Quantum Physics

Description
Computer algebra techniques are used in theoretical physics since the late sixties. Nowadays, with improved hardware and software, more and more non-trivial results, e.g. in perturbation theory, could not have been achieved without the use of computer algebra programs. While for physicists the results and the interpretation of their research is naturally most important it is realized at a larger scale now that computer algebra systems and special-purpose programs written in the corresponding mathematical high-level languages can be extremely useful (and fun) when doing calculationally intensive investigations. This session has as its goal to bring together researchers in theoretical physics who have used computer algebra in a substantial part of their research.

Talks

• FeynCalc 3.0 - A Mathematica Package for Feynman Diagram Calculations in High Energy Physics
  Rolf Mertig
  Abstract: FeynCalc 3.0 is a collection of tools and tables for theoretical High Energy Physics. The implemented algorithms and databases and their applications to higher order quantum corrections in elementary particle physics are described. As a research application the outline of the perturbative QCD calculation of 2-loop Operator Product Exansion - type Feynman diagrams for the spin-dependent next-to-leading order Gribov-Lipatov-Altarelli-Parisi splitting functions is presented. Some software engineering aspects of maintaing the several hundreds Mathematica (sub-) packages of FeynCalc 3.0 are given.

• High order WKB approximation and singular perturbation theory
  Michael Trott
  Abstract: In the first part high order WKB quantization formulas for one-dimensional systems are derived by alternating repeated automatic partial integration with respect to x and V'(x). At the end nonintegrable singularities are rewritten as multipe energy derivatives to allow numerical treatment of the integrals. The second part discusses the second order dependence of the eigenvalues of a finite quantum well in an electric field. Because the system has a continous energy spectrum, classical perturbation theory yields untractable integrals. Starting from the exact solution a singular perturbation theory is performed to yield relatively simple closed form expressions for all eigenvalues.