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  • 1
    Electronic Resource
    Electronic Resource
    Potential Antifungal Activity and Structure–Activity Relationships of Some 2-Amino Acid Substituted Benzo-1,3,2-Dioxaphospholene, Oxazaphospholine and Diazaphospholine 2-Ones (2000)
    Springer
    Bulletin of environmental contamination and toxicology 65 (2000), S. 421-426 
    Details
    ISSN: 1432-0800
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering , Medicine
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s0012800024
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  • 2
    Electronic Resource
    Electronic Resource
    Quantitative Structure–Activity Relationships (QSAR) of Two Series of O-Aryl or N-Aryl O-Ethyl Phosphoramidate and Phosphorodiamidate Fungicides Incorporating Amino Acid Ethyl Esters (2000)
    Springer
    Bulletin of environmental contamination and toxicology 65 (2000), S. 415-420 
    Details
    ISSN: 1432-0800
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering , Medicine
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s0012800023
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  • 3
    Electronic Resource
    Electronic Resource
    A note on the application of the semiclassical wave packet dynamics (1989)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 90 (1989), S. 1036-1042 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The optimal choice of the initial parameters of the Gaussian wave packets in the time dependent quantum mechanical calculations using a Gaussian wave packet representation of the wave function is discussed. The proposed procedure is illustrated with the simple case of one dimensional scattering and the propagation of the ground state of the Morse potential.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.456156
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  • 4
    Electronic Resource
    Electronic Resource
    On some less familiar properties of anharmonic oscillators (1989)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 91 (1989), S. 300-306 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: By considering asymmetric anharmonic oscillators with polynomial potentials of degrees 4, 6, and 8, it is shown that the periods and actions in different potential wells are closely related. The Einstein–Brillouin–Keller (EBK) semiclassical energies are compared against the corresponding quantum energies. It is shown that when all the EBK quantum levels are taken into account, the counting of the levels follow a pattern that is analogous to that for a single minimum oscillator.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.457517
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  • 5
    Electronic Resource
    Electronic Resource
    The Birkhoff–Gustavson normal form of one-dimensional double-well Hamiltonians (1989)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 30 (1989), S. 1238-1244 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The Birkhoff–Gustavson normal form (BGNF) is employed to study general double-well anharmonic oscillators with polynomial potentials of degree 4. Via an analytic continuation of the BGNF series, expressions are presented that provide classical and semiclassical results for all energies. A surprising observation of the classical period and an interesting feature of the semiclassical quantum numbers are reported. It is shown that except for a small region near the top of the potential barrier, the BGNF approach yields accurate quantum energies.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528350
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  • 6
    Electronic Resource
    Electronic Resource
    The quantum normal form and its equivalents (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2565-2572 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A quantum analog, called the quantum normal form, of the classical Birkhoff–Gustavson normal form is presented. The algebraic relationship between the quantum and Birkhoff–Gustavson normal forms has been established by developing the latter using Lie transforms. It is shown that the Birkhoff–Gustavson normal form can be obtained from the quantum normal form. Using an anharmonic oscillator and a Henon–Heiles system as test cases, the equivalence between the quantum normal form and the Rayleigh–Schrödinger perturbation method is shown. This equivalence provides an algebraic connection between the Birkhoff–Gustavson normal form and the Rayleigh–Schrödinger perturbation approach. The question of Weyl and torus quantizations of the Birkhoff–Gustavson normal form is discussed in the light of the quantum normal form.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526775
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  • 7
    Electronic Resource
    Electronic Resource
    On the summation of the Birkhoff–Gustavson normal form of an anharmonic oscillator (1986)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 27 (1986), S. 1806-1812 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The classical Birkhoff–Gustavson normal form (BGNF) has played an important role in finding approximate constants of motion, and semiclassical energies. In this paper, this role is examined in detail for the well-known anharmonic oscillator H=1/2(p2+x2+gx4). It is shown that, with appropriate restrictions, this is the only perturbation series that preserves the period of this system. This series has a nonzero radius of convergence in contrast to the zero radius of convergence of its quantum analog, the Rayleigh–Schrödinger perturbation series. In addition, the BGNF is generated to high order, and a technique is given based on Padé approximants for summing this series. The summation of this series makes possible an accurate comparison of torus quantization energies with the known quantum energies over the entire range of quantum numbers. This example also demonstrates that divergence of the BGNF series of a Hamiltonian is not sufficient to refute its global integrability.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527048
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  • 8
    Electronic Resource
    Electronic Resource
    A floating one centre perturbation treatment for H2+-like moleculesThis research was supported by a grant from the National Research Council of Canada. (1972)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 6 (1972), S. 949-966 
    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: Closed form one centre partial wave perturbation results are obtained through second order in the energy for H2+-like molecules with arbitrary nuclear charges. The expansion centre for the method is taken at an arbitrary point along the internuclear axis and the zeroth-order wave function is a screened “1s” function centred at the expansion point. Various fixed one centre calculations of other workers for the lsσ states of H2+ and HeH++ and for the 2pσ state of HeH++ are generated as limiting cases of this more general treatment. The floating one centre perturbation results for the 1sσ states of H2+ and HeH++ are used as models for discussing the usefulness of allowing the expansion centre in the one centre method to be a function of nuclear configuration.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560060513
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  • 9
    Electronic Resource
    Electronic Resource
    On the convergence of one centre partial wave treatments for diatomic molecules. H2+ (1sσg) and coulomb versus electron exchange intermolecular forces (1977)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 12 (1977), S. 35-59 
    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: A semi-analytical solution for the nucleus and the internuclear midpoint centred partial wave equations representing the Schrödinger equation for the H2+-like molecule is discussed. Explicit proton and internuclear midpoint centred results for the interaction energy and the wave function for the 1sσg state of H2+ are obtained as a function of the internuclear distance R and the number of coupled differential equation N N ≦ 14 used to represent the Schrödinger equation for the molecule. These, together with some energy optimized floating one centre results for the interaction energy, are used to (1) discuss the convergence of the partial wave calculation as a function of R,N, and the position of the expansion centre, (2) discuss the concept of Coulomb versus electron exchange interaction energies, and (3) discuss briefly the convergence problems of analogous one centre perturbation theory treatments for the ground state H2+ molecule. The electron exchange H2+ (1sσg) molecule provides a severe test for the uefulness of partial wave methods.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560120106
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  • 10
    Electronic Resource
    Electronic Resource
    Floating one-center perturbation treatments for H2+-like molecules based on screened hydrogen atom or molecular puff unperturbed problems (1974)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 8 (1974), S. 119-136 
    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: Various floating one-center perturbation schemes are developed for H2+-like molecules. Previous work for the ‘1s’ hydrogen atom approach is extended through third order in the energy. In the molecular puff approach an exact ‘closed form’ solution is obtained for the zeroth-order problem, which corresponds to a double layer molecular puff. Semianalytical results for the first-order correction to the floating molecular puff wave function and for the energy through third order are developed which offer a convenient alternative to previous approaches. Explicit calculations for ground state H2+ show that for R 〉 3aO the ‘1s’ and the more complicated ‘puff’ treatments are equivalent and that neither the ‘1s’nor the molecular puff function is an adequate zeroth-order wave function for the important intermediate values of R. The usefulness of some of these methods in a variety of problems, where one-center zeroth-order wave functions do appear to be adequate, is discussed briefly.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560080113
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