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  • 1
    Electronic Resource
    Electronic Resource
    Asymptotic (semiclassical) equivalence for Schrödinger equations with singular potentials and for related systems of two first-order equations (1993)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 34 (1993), S. 3351-3377 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The asymptotic equivalence of systems of two ordinary first-order linear differential equations with complex independent variable and a small parameter at the derivatives is analyzed in the case of arbitrary numbers and multiplicities of turning points and singular points. The set of all the transformation matrices realizing the equivalence is described and a recursive procedure for constructing these matrices is developed. By persistently using the determinant properties of the transformation matrices, the number of integration operations at each step of this procedure is halved compared with the algorithms known before. The theory is specialized to the case of time-independent one-dimensional Schrödinger equations with singular potentials. Some generalizations to multichannel Schrödinger equations are also presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530081
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Adiabatic and post-adiabatic representations for multichannel Schrödinger equations (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 536-559 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The properties of the adiabatic representation of a multichannel Schrödinger equation are analyzed by exploiting the Hamiltonian and symplectic nature of the coefficient and transformation matrices, respectively. Use of this algebraic structure of the problem is shown to be in line with an approach developed by Fano and Klar [Klar and Fano, Phys. Rev. Lett. 37, 1132 (1976); Klar, Phys. Rev. A 15, 1452 (1977)] in their introduction of the postadiabatic potentials. The formal calculations due to Klar and Fano which halve the order of the matrices involved are given a rigorous mathematical background and described in a more general setup from the viewpoint of the theory of Hamiltonian and symplectic linear operators. An infinite sequence of postadiabatic representations is constructed and an algorithm for the choice of a symplectic transformation matrix for each representation is proposed. The interaction of fluorine atoms with hydrogen halides is considered as an example: In these cases, it is found that the first-postadiabatic representation shows lower coupling than the adiabatic one, and this provides a proper choice for a decoupling approximation. The present results, and in particular the recipes for obtaining the eigenvalues and eigenvectors of relevant matrices manipulating matrices of half the size, offer interesting perspectives for the numerical integration of multichannel Schrödinger equations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530652
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Multiple impacts and energy transfer in a three-body system for noncollinear collisions (1993)
    Springer
    Theoretical chemistry accounts 87 (1993), S. 195-213 
    Details
    ISSN: 1432-2234
    Keywords: Energy transfer ; Atom-diatom collisions ; Impulsive model ; Multiple impacts ; Noncollinear configurations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Summary Within the impulsive framework, the energy transfer processes in collisions of atoms with diatomic molecules are considered. In the case of noncollinear collisions involving multiple impacts between the particles, analytic expressions for the amount of the collision energy transferred to the internal degrees of freedom of the molecule have been derived. The limiting cases of these expressions are the well-known Mahan (a single impact) and Mahan-Shin (collinear collisions) formulas. The efficiency of energy transfer in collisions of cesium halide molecules with xenon atoms has been computed as an example; the results obtained agree well with the data of accurate trajectory calculations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01112933
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Post-adiabatic approach to atomic and molecular processes: The van der Waals interactions of some open shell systems (1995)
    Springer
    Theoretical chemistry accounts 90 (1995), S. 225-256 
    Details
    ISSN: 1432-2234
    Keywords: Multichannel Schrödinger equation ; Diabatic, adiabatic and post-adiabatic representations ; Van der Waals interactions of O, F, Cl atoms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Summary Various properties of post-adiabatic representations of multichannel Schrödinger equations are described in the general context of adiabatic and classical path approximations as used in atomic and molecular physics. The van der Waals interactions of fluorine, chlorine, and oxygen atoms with rare gases, hydrogen, methane, and hydrogen halides are considered: it is found that in some of these systems, the first-order post-adiabatic scheme exhibits a smaller coupling than the adiabatic representation, thus providing an appropriate choice of the basis functions for a decoupling approximation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01113470
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Post-adiabatic approach to atomic and molecular processes: The van der Waals interactions of some open shell systems (1995)
    Springer
    Theoretica chimica acta 90 (1995), S. 225-256 
    Details
    ISSN: 0040-5744
    Keywords: Key words: Multichannel Schrödinger equation ; Diabatic ; adiabatic and post-adiabatic representations ; Van der Waals interactions of O ;  F ;  Cl atoms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Summary.  Various properties of post-adiabatic representations of multichannel Schrödinger equations are described in the general context of adiabatic and classical path approximations as used in atomic and molecular physics. The van der Waals interactions of fluorine, chlorine, and oxygen atoms with rare gases, hydrogen, methane, and hydrogen halides are considered: it is found that in some of these systems, the first-order post-adiabatic scheme exhibits a smaller coupling than the adiabatic representation, thus providing an appropriate choice of the basis functions for a decoupling approximation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01113470
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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