ALBERT

All Library Books, journals and Electronic Records Telegrafenberg

feed icon rss

Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

Export
  • 1
  • 2
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 98 (1993), S. 3866-3875 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: An implementation of exterior complex scaling using the finite elements method with high degree polynomials is presented. We apply the method to find the resonances of the potential 7.5r 2e−r and of a phenomenological coupled channel model of the CaH molecule. In both cases the method is quickly convergent and extremely stable numerically. Convergence could be pushed to the point where the real parts of most resonance energies were independent of the complex scaling angle and of the exterior scaling radius within machine precision (14 significant digits). All imaginary parts were stable to at least eight significant digits. Several resonances of CaH which had evaded searches with a finite difference method could be located.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 3
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2648-2658 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The radial equation (or set of equations) derived in scattering theory is analyzed by means of Titchmarsh–Weyl theory for singular second-order differential equations. In particular we have focused on the spectral density concept and the corresponding relation to the scattering cross section. The method of complex deformations is brought in as a necessary ingredient in the evaluation of the underlying pole strings, which together with the background build up the actual dispersion relation data. The analysis is supported by numerical applications to a centrifugal family of simple potentials.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 4
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 27 (1986), S. 2629-2639 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The Titchmarsh–Weyl theory is applied to the Schrödinger equation in the case when the asymptotic form of the solution is not known. It is assumed that the potential belongs to the Weyl's limit-point classification. A rigorous analytical continuation of the Green's function, obtained from the solution regular at the origin and the square integrable Weyl's solution (regular at infinity), to the "unphysical'' Riemann energy sheet is carried out. It is demonstrated how the Green's function can be uniquely constructed from the Titchmarsh–Weyl m-function and its Nevanlinna representation. The behavior of the m-function in the neighborhood of poles is investigated. The m-function is decomposed in a, so called, generalized real part (Reg) and a generalized imaginary part (Img). Reg(m) is found to have a significant argument change upon pole passages. Img(m) is found to be a generalized spectral density. From the generalized spectral density, a spectral resolution of the differential operator and its resolvent is derived. In the expansion contributions are obtained from bound states, resonance states (Gamow states), and the "deformed continuum'' given by the generalized spectral density.The present expansion theorem is applicable to the general partial differential operator via a decomposition into partial waves. The numerical procedure involves all quantum numbers l and m, but for convenience, and with the inverse problem in mind, this study is focused on the case when the rotational quantum number equals zero. The theory is tested numerically and analyzed for an analytic model potential exhibiting a barrier and decreasing exponentially at infinity. The potential is Weyl's limit point at infinity and allows for an analytical continuation into a sector in the complex plane. An attractive feature of the generalized spectral density of the present potential is that the poles close to the real axis seem to exhaust or deflate the above-mentioned density inside the pole string. Outside this string the density rapidly approaches that of a free particle. This information is used to derive an approximate representation of the m-function in terms of poles and residues as well as free-particle background. In order to display the features mentioned above, the present study is accompanied with several plots of analytically continued quantities related to the Green's function.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 5
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 23 (1983), S. 865-874 
    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 Titchmarsh-Weyl theory for a singular second-order differential equation is presented. The equations, however, are arranged such that the theory is immediately applicable to the multichannel formulation. The mathematical basis of the Titchmarsh-Weyl theory (TWT) is outlined and the Titchmarsh-Weyl m function is presented. Relations to the associated Green's function and the spectral function are given. It is shown how some quantities common in scattering theory can be expressed in terms of the TWT. The method of complex rotation is then applied to the TWT to create a complex rotated analog of the Titchmarsh-Weyl theory. This is then extended as exterior complex scaling is introduced. An outline of a proof for the method of exterior complex scaling is presented and some numerical results of the complete theory are given.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 6
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 22 (1982), S. 445-457 
    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: Weyl's theory for a set of N-coupled singular second-order differential equations is analyzed in relation to S-matrix theory and a dilated version is presented. Applications of this theory to two single channel scattering model problems and a two-channel model problem are given. Some implications of the present theory are discussed.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 7
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 14 (1978), S. 443-456 
    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 extended virial theorem, obtained from a Fourier-Laplace transformation of equations of motion, is applied to the phenomenon of predissociation. The underlying resonance energy model rigorously defined by means of the theory of dilation analytic operators prescribes in detail the balance between the various energy contributions in a way analogous to the situation prevailing in a stationary system. The extended virial theorem is applied to predissociation, particularly in connection with the interpretation of the nearly degenerate G 1Π ∼ I 1Π energy spectrum in SiO. It was previously found for the rovibronic spectra assigned to G 1Π - X 1Σ+ and I1Π - X1 Σ+, that every G - X band is accompanied by a I - X band. Whereas the I 1Π state does not seem to undergo predissociation, the G state shows increasing predissociation with increasing vibrational quantum number. We show that the virial theorem generalized to include continuum phenomena offers an interpretation of the nearly degenerate spectra of SiO as well as of the concomitant isotope shift of SiO16 and SiO18 with respect to both resonance positions and widths.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 8
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 30 (1986), S. 73-80 
    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 R matrix theory in its simplest form is discussed and analyzed in terms of the classical Titchmarsh-Weyl's theory for a singular second order differential equation. It is observed that the R matrix described as an abstract R operator is contained in the framework of Weyls classical extension to an infinite interval of finite Sturm-Liuoville theory. As a result we find that the exterior complex rotation method can be synthesized with the R matrix theory to obtain a method for deriving the S matrix poles out in the complex energy or momentum planes.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 9
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 23 (1983), S. 1047-1056 
    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 AGP wave function is used to describe the ground state potential energy curves of Li2 and CH+. Moderate size basis sets are used. The computational aspects of the AGP optimization are discussed and the nature of the AGP wave function versus internuclear separation is examined.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 10
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 31 (1987), S. 707-731 
    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: Examples from music and nuclear, as well as atomic and molecular, physics are given to introduce and illustrate the resonance concept. Some fundamental concepts of scattering theory such as the differential and the total cross section are presented. The concept of the collision complex is illustrated with a light particle scattering reaction in nuclear physics. The concept of channels is introduced, and this formalism (which is so far empirical in nature) is dressed in the language of quantum mechanics. Finally I show that our descriptions of phenomena in nuclear physics can also be used in atomic and molecular physics.
    Additional Material: 18 Ill.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...