Browsing by Subject "Schrodinger equation"

Filter results by typing the first few letters
Now showing 1 - 2 of 2
  • Thumbnail Image
    ItemOpen Access
    Fast multipole methods in service of various scientific disciplines
    (IEEE, 2014) Gürel, Levent
    For more than two decades, several forms of fast multipole methods have been extremely successful in various scientific disciplines. Reduced complexity solutions are obtained for solving different forms of equations that are derived from Maxwell's equations, such as Helmholtz's equation for electrodynamics and Laplace's equation for electrostatics. Fast multipole solvers are developed for and applied to the integral equations derived from Helmholtz's and Laplace's equations. Fast multipole solvers are kernel-dependent techniques, i.e., they rely on certain analytical properties of the integral-equation kernels, such as diagonalizability. Electromagnetics is not the only discipline benefiting from the fast multipole methods; a plethora of computations in various disciplines, such as the solution of Schroedinger's equation in quantum mechanics and the calculation of gravitational force in astrophysics, to name a few, exploit the reduced-complexity nature of the fast multipole methods. Acoustics, molecular dynamics, structural mechanics, and fluid dynamics can be mentioned as other disciplines served by the fast multipole methods. © 2014 IEEE.
  • Thumbnail Image
    ItemOpen Access
    Time dependent study of quantum bistabiliity
    (1995) Ecemiş, Mustafa Ihsan
    The analysis of quantum transport phenomena in small systems is a prominent topic of condensed matter physics due to its numerous technological applications. The current analytical theories are not adequate for studying realistic problems. Computational methods provide the most convenient approaches. Numerical integration of the time-dependent Schrödinger equation is one of the most powerful tools albeit the implementation of the blackbody boundary conditions is problematic. In this work, a novel method which render possible this implementation is described. A number of sample calculations are presented. The method is applied to several one- and two-dimensional systems. A description of the time-dependent behavior of quantum bistable switching is given.