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Dirichlet-to-Neumann and Neumann-to-Dirichlet embedding methods for bound states of the Schrodinger equation.
PublikacjaPrzeformułowano metodę Inglesfielda, stosowaną do obliczania własności stanów związanych równania Schrodingera, stosując formalizm operatorów całkowych Dirichleta-do-Neumanna(DtN) i Neumanna-do-Dirichleta (NtD). Wykorzystano zasady wariacyjne dla energii dopuszczające użycie funkcji próbnych nieciągłych wraz z pochodnymi. Podano metodę konstrukcji jąder operatorów DtN i NtD za pomocą rozwiązań zagadnienia własnego typu Steklova....
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Electronic structure and time-dependent description of rotational predissociation of LiH
PublikacjaThe adiabatic potential energy curves of the ^1Sigma+ and ^1Pi states of the LiH molecule were calculated. They correlate asymptotically to atomic states, such as 2s + 1s, 2p + 1s, 3s + 1s, 3p + 1s, 3d + 1s, 4s + 1s, 4p + 1s and 4d + 1s. A very good agreement was found between our calculated spectroscopic parameters and the experimental ones. The dynamics of the rotational predissociation process of the 1^1Pi state were studied...
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Coupled nonlinear Schrödinger equations in optic fibers theory
PublikacjaIn this paper a detailed derivation and numerical solutions of CoupledNonlinear Schr¨odinger Equations for pulses of polarized electromagnetic wavesin cylindrical fibers has been reviewed. Our recent work has been compared withsome previous ones and the advantage of our new approach over other methods hasbeen assessed. The novelty of our approach lies is an attempt to proceed withoutloss of information within the frame of basic...
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Numerical Characterization of Thresholds for the Focusing 1d Nonlinear Schrödinger Equation
PublikacjaThe focusing nonlinear Schrödinger equation arises in various physical phenomena and it is therefore of interest to determine mathematical conditions on the initial data that guarantee whether the corresponding solution will blow up in finite time or exist globally in time. We focus on solutions to the mass‐supercritical nonlinear Schrödinger equation (1) in 1D case. In particular, we investigate numerical thresholds between blow...