finite blowing-up time.Furthermore, we reports an asymptotic behavior of the blow-up solution approaching $T_\infty$ time singularity.

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