Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
Results
Showing 1 to 20 of 117 for “"Schrodinger"”.
-
Hamiltonian bifurcations in Schrodinger trimers
The phase space of the three-mode discrete NLS in the nonlinear regime with periodic boundary conditions is investigated by reducing the degree of freedom from three down to two. The families of standing waves are enumerated and normal forms are used to describe several families of relative …
-
Dispersive Estimates for the Schrodinger Equation
… 3 we consider a problem involving the non-linear Schrodinger equation. In particular, we consider the following equation that arises in fiber optic communication systems, iut+dtu xx+u2u=0. We can reduce this to a non-linear, non-local eigenvalue equation that describes the so-called dispersion …
-
Global dynamics of Schrodinger and Dirac equations
Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2020-08-01
-
Asymptotic stability and completeness in 2D nonlinear Schrodinger equation
In this thesis we obtained new results on the asymptotic stability of ground states of the nonlinear Schrödinger equation in space dimension two. Under our hypotheses, the result actually shows asymptotic completeness in the regime of small initial data, i.e. any small initial data evolves into a …
-
Study of the applications of the nonlinear Schrodinger equation.
Thesis (B.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1978.
-
Krein's identity and trace formulas for half-line Schrodinger operators
We consider self-adjoint extensions of the minimal operator generated by the differential expression $\cL = - d^2/dx^2+V$ on the half-line $[0,\infty)$, where $V$ is a real-valued function integrable with respect to the weight $1+x$. The self-adjoint extensions are of Schr\"odinger-type and form a …
-
Diagonalization of 1-D Schrodinger Operators with Piecewise Constant Potentials
<p>In today's world our lives are very layered. My research is meant to adapt current inefficient numerical methods to more accurately model the complex situations we encounter. This project focuses on a specific equation that is used to model sound speed in the ocean. As depth increases, the sound …
-
Finite element solution of the S-limit Schrodinger equation of helium
The Schroedinger equation, for all but the simplest systems, is an elliptic partial differential equation. Almost every method of solution is based on the expansion of the unknown solution in terms of a set of known global functions. Only a few calculations, using strictly numerical techniques …
-
Study of special algorithms for solving Sturm-Liouville and Schrodinger equations
… voor het oplossen van Sturm-Liouville en Schrodinger vergelijkingen. Ook de Matlab-implementatie van de methoden wordt besproken.
-
Asymptotic Stability of the Ground States of the Nonlinear Schrodinger Equation
"We consider a class of nonlinear Schrodinger equations in N = 3, 4, 5 space dimensions with an attractive potential. The nonlinearity is local but rather general encompassing for the first time both subcritical and supercritical (in L2( RN )) nonlinearities. We study the asymptotic stability of …
-
Nonhomogeneous Initial Boundary Value Problems for Two-Dimensional Nonlinear Schrodinger Equations
… value problems (IBVPs) of a class of nonlinear Schrodinger equations posed on a half plane R x R+ and on a strip domain R x [0,L] with Dirichlet nonhomogeneous boundary data in a two-dimensional plane. Compared with pure initial value problems (IVPs), IBVPs over part of entire space with …
-
Boundary Controllability and Stabilizability of Nonlinear Schrodinger Equation in a Finite Interval
The dissertation focuses on the nonlinear Schrodinger equation iu_t+u_{xx}+kappa|u|^2u =0, for the complex-valued function u=u(x,t) with domain t>=0, 0<=x<= L, where the parameter kappa is any non-zero real number. It is shown that the problem is locally and globally well-posed for appropriate …
-
Two Random Multiplicative Processes: Multiplicative Cascades and Eigenvectors of the Random Schrodinger Operator
… of the one-dimensional discrete random Schrodinger operator. This is the Hamiltonian operator on the lattice of integers given by the discrete Laplacian plus an independent, identically distributed delta potential at each point. We restrict this operator to a finite box, pick an …
-
The time-independent Schrodinger equation with Dirac delta potentials in an infinite potential well
The infinite potential well is one of the most well-known models in quantum mechanics, as well as the Dirac delta potential. In the first part of the thesis, one Dirac delta potential is considered using the time-independent Schr\"{o}dinger equation, the typical boundary conditions for an infinite …
-
Vague convergence of spectral shift functions for periodic restrictions of one-dimensional Schrodinger operators
We prove weak and vague convergence results for spectral shift functions associated with self-adjoint one-dimensional Schr\"odinger operators on intervals of the form $(-\ell,\ell)$ with periodic boundary conditions to the full-line spectral shift function in the infinite volume limit $\ell\to …
-
Heat trace and heat content asymptotics for Schrodinger Operators of stable processes/fractional Laplacians
<p>Let <em>V</em> be a bounded and integrable potential over <strong>R</strong><em><sup>d</sup></em> and 0 < α ≤ 2. We show the existence of an asymptotic expansion by means of Fourier Transform techniques and probabilistic methods for the following quantities [special characters omitted] and …
-
Coupled mode reductions and rotating wave approximations in nonlinear equations
… mode theory in the cubic-quintic nonlinear Schrodinger/Gross Pitaevskii (NLS/GP) equation with a linear double-well potential and study justifications of the rotating wave approximations in lattice systems. First, we study the long-time dynamics near a symmetry breaking bifurcation point of …
Page 1 of 6