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Showing 1 to 8 of 8 for “"Schrödinger equation"”.
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Nonlinear Schrödinger equation on graphs with physical potentials
L'abstract è presente nell'allegato / the abstract is in the attachment
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TWO RESULTS ON THE GLOBAL DYNAMICS OF PDES ON THE CIRCLE.
… global in time approximation for two nonlinear Schrödinger equations. Chapter 1 focuses on the non-relativistic limit of the one-dimensional cubic nonlinear Klein-Gordon equation, which is known (formally) to converge to the cubic nonlinear Schrödinger equation as c → ∞. More precisely, it is …
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The dynamics of bose gases
… sequence of coupled partial differential equations that models the dynamics of Bose gases and arises in the derivation of the cubic and quintic nonlinear Schrödinger equations from an N-body linear Schrödinger equation. In Chapter 2, we consider the cubic case in R³ and derive the GP …
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Theoretical studies of few-body problems
… and molecular targets produce many outcomes. The Schrödinger equation is not analytically soluble for more than two mutually interacting particles. As a result, theory must resort to using approximations, the validity of which is determined by comparison with experiment. This work is focused on …
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Fully differential cross sections for four-body scattering processes
… However, for Coulomb forces, the solution of the Schrödinger equation can only be obtained analytically for two mutually interacting particles. As a result, when more than two particles are involved, theory must resort to approximations. The validity of these approximations is then determined by …
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Geometrical approximation methods for the discrete spectra of Schrödinger operators
… reliable bounds for the eigenvalues of the Schrödinger operator [Special characters omitted.] . We introduce a three-parameter variational function, to determine an upper bound to the ground-state energy, of the supersingular spiked harmonic oscillator potentials [Special characters …
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Development of intersubband terahertz lasers using multiple quantum well structures
… is a self-consistent solution among the Schrödinger equation, Poisson equation, and rate equations. Electrons are injected by resonant tunneling to populate the upper subband; the lower subband is depopulated by fast longitudinal optical (LO) phonon scattering. THz emission devices …
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Spectral Optimization Problems Controlling Wave Phenomena
… the PDE constraint is a time-independent wave equation and the objective function governs some aspect of wave motion. We consider the shape optimization of functions of Dirichlet-Laplacian eigenvalues associated with the set of star-shaped, symmetric, bounded planar regions with smooth …