Abstract
In the relativistic and the nonrelativistic theoretical treatment of moderate and high-power laser-matter interaction, the generalized Bessel function occurs naturally when a Schrödinger-Volkov and Dirac-Volkov solution is expanded into plane waves. For the evaluation of cross sections of quantum electrodynamic processes in a linearly polarized laser field, it is often necessary to evaluate large arrays of generalized Bessel functions, of arbitrary index but with fixed arguments. We show that the generalized Bessel function can be evaluated, in a numerically stable way, by utilizing a recurrence relation and a normalization condition only, without having to compute any initial value. We demonstrate the utility of the method by illustrating the quantum-classical correspondence of the Dirac-Volkov solutions via numerical calculations.
Recommended Citation
E. Lötstedt and U. D. Jentschura, "Recursive Algorithm for Arrays of Generalized Bessel Functions: Numerical Access to Dirac-Volkov Solutions," Physics Veview E, American Physical Society (APS), Feb 2009.
The definitive version is available at https://doi.org/10.1103/PhysRevE.79.026707
Department(s)
Physics
Sponsor(s)
German Research Association
Keywords and Phrases
Relativistic Corrections; Bessel functions; Quantum electrodynamics; Quantum optics; Schrodinger equation
Document Type
Article - Journal
Document Version
Final Version
File Type
text
Language(s)
English
Rights
© 2009 American Physical Society (APS), All rights reserved.
Publication Date
01 Feb 2009
