1. Pre-Introduction 2 2. Introduction and background 2 3. Three (sample) principal results 5 4. A criterion for ac spectrum 6 5. Expansions for generalized eigenfunctions 9 6. WKB approximation 10 7. Transmission and reflection coefficients 11 8. Reduction and expansion 13 9. Maximal operators 14 10. Multilinear operators and maximal variants 18 11. Wave operators and time-dependent scattering ...

In this paper we investigate the semiclassical behavior of the lowest eigenvalues of a model Schrödinger operator with variable magnetic field. This work aims at proving an accurate asymptotic expansion for these eigenvalues, the corresponding upper bound being already proved in the general case. The present work also aims at establishing localization estimates for the attached eigenfunctions. ...

We present a spectrum-splitting approach to conduct all-electron Kohn-Sham density functional theory (DFT) calculations by employing Fermi-operator expansion of the Kohn-Sham Hamiltonian. The proposed approach splits the subspace containing the occupied eigenspace into a core-subspace, spanned by the core eigenfunctions, and its complement, the valence-subspace, and thereby enables an efficient...

An integral representation is found for hypergeometric coherent states. It contains a generalized function. asymptotic expansion of states near z=1 constructed. This used to find eigenfunctions the Hamiltonian hydrogen atom in magnetic field lower boundaries spectral clusters.

We have developed and tested a version of the resolvent (or Green's function) method, based on the shift-inverse of the Maxwellian operator, that ensures stable convergence of iterative computations of localized defect modes of H-polarization in two-dimensional (2D) photonic crystals. The defect states are obtained by solving the eigenvalue problem for an associated compact operator with the ex...

Photonic crystal fibres are novel optical devices that can be designed to guide light of a particular frequency. This requires two phenomena to occur. First, the frequency of light must be in a gap of the spectrum of the fibre’s cladding (usually a periodic arrangement of air holes), so that the cladding acts as a barrier to that frequency of light. Second, the perturbation or defect in the mid...

Vibrational eigenfunctions are calculated on-the-fly using semiclassical methods in conjunction with ab initio density functional theory classical trajectories. Various semiclassical approximations based on the time-dependent representation of the eigenfunctions are tested on an analytical potential describing the chemisorption of CO on Cu(100). Then, first principles semiclassical vibrational ...

In this work we construct algebraic equation for elements of spectrum of linearized Fokker Planck differential operator for incompressible fluid. We calculate roots of this equation using simple numeric method. For all these roots real part is positive, that is corresponding solutions are damping. Eigenfunctions of linearized Fokker Planck differential operator for incompressible fluid are expr...

In the context of global mean square error concerning number random variables in representation, Karhunen–Loève (KL) expansion is optimal series method for field discretization. The computational efficiency and accuracy KL are contingent upon accurate resolution Fredholm integral eigenvalue problem (IEVP). paper proposes an interpolation based on different basis functions such as moving least s...