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Showing 1 to 14 of 14 for “"Schrodinger equations"”.
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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.
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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 …
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Group theoretic properties of some Schröedinger equations : systematic derivation
… I study the group theoretic structure of the Schrodinger equations of simple systems by making use of a new systematic method. Group theoretic analysis of Schrodinger equations have been made previously by numerous physicists. The groups found may be classified as: a) geometrical groups; b) …
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Discrete Fourier restriction phenomenon associated with some periodic dispersive equations
… Fourier restriction phenomenon associated with Schrodinger equations. We study the size of the Fourier transform of a periodic function on a truncated discrete paraboloid. We develop two ways to tackle the problem, and the second one recovers Bourgain's level set result on Strichartz estimates …
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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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Excited State Dynamics and Energy Transfer Studies of Aromatic Molecules
… which solve the nuclear and electronic Schrodinger equations "on the fly". In this work, we also examine the effects of both meta- and para-conjugation in the ground and excited states on the electronic communication in phenylethynylenes. These studies suggest that the electronic …
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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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Group theoretical studies of the periodic chart and of configuration mixing in the ground state of helium
… of all atoms. <sup>24</sup> Investigating the Schrodinger equation with this generalized Hamiltonian, it should be possible to relate the properties of different atoms and find the structure of the periodic chart from fundamental principles of dynamics and group theory. One can can use the same …
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Localisation of Bose-Einstein condensates in optical lattices
… a discrete model using the Discrete Nonlinear Schrodinger equation. Spatially localised modes, known as lattice solitons in the continuous model, or discrete breathers in the discrete model, can occur and are the focus of this thesis. Theoretical and computational studies of these localised …
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A variational theory of nuclear matter
… function is generated by a series of two-body Schrodinger equations with boundary conditions which require the wave function to heal at a distance d. The wave function is parameterized by d and by the magnitudes of the non-central correlations. Expectation values with variational wave functions …
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Nonlinear photonics with applications in lightwave communications
… cross-phase modulation by solving the nonlinear Schrodinger equations using the split step method. Silicon has strong two photon absorption at telecommunication wavelengths, i.e. 1550 nm, and therefore all nonlinear losses (i.e. TPA and free carriers generated through TPA) are included in the …
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Existence and Stability of Solitary Waves for NLS with Defects
… waves to dispersive partial differential equations and, in particular to nonlinear Schr\"odinger equations with defects nonlinearity. First we identify necessary and sufficient conditions for the existence of appropriately localized waves for the inhomogeneous semi-linear Schr\"odinger …
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Numerical Methods and Their Analysis for Some Nonlinear Dispersive Equations
… solutions of several classes of dispersive equations, namely, the coupled Schrodinger-Poisson (SP) type system, the Klein-Gordon (KG) equation, the sine-Gordon (SG) and perturbed Schrodinger (PNLS) equations. For SP type system, various numerical methods were compared for ground states …