Approximate and numerical solutions of the Schrödinger equation

2009 ◽  
pp. 303-337
Author(s):  
E. A. B. Cole
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Numerical Solutions

A STUDY ABOUT THE SOLUTIONS OF SCHRÖDINGER EQUATION WITH AN ASYMPTOTICALLY LINEAR POTENTIAL

1996 ◽  
Vol 11 (03) ◽  
pp. 207-209 ◽  
Author(s):  
ELSO DRIGO FILHO
Keyword(s):  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Analytical Solutions ◽  
Schrodinger Equation ◽  
Numerical Solutions ◽  
Expansion Method ◽  
Linear Potential ◽  
Asymptotically Linear

We determine the solutions of the Schrödinger equation for an asymptotically linear potential. Analytical solutions are obtained by superalgebra in quantum mechanics and we establish when these solutions are possible. Numerical solutions for the spectra are obtained by the shifted 1/N expansion method.

scholarly journals Numerical solutions of the time-dependent Schrödinger equation in two dimensions

2017 ◽  
Vol 95 (2) ◽  
Author(s):  
Wytse van Dijk ◽  
Trevor Vanderwoerd ◽  
Sjirk-Jan Prins
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Numerical Solutions ◽  
Two Dimensions ◽  
Time Dependent

scholarly journals FULLY DISCRETE SCHEMES FOR THE SCHRÖDINGER EQUATION: DISPERSIVE PROPERTIES

2007 ◽  
Vol 17 (04) ◽  
pp. 567-591 ◽  
Author(s):  
LIVIU I. IGNAT
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Numerical Solutions ◽  
Continuous Model ◽  
Local Smoothing ◽  
Euler Approximation ◽  
One Dimensional ◽  
Fully Discrete ◽  
Backward Euler ◽  
The One

We consider fully discrete schemes for the one-dimensional linear Schrödinger equation and analyze whether the classical dispersive properties of the continuous model are presented in these approximations. In particular, Strichartz estimates and the local smoothing of the numerical solutions are analyzed. Using a backward Euler approximation of the linear semigroup we introduce a convergent scheme for the nonlinear Schrödinger equation with nonlinearities which cannot be treated by energy methods.

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