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  • 1
    Publication Date: 2011-08-18
    Description: Computational methods are reported for construction of discrete and continuum Schroedinger states in atoms and molecules employing explicit Hilbert space procedures familiar from bound state studies. As theoretical development, the Schroedinger problem of interest is described, the Cauchy-Lanczos bases and orthonormal polynomials used in constructing L-squared Stieltjes-Tchebycheff (ST) approximations to the discrete and continuum states are defined, and certain properties of these functions are indicated. Advantages and limitations of the ST approach to spectral studies relative to more conventional calculations are discussed, and aspects of the approach in single-channel approximations to larger molecules are described. Procedures are indicated for construction of photoejection anisotropies and for performing coupled-channel calculations employing the ST formalism. Finally, explicit descriptive intercomparisons are made of the nature and diagnostic value of ST functions with more conventional scattering functions.
    Keywords: ATOMIC AND MOLECULAR PHYSICS
    Type: Physical Review A - General Physics, 3rd Series (ISSN 0556-2791); 28; Oct. 198
    Format: text
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  • 2
    Electronic Resource
    Electronic Resource
    Woodbury, NY : American Institute of Physics (AIP)
    Applied Physics Letters 76 (2000), S. 1513-1515 
    ISSN: 1077-3118
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Various methods for compensating birefringence depolarization in solid-state rods are theoretically and experimentally analyzed and compared. Gaussian and flat top beam profiles are investigated. The efficiency in depolarization loss reduction using different techniques is discussed in terms of beam profile, rod fill factor, and thermal heat load. In Nd:yttrium–aluminum–garnet, the depolarization loss can be efficiently reduced below 5% with a compensating quarter-waveplate, up to 20 W heat load for a flat top beam and up to 70 W for a gaussian beam. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 3
    Publication Date: 2012-08-28
    Print ISSN: 1945-0877
    Electronic ISSN: 1937-9145
    Topics: Biology , Medicine
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  • 4
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Methods are reported for construction of closed-form optical potentials that provide useful L2-basis-set approximations to the discrete and continuum Schrödinger states of self-adjoint Hamiltonian operators. The potentials are obtained employing information from a finite (Lanczos) reference space only, but nevertheless correspond to explicit summation over an infinite-dimensional remainder space. Connections are indicated between the Stieltjes-Tchebycheff orbital solutions of the resulting optical-potential Schrödinger problem and previously described corresponding moment-theory approximations to spectral densities and distributions. Use of a Lanczos basis insures that the orbital eigenvalues are generalized Gaussian or Radau quadrature points of the spectral density, and that their (reciprocal) norms provide the associated quadrature weights. Convergence of the orbitals in the limit of high order is obtained to Schrödinger eigenstates of finite norm in the discrete spectral region, and to scattering states of improper (infinite) norm in the essential portion of the spectrum. In finite orders the spatial characteristics of the Stieltjes-Tchebycheff orbitals correspond to spectral averages in the neighborhoods of the quadrature points over the correct Schrödinger states. Explicit closed-form expressions are obtained for the spectral content of individual orbitals in terms of orthogonal polynomials without reference to the correct Schrödinger states. A computational application to regular Coulomb l waves illustrates the nature and convergence of the development.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
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  • 5
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Computational studies are reported of Stieltjes orbitals for Hilbert-space descriptions of discrete and continuum molecular electronic eigenstates. Particular attention is focused on the identification of N → V π(π → π*) and N → Vσ(σ → σ*) intravalence contributions to photoexcitation and ionization spectra in CO and H2CO molecules. Three-dimensional graphical representations of appropriate Stielties orbitals serve to identify the σ → σ* transitions of Mulliken as photoionization resonances above threshold in these compounds, whereas the corresponding π → π* contributions are spectrally localized as familiar discrete excited states. The development illustrates the nature and properties of Stieltjes orbitals, and demonstrates their utility in studies of both discrete and continuum excitation spectra on a common basis.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
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