69 research outputs found
Mathematical surprises and Dirac's formalism in quantum mechanics
By a series of simple examples, we illustrate how the lack of mathematical
concern can readily lead to surprising mathematical contradictions in wave
mechanics. The basic mathematical notions allowing for a precise formulation of
the theory are then summarized and it is shown how they lead to an elucidation
and deeper understanding of the aforementioned problems. After stressing the
equivalence between wave mechanics and the other formulations of quantum
mechanics, i.e. matrix mechanics and Dirac's abstract Hilbert space
formulation, we devote the second part of our paper to the latter approach: we
discuss the problems and shortcomings of this formalism as well as those of the
bra and ket notation introduced by Dirac in this context. In conclusion, we
indicate how all of these problems can be solved or at least avoided.Comment: Largely extended and reorganized version, with new title and abstract
and with 2 figures added (published version), 54 page
State of the Art Research In Austria: Dexhelpp - Decision Support For Health Policy and Planning: Methods, Models and Technologies Based On Existing Health Care Data
Assessment of Lung Cancer Treatment by Disease Phase Using National Cancer Registry Data Linked with Treatment Pathway cost Data in Austria
Preconditioning techniques in linear model order reduction
Krylov subspace methods have become very popular, not only for solving large scale linear systems, but also in the area of model order reduction. It is also well known that the performance of iterative solution techniques depends crucially on the choice of preconditioning matrix. Within the area of model order reduction, the concept of preconditioning has not yet been introduced. However, recent reduction problems arising in electronics applications clearly demonstrate the need for some kind of preconditioning step prior to the actual model order reduction. In this paper, we present initial ideas and some test results
Interactive Structure Design and Simulation of Nonlinear Systems from a Multiobjective Viewpoint Using the Lotka-Volterra Approach
- …