scholarly journals Pedagogical applications of the one-dimensional Schrödinger’s equation to proximity effect systems: Comparison of Dirichlet and Neumann boundary conditions

2009 ◽  
Vol 77 (4) ◽  
pp. 360-364 ◽  
Author(s):  
P. R. Broussard
Keyword(s):  
Boundary Conditions ◽  
Proximity Effect ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
One Dimensional ◽  
Schrödinger’S Equation ◽  
The One ◽  
Schrödinger's Equation

scholarly journals Order parameter profiles in a system with Neumann – Neumann boundary conditions

2018 ◽  
Vol 145 ◽  
pp. 01009 ◽  
Author(s):  
Vassil M. Vassilev ◽  
Daniel M. Dantchev ◽  
Peter A. Djondjorov
Keyword(s):  
Boundary Conditions ◽  
Order Parameter ◽  
Neumann Boundary ◽  
Elliptic Functions ◽  
Thermodynamic System ◽  
Neumann Boundary Conditions ◽  
Ginzburg Landau ◽  
One Dimensional ◽  
The One ◽  
Field Plane

In this article we consider a critical thermodynamic system with the shape of a thin film confined between two parallel planes. It is assumed that the state of the system at a given temperature and external ordering field is described by order-parameter profiles, which minimize the one-dimensional counterpart of the standard ϕ4 Ginzburg–Landau Hamiltonian and meet the so-called Neumann – Neumann boundary conditions. We give analytic representation of the extremals of this variational problem in terms ofWeierstrass elliptic functions. Then, depending on the temperature and ordering field we determine the minimizers and obtain the phase diagram in the temperature-field plane.

scholarly journals On the spectrum of one dimensional p-Laplacian for an eigenvalue problem with Neumann boundary conditions

2013 ◽  
Vol 33 (1) ◽  
pp. 9
Author(s):  
Ahmed Dakkak ◽  
Siham El Habib ◽  
Najib Tsouli
Keyword(s):  
Eigenvalue Problem ◽  
Boundary Conditions ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Laplacian Operator ◽  
Strict Monotonicity ◽  
Indefinite Weight ◽  
One Dimensional ◽  
Weight One

This work deals with an indefinite weight one dimensional eigenvalue problem of the p-Laplacian operator subject to Neumann boundary conditions. We are interested in some properties of the spectrum like simplicity, monotonicity and strict monotonicity with respect to the weight. We also aim the study of zeros points of eigenfunctions.

scholarly journals On combined optical solitons of the one-dimensional Schrödinger’s equation with time dependent coefficients

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 65-68 ◽  
Author(s):  
Bulent Kilic ◽  
Mustafa Inc ◽  
Dumitru Baleanu
Keyword(s):  
Soliton Solutions ◽  
First Integral ◽  
Optical Solitons ◽  
Time Dependent ◽  
Ansatz Method ◽  
One Dimensional ◽  
Optical Metamaterials ◽  
Schrödinger’S Equation ◽  
The One ◽  
Schrödinger's Equation

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.

The eigenvalue gap for one-dimensional Schrödinger operators with symmetric potentials

2009 ◽  
Vol 139 (2) ◽  
pp. 359-366 ◽  
Author(s):  
Min-Jei Huang ◽  
Tzong-Mo Tsai
Keyword(s):  
Boundary Conditions ◽  
Schrödinger Operators ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Schrodinger Operators ◽  
One Dimensional ◽  
Eigenvalue Gap

We consider the eigenvalue gap for Schrödinger operators on an interval with Dirichlet or Neumann boundary conditions. For a class of symmetric potentials, we prove that the gap between the two lowest eigenvalues is maximized when the potential is constant. We also give some related results for doubly symmetric potentials.

scholarly journals A Collocation Method for Numerical Solution of Hyperbolic Telegraph Equation with Neumann Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
R. C. Mittal ◽  
Rachna Bhatia
Keyword(s):  
Boundary Conditions ◽  
Numerical Experiments ◽  
Neumann Boundary ◽  
Telegraph Equation ◽  
Neumann Boundary Conditions ◽  
Basis Functions ◽  
One Dimensional ◽  
First Order ◽  
Spline Basis ◽  
Good Agreement

We present a technique based on collocation of cubic B-spline basis functions to solve second order one-dimensional hyperbolic telegraph equation with Neumann boundary conditions. The use of cubic B-spline basis functions for spatial variable and its derivatives reduces the problem into system of first order ordinary differential equations. The resulting system subsequently has been solved by SSP-RK54 scheme. The accuracy of the proposed approach has been confirmed with numerical experiments, which shows that the results obtained are acceptable and in good agreement with the exact solution.

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