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Showing 1 to 20 of 93 for “"Schrödinger equation"”.
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Schrödinger equation with periodic potentials.
The Schrödinger equation ... is considered. The solution of this equation is reduced to the problem of finding the eigenvectors of an infinite matrix. The infinite matrix is truncated to a finite matrix. The approximation due to the truncation is carefully studied. The band structure of the …
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Dispersive estimates for the Schrödinger equation
Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2010-06-30T12:54:50Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Green_William.pdf: 999536 bytes, checksum: 87eb33f24c92fd62a4874b5db34bf8da (MD5)
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On the discrete nonlinear Schrödinger equation with PT-Symmetry
… method for the nonlocal semi-discrete nonlinear Schrödinger equation (known as Ablowitz-Ladik equation) with parity-time symmetry proposed in Ablowitz and Musslimani’s paper. This includes the eigenfunctions (Jost solutions) of the associated Lax pair, the scattering data and the fundamental …
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On Multi-component Nonlinear Schrödinger Equation with PT-Symmetry
… of nonlocal reductions of the nonlinear Schrödinger equation with parity- time (PT)-symmetry related to symmetric spaces. This includes: the spectral properties of the associated Lax operator, Jost solution, the scattering matrix, the minimal sets of scattering data and the fundamental …
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High accuracy computational methods for the semiclassical Schrödinger equation
The computation of Schrödinger equations in the semiclassical regime presents several enduring challenges due to the presence of the small semiclassical parameter. Standard approaches for solving these equations commence with spatial discretisation followed by exponentiation of the discretised …
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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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The Structure of Multipulse Solitons in the Generalised Nonlinear Schrödinger Equation
… a detailed study of the generalised nonlinear Schrödinger equation (GNLSE) with quartic dispersion and show that it supports infinitely many multipulse solitons for a wide parameter range of the dispersion terms. These solitons exist through the balance between the quartic and quadratic …
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The direct scattering study of the parametrically driven nonlinear Schrödinger equation
Includes abstract. Includes bibliographical references.
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Global SL(2,R) representations of the Schrödinger equation with time-dependent potentials.
… of the solution space of the one-dimensional Schrödinger equation with time-dependent potentials that possess sl₂-symmetry. We give explicit local intertwining maps to multiplier representations and show that the study of the solution space for potentials of the form V (t, x) = …
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Radial, vortex, and spiral solutions to the nonlinear Schrödinger equation and other reaction--diffusion systems
… systems, focusing primarily on the nonlinear Schrödinger equation. Three types of solutions are investigated: radial solutions (with no angular dependence), vortex solutions (with angular dependence but no radial phase dependence), and spiral solutions (which have radial phase dependence). The …
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Study of Vortex Ring Dynamics in the Nonlinear Schrödinger Equation Utilizing GPU-Accelerated High-Order Compact Numerical Integrators
… interactions of vortex rings in the nonlinear Schrödinger equation (NLSE). Single ring dynamics for both bright and dark vortex rings are explored including their traverse velocity, stability, and perturbations resulting in quadrupole oscillations. Multi-ring dynamics of dark vortex rings are …
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The relativistic Schrödinger equation and its application to pseudoscalar meson baryon scattering in a broken SU(3) symmetry model
… 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 potential is …
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On Adiabatic Quantum Molecular Dynamics
… number of nuclei and electrons described by the Schrödinger equation. The full molecular equation is difficult to solve and compute approximations for due to the highly oscillatory nature of the solutions in space and time and due to the high dimensionality of the state space. In the spirit of …
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The Born-Oppenheimer approximation in scattering theory
We analyze the Schrödinger equation i𝜖 ¬<sup>2</sup>â /â tΨ = H(𝜖)Ψ, where H(â ¬) = - f24 Î x + h(X) is the hamiltonian of a molecular system consisting of nuclei with masses of order 𝜖¬<sup>-4</sup> and electrons with masses of order 1. The Born-Oppenheimer approximation consists of the …
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Zur Approximation elektronischer Wellenfunktionen durch anisotrope Gauß-Funktionen
The electronic Schrödinger equation is one of the most important equations in quantum mechanics and provides an explanation of the behaviour of atoms and molecules. The solutions of the eigenvalue problem - the wave functions - describe the state of the modelled quantum mechanic system and can be …
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Asymptotic stability and completeness in 2D nonlinear Schrodinger equation
… 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 superposition of a solitary wave (ground state) and …
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Numerical Treatment of Schrödinger’s Equation for One-Particle and Two-Particle Systems Using Matrix Method
… These calculations are dependent on solving the Schrödinger equation using molecular orbital theory techniques. They are either approximate solutions to actual equations or exact solutions to approximate equations. Exact solutions have not found favor due to the computational expense of the …
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