One-loop Renormalization of the Qcd Schrr Odinger Functional

The Erwin Schrr Odinger International Institute for Mathematical Physics Improved Power Counting and Fermi Surface Renormalization

On Trace Formulas

We review a variety of recently obtained trace formulas for one-and multi-dimensional Schrr odinger operators. Some of the results are extended to Sturm-Liouville and matrix-valued Schrr odinger operators. Furthermore, we recall a set of trace formulas in one, two, and three dimensions related to point interactions as well as a new uniqueness result for three-dimensional Schrr odinger operators...

i Preface

The work presented in this Thesis is the result of close collaboration with several scientists, and the main part of the work has been published before in the articles 1{17], and the conference proceedings 18{26] or is going to be published 27]. The most important 13 articles 1{13] form the core of the Thesis. The Thesis consists of a review, the purpose of which is to relate the 13 articles an...

Institute for Mathematical Physics on Separation of Variables in the Schrr Odinger Equation for a Particle Interacting with External Field on Separation of Variables in the Schrr Odinger Equation for a Particle Interacting with External Eld

We obtain the most general form of the vector-potential of the electromagnetic eld A enabling separation of variables in the (1+2)-dimensional Schrr odinger equation (SE). Using this result we have carried out variable separation for a class of Schrr odinger equations that contains as particular cases SE with Coulomb scalar potential and SE for a particle interacting with the constant magnetic ...

Orthogonal Spline Collocation Methods for Schrr Odinger-type Equations in One Space Variable

We examine the use of orthogonal spline collocation for the semi-discretization of the cubic Schrr odinger equation and the two-dimensional parabolic equation of Tappert. In each case, an optimal order L 2 estimate of the error in the semidiscrete approximation is derived. For the cubic Schrr odinger equation, we present the results of numerical experiments in which the integration in time is p...