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  • 1
    Electronic Resource
    Electronic Resource
    A mathematical proof of a result derived from the application of the Thompson–Lampard theorem of electrostatics (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 953-965 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We give an entirely mathematical demonstration and a generalization of a recent result obtained from the application of the Thompson–Lampard theorem of electrostatics, i.e., ∑n even[8 sin2(nπa/2)sinh2(nπa/2)]/[n sinh(nπ)]+∑n odd[8 cos2(nπa/2)cosh2(nπa/2)]/[n sinh(nπ)]=ln 2. It is shown that, as it should be, the result of the left-hand side, ln 2, is independent of the value of a. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1332123
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  • 2
    Electronic Resource
    Electronic Resource
    An n-dimensional interpretation of the δ -expansion for the Thomas–Fermi equation (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3916-3921 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The recent success of the δ-expansion in the solution of the Thomas–Fermi equation is interpreted to be due to the selection of an expansion parameter that interpolates between the dimension of interest, n=3, and the dimension where the problem is exactly soluble, n=2.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530833
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  • 3
    Electronic Resource
    Electronic Resource
    On the calculation of a limit for infinite systems from data on finite systems (1997)
    Springer
    Theoretical chemistry accounts 98 (1997), S. 65-67 
    Details
    ISSN: 1432-2234
    Keywords: Key words: Polymers ; Benzenoids ; Resonance ; Conjugation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract. We propose a mathematical model for the calculation of physical or chemical properties of infinite polymers, based on data for structurally closely related finite molecules. The modelling is phenomenological but permits a physical interpretation of the parameters involved in the equations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002140050279
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  • 4
    Electronic Resource
    Electronic Resource
    Higher-order Fibonacci numbers (1996)
    Springer
    Journal of mathematical chemistry 20 (1996), S. 79-94 
    Details
    ISSN: 1572-8897
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mathematics
    Notes: Abstract We consider a generalization of Fibonacci numbers that was motivated by the relationship of the HosoyaZ topological index to the Fibonacci numbers. In the case of the linear chain structures the new higher order Fibonacci numbers h F n are directly related to the higher order Hosoya-typeZ numbers. We investigate the limitsF n /F n−1 and the corresponding equations, the roots of which allow one to write a general expression forhFn. We also report on the h F counting polynomials that give the partition of the h F numbers in contributions arising fromk pairs of disjoint paths of lengthh. It is interesting to see that the partitions of h F are “hidden” in the Pascal triangle in a similar way to the partitions of the Fibonacci numbers that were discovered some time ago by Hoggatt. We end with illustrations of the recursion formulas for the higher order Hosoya numbers for several families of graphs that are based on the corresponding recursions for the higher Fibonacci numbers.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01165157
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  • 5
    Electronic Resource
    Electronic Resource
    On the search for the best correlation between graph theoretical invariants and physicochemical properties (1993)
    Springer
    Journal of mathematical chemistry 13 (1993), S. 95-106 
    Details
    ISSN: 1572-8897
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mathematics
    Notes: Abstract We have examined the correlation of the Randić connectivity index with the Hosoya topological index, the Wiener number and the molecular identification number in search of the optimal functional relation between those indices and the boiling points of alkanes. We found that some functional relations used empirically in the literature can be understood using the known fact that the Randić connectivity index is the most successful single descriptor of molecular structure.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01165556
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  • 6
    Electronic Resource
    Electronic Resource
    A proof of the equivalence of two formulas for the matrix elements of the Morse potential (1997)
    Springer
    Journal of mathematical chemistry 22 (1997), S. 255-257 
    Details
    ISSN: 1572-8897
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mathematics
    Notes: Abstract Two important formulas for the matrix elements of the Morse potential are shown to be equivalent. The proof rests on certain theorems relating generalized hypergeometric functions of unit argument.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019188201154
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  • 7
    Electronic Resource
    Electronic Resource
    On the Hellmann–Feynman theorem and the corrections to the energy in the Rayleigh–Schrödinger perturbation theory (2000)
    Springer
    Journal of mathematical chemistry 28 (2000), S. 201-206 
    Details
    ISSN: 1572-8897
    Keywords: Hellmann–Feynman theorem ; perturbation theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mathematics
    Notes: Abstract In this work we present an alternative method, based on the Hellmann–Feynman theorem, to generate energy corrections within the standard Rayleigh–Schrödinger perturbation theory. As a result, compact expressions for the corrections to the energy at different orders are obtained. We also review a method that allows us to calculate the corrections to the wave function needed in the energy calculations. Finally, our results are compared with those obtained by other authors by a different technique.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1018808830396
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  • 8
    Electronic Resource
    Electronic Resource
    Analytical formulas for the eigenvalues and eigenfunctions of a d-dimensional hydrogen atom with a potential defined by Gauss' law (1996)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 57 (1996), S. 7-15 
    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 solution of the Schrödinger equation for the d-dimensional hydrogen atom in a d-dependent potential defined by Gauss' law has been studied by the shifted 1/d method and the δ expansion. These methods provide analytical formulas for the eigenvalues and eigenfunctions which have been tested against “exact” numerical values obtained recently. The comparison shows that the results obtained with the analytical expressions are in excellent accord with the numerical ones and, on the other hand, provide a theoretical justification for a proposed empirical expression for the energies of the two-dimensional hydrogen atom with a logarithmic potential energy function. © 1996 John Wiley & Sons, Inc.
    Additional Material: 4 Tab.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 9
    Electronic Resource
    Electronic Resource
    Exact solution to a general quantum mechanical problem with time-dependent boundary conditions (1997)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 63 (1997), S. 827-833 
    Details
    ISSN: 0020-7608
    Keywords: time-dependent Schrödinger equation ; time-dependent boundary conditions ; time-dependent quadratic potential ; time-dependent quantum mechanical problem ; time-dependent invariant ; Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Exact analytical solutions are found for the quantum mechanical problem of a particle subject to a time-dependent potential with time-dependent boundary conditions. The method of solution employs time-dependent invariants, rescaling of space and time variables along with an unitary transformation. Several applications are discussed. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 827-833, 1997
    Type of Medium: Electronic Resource
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