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    Öğe
    An extension of quantum Hamilton-Jacobi formalism to N-spatial dimensions and its applications
    (Springer Heidelberg, 2023) Durmus, Aysen; Ozfidan, Aysel
    Due to the importance of hyperspherical coordinates, we report the quantum Hamilton-Jacobi formalism in N=2 spatial dimensions. The quantum momentum function equations in N-dimensions have been constructed within the framework of non relativistic theory. We also study the singularity structure of the quantum momentum function, which yields the determination of the bound state spectra of stationary quantum systems. In order to confirm the reliability of quantum Hamilton-Jacobi formalism in N-dimensions, we present the numerical data in support of the theoretical results obtained in the context of non-relativistic domain. We analyze the pole structure of the quantum momentum function for the H2 molecule in the ground electronic state interacting with Kratzer oscillator in hyperspherical coordinates. Numerical results reveal clearly that moving poles of the quantum momentum function depend on nodes in the hyperradial wave function of related molecule. We also discuss in detail the influence of dimensions on the quantum momentum function.
  • [ X ]
    Öğe
    Relativistic treatment of alkaline earth dimers in the presence of non-central molecular potential in N-dimensions
    (Elsevier, 2021) Durmus, Aysen; Ozfidan, Aysel
    Within the framework of relativistic theory, N-dimensional non-central Morse potential as anharmonic model is considered thoroughly to describe the internuclear motion of alkaline earth dimers in the different electronic states. We illustrate the surface plots of alkaline earth dimers to examine the effect of angular potential, due to existence of molecular systems in which spherical symmetry disappears. Also, the contribution of angle dependent interaction to the relativistic energy spectra has been investigated in N-dimensions. We determine the relativistic vibrational transition frequencies in the lower vibrational states for the X-1 Sigma(+)(g) ground state of Mg-24(2), Ca-40(2), (MgCa)-Mg-24-Ca-40 and A(1)Sigma(+)(u) excited state of Sr-88(2) alkaline earth diatomic molecules. The theoretical results have been compared with Rydberg-Klein-Rees (RKR) and the inverted perturbation approach (IPA) experimental data. We also discussed the validity of Pekeris approximation around the equilibrium distance as well as the repulsive and attractive regions for alkaline earth dimers.