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  • 1
    Electronic Resource
    Electronic Resource
    Incompletely symmetric non-bloch electron states in perfect cubic crystals. II. Density of states in the FCC lattice (1978)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 14 (1978), S. 153-162 
    Details
    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: The electron density of both the perturbed and unperturbed crystal can be made up of individual terms described by the basis functions of irreducible representations of the crystal point group. For the perfect FCC lattice, a detailed comparison was made between the density of states, calculated in terms of the LCAO wave functions classified according to representations of the crystal point group, and the density of states, provided by the Bloch theory.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560140203
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Incompletely symmetric non-bloch electron states in perfect cubic crystals. III. Density of dynamical observables in the FCC lattice (1978)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 14 (1978), S. 163-169 
    Details
    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: The operators of dynamical observables of the crystal electron (velocity vector components. reciprocal mass tensor components and their functions) commute with the energy operator; hence, the averages of these observables can be adequately approximated by the eigenfunctions for the energy operator. Calculations of the averages were based on the LCAO eigenfunctions classified according to incompletely symmetric irreducible representations of the point group of the cubic crystal, and a similar classification was made for the averages.
    Additional Material: 3 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560140204
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    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    Incompletely symmetric non-bloch electron states in perfect cubic crystals. I. Eigenproblem and its solution (1978)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 14 (1978), S. 127-152 
    Details
    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: In the studies on impure metals where the perturbation potential due to the impurity has symmetry of the point group of the crystal, subdivision of the electron density of the pure metal into irreducible representations of the point group is of significance. A method is presented for the calculation of wave functions of the perfect cubic crystal which transform according to the incompletely symmetric irreducible representations of the point group. The functions were evaluated in the LCAO approximation using s-type AOS for the face centered cubic lattice. These are in the form of standing waves, and their coefficient functions are linear combinations of the products of the cubic harmonics of a suitable type and the spherical Bessel functions. Properties of the solutions obtained were examined. Numerical calculations were made for four irreducible representations of the point group.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560140202
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    Paper (German National Licenses)
    Fulltext
  • 4
    Electronic Resource
    Electronic Resource
    Description of chaotic motion by an invariant probability density (1991)
    Springer
    Nonlinear dynamics 2 (1991), S. 291-304 
    Details
    ISSN: 1573-269X
    Keywords: Chaos ; Fokker-Planck-Equation ; probability density ; global description of motion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract An observation of single trajectories exhibiting chaotic motion turns out to be disadvantageous because even smallest variations of the initial conditions grow exponentially in time and result in an unpredictable long-time behaviour. The paper gives a different approach based on a probability distribution of the state space variables which is invariant on the area of attraction and results in a global description of chaotic motion.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00045298
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Rattling models from deterministic to stochastic processes (1990)
    Springer
    Nonlinear dynamics 1 (1990), S. 63-74 
    Details
    ISSN: 1573-269X
    Keywords: backlash ; impacts ; discrete mappings ; Fokker-Planck equation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Rattling in gears is a consequence of backlashes. It can be generated in those gear-wheels of a car transmission system, which are not under load. Models of rattling are established in three stages. from a straightforward patching method we proceed to a discrete mapping description and to a stochastic model applying the well-known Fokker-Planck equation. All three model stages are consistent and, moreover, they represent a good picture of the real world, which has been proven by tests.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01857585
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    Paper (German National Licenses)
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