Hamburg 2009 – scientific programme

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A: Fachverband Atomphysik

A 34: Poster II

A 34.12: Poster

Thursday, March 5, 2009, 16:30–19:00, VMP 9 Poster

Recursive Algorithm for Generalized Bessel Functions — •Erik Lötstedt¹ and Ulrich D. Jentschura^1,2 — ¹Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, D-69117 Heidelberg — ²Department of Physics, Missouri University of Science and Technology, Rolla MO65409, USA

The generalized Bessel function (GBF), introduced by Reiss [1], is ubiquitous in the theoretical treatment of laser-matter interaction. By providing a Fourier expansion of the laser-dressed electron states, this special function can be used to write down analytic expressions for quantum mechanical matrix elements of laser-related processes, both nonrelativistic and relativistic ones. However, there are few reliable numerical algorithms to evaluate the GBF, compared to, for example, the vast amount of literature and software existing for the usual Bessel function. We demonstrate a new recursive algorithm for numerical evaluation of large arrays of GBFs [2], which is both fast and accurate. The algorithm is based on the recurrence relation satisfied by the GBF.

[1] H. R. Reiss, J. Math. Phys. 3, 59 (1962).

[2] E. Lötstedt and U. D. Jentschura, submitted (2008).