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Showing 1 to 20 of 66 for “"schrodinger equation"”.
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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 …
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Asymptotic stability and completeness in 2D nonlinear Schrodinger equation
… 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 superposition of a solitary wave (ground state) and a radiative …
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Study of the applications of the nonlinear Schrodinger equation.
Thesis (B.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1978.
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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 …
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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 …
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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 …
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The time-independent Schrodinger equation with Dirac delta potentials in an infinite potential well
… using the time-independent Schr\"{o}dinger equation, the typical boundary conditions for an infinite well and normalization conditions to obtain the wave function $\psi(x)$. The system naturally imposes an additional condition at $\psi(0)$ due to the Dirac delta function, which yields the …
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The relativistic Schrödinger equation and its application to pseudoscalar meson baryon scattering in a broken SU(3) symmetry model
… within the framework of the relativistic Schrodinger equation and in the four lowest partia1 waves. The driving force (potential) is obtained by ca1culating the allowed single particle exchange processes for which thee~oharged particles have spin less than or equal to l/2. The on shell …
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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 …
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Signal Flow Graph Approach to Multiphoton Analysis and Transient Characteristics of Mode-Locked Far Infrared Lasers
… developed in this study. It is shown that the Schrodinger equation for the multiphoton interactions can be represented as signal flow graphs in the semiclassical limit. A few examples are given to illustrate the construction, manipulation and application of the graphs.
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Modulation of non-linear wave in a fluid-filled thick elastic tube
… the reductive perturbation method. The governing equation for the incompressible inviscid fluid model was shown to be the non-linear Schrodinger equation (NLSE). As the dissipative non-linear Schrodinger equation (DNLSE), the control equation of the incompressible viscous fluid model was derived. …
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Application of the relativistic Schrödinger equation to the bootstrap problem
The relativistic Schrodinger equation is used to investigate the meson bootstrap problem. The forces are computed from the usual Feynman graphs for single particle exchanges. At first, pseudoscalar-pseudoscalarmeson scattering is considered in a multichannel calculation. The vector mesons obtained …
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Next-Generation Flash Memories Using Two-Dimensional Materials
… in the channel is calculated using the Poisson-Schrodinger equation; the numerical algorithm is based on the Newton-Raphson (NR) method. A comparative study is done on two different Floating Gate Transistor (FGT) based on the proposed model. Silicon dioxide (SiO₂) and Hafnium dioxide (HfO₂) are …
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On Initial-Boundary Value Problems for the Nonlinear Schroedinger Equation and the Ginzburg-Landau Equation
… thesis. Well-posedness of the forced nonlinear Schrodinger equation (NLS) is shown in Chapter 1. The global solution to an initial-boundary value problem for the NLS is proved in Chapter 2. Global existence of the full-line problem for the Ginzburg-Landau equation (GL) is shown in Chapter 3. In …
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High-accuracy and high-precision infrared spectroscopy of fundamental molecular ions using noise immune cavity enhanced optical heterodyne velocity modulation spectroscopy
"Solving the Schrodinger equation for molecules is anything but trivial given the multi-body nature of the problem, and exact solutions are not achievable ab initio. Therefore, quantum mechanical calculations on molecules require approximate treatment in order to calculate quantities such as energy …
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A study of vibrating-rotating motions of polyatomic molecules
… were obtained by solving the time-independent Schrodinger equation. The Hamiltonian of the system was expressed in both rectilinear and curvilinear coordinates, Potential energy surfaces were obtained from fitting either ab initio or experimental data points by a series expansion of convenient …
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A new method of modelling tuneable lasers with functional composition
… tuneable lasers. Using the generalized nonlinear Schrodinger equation as a starting point, expressions for the transformations undergone by the pulse are derived for each of the five components (gain, loss, dispersion, modulation, and nonlinearity) within the laser cavity. These transformations …
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Effect of Nanoscale Defects on Electrical and Optical Properties in Iii-V Semiconductors
The Schrodinger equation, in a real space k·p Hamiltonian formation, is solved using the finite element method to study effects of edge and screw dislocations on optical properties in GaN. Energy levels and corresponding wave functions are obtained for the conduction and valence bands, and …
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Investigation into the properties and application of the Diffusion Monte Carlo method
… state wave function for systems governed by the Schrodinger equation. In this paper, familiar problems like the ground state energy of the harmonic oscillator and the Morse oscillator shall be solved using the DMC method and compared to their well-known analytic results. This will support the …
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