A pedagogical extension of the one-dimensional Schrödinger’s equation to symmetric proximity effect system film sandwiches

AbstractThis paper integrates dispersive optical solitons in special optical metamaterials with a time dependent coefficient. We obtained some optical solitons of the aforementioned equation. It is shown that the examined dependent coefficients are affected by the velocity of the wave. The first integral method (FIM) and ansatz method are applied to reach the optical soliton solutions of the one-dimensional nonlinear Schrödinger’s equation (NLSE) with time dependent coefficients.

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Numerical solution of the one-dimensional time-independent Schrödinger’s equation by recursive evaluation of derivatives

Applied Mathematics and Computation ◽

10.1016/j.amc.2010.01.002 ◽

2010 ◽

Vol 215 (12) ◽

pp. 4400-4405 ◽

Cited By ~ 6

Author(s):

Asai Asaithambi

Keyword(s):

Numerical Solution ◽

One Dimensional ◽

Schrödinger’S Equation ◽

The One ◽

Recursive Evaluation ◽

Schrödinger's Equation

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A New Explicit Four-Step Symmetric Method for Solving Schrödinger’s Equation

Mathematics ◽

10.3390/math7111124 ◽

2019 ◽

Vol 7 (11) ◽

pp. 1124 ◽

Cited By ~ 1

Author(s):

Saleem Obaidat ◽

Said Mesloub

Keyword(s):

Stability Analysis ◽

Linear Method ◽

Phase Lag ◽

One Dimensional ◽

Schrödinger’S Equation ◽

First Derivative ◽

Algebraic Order ◽

The One ◽

Schrödinger's Equation ◽

Symmetric Method

In this article we have developed a new explicit four-step linear method of fourth algebraic order with vanished phase-lag and its first derivative. The efficiency of the method is tested by solving effectively the one-dimensional time independent Schrödinger’s equation. The error and stability analysis are studied. Also, the new method is compared with other methods in the literature. It is found that this method is more efficient than these methods.

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Exact and approximate solutions of Schrödinger’s equation for a class of trigonometric potentials

Open Physics ◽

10.2478/s11534-012-0147-3 ◽

2013 ◽

Vol 11 (1) ◽

Cited By ~ 11

Author(s):

Hakan Ciftci ◽

Richard Hall ◽

Nasser Saad

Keyword(s):

Differential Equation ◽

Coordinate Transformation ◽

Iteration Method ◽

Order Differential Equation ◽

Approximate Solutions ◽

Asymptotic Iteration Method ◽

Perturbation Expansions ◽

One Dimensional ◽

Schrödinger’S Equation ◽

Schrödinger's Equation

AbstractThe asymptotic iteration method is used to find exact and approximate solutions of Schrödinger’s equation for a number of one-dimensional trigonometric potentials (sine-squared, double-cosine, tangent-squared, and complex cotangent). Analytic and approximate solutions are obtained by first using a coordinate transformation to reduce the Schrödinger equation to a second-order differential equation with an appropriate form. The asymptotic iteration method is also employed indirectly to obtain the terms in perturbation expansions, both for the energies and for the corresponding eigenfunctions.

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A new implicit symmetric method of sixth algebraic order with vanished phase-lag and its first derivative for solving Schrödinger's equation

Open Mathematics ◽

10.1515/math-2021-0009 ◽

2021 ◽

Vol 19 (1) ◽

pp. 225-237

Author(s):

Saleem Obaidat ◽

Rizwan Butt

Keyword(s):

Phase Lag ◽

Step Method ◽

Method Performance ◽

Schrödinger’S Equation ◽

First Derivative ◽

Algebraic Order ◽

The One ◽

Schrödinger's Equation ◽

Better Than ◽

Symmetric Method

Abstract In this article, we have developed an implicit symmetric four-step method of sixth algebraic order with vanished phase-lag and its first derivative. The error and stability analysis of this method are investigated, and its efficiency is tested by solving efficiently the one-dimensional time-independent Schrödinger’s equation. The method performance is compared with other methods in the literature. It is found that for this problem the new method performs better than the compared methods.

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Numerically Efficient Computation of Eigensolution Spectrum in One-Dimensional Heterostructures

International Journal of Modern Physics C ◽

10.1142/s0129183198000893 ◽

1998 ◽

Vol 09 (07) ◽

pp. 927-934 ◽

Cited By ~ 1

Author(s):

F. Farrelly ◽

A. Petri

Keyword(s):

Transfer Matrix ◽

Density Of States ◽

Spatial Behavior ◽

Efficient Computation ◽

Matrix Methods ◽

One Dimensional ◽

Schrödinger’S Equation ◽

Schrödinger's Equation

We describe a method that allows an efficient determination of the density of states of one-dimensional heterostructures. We show that the propagation of an appropriate vector through the structure together with the use of the node theorem is much more effective than transfer matrix methods in those cases in which highly degenerate spectra are present. As a by-product, spatial behavior of solutions is also easily obtained. A case of elastic propagation is discussed in detail and application to Schrödinger's equation is presented.

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