UNIVERSITY OF BUCHAREST
FACULTY OF PHYSICS

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Conference: Bucharest University Faculty of Physics 2017 Meeting


Section: Theoretical Physics and Applied Mathematics


Title:
Two simple applications of B-spline functions in practical quantum and classical calculations


Authors:
Mihai DONDERA


Affiliation:
Department of Theoretical Physics, Mathematics, Optics, Plasma and Lasers, Faculty of Physics, University of Bucharest


E-mail
don@barutu.fizica.unibuc.ro


Keywords:
B-splines, Perturbation theory, Inhomogeneous radial Schrodinger equation, Classical motion equations.


Abstract:
Since the publication of powerful algorithms for the stable evaluation of B-spline functions (of any order) and of their derivatives [1], the B-splines were used for solving a large category of problems in atomic and molecular physics - see [2] for useful references in this field. The first application we present is related to a recent investigation of the stimulated Raman scattering on a Hydrogen atom of a radiation pulse. As shown in [3], the main mathematical object involved in perturbation theory treatment of the process is the KHW matrix element. The calculation of this matrix element can be finally reduced in the case of central field to the evaluation of radial integrals involving solutions of homogeneous and inhomogeneous radial Schrodinger equation. The B-splines are used to solve the Schrodinger equation in both cases. We describe the corresponding method and present some numerical results. In the second application we explore the possibility to use B-spline functions to solve the classical motion equations of an electron in an external field, taking into account the effect of radiation emission, manifested in equations through terms containing higher order derivatives of the electron velocity.


References:

[1] C. de Boor, A Practical Guide to Splines, 1978 (New York: Springer)

[2] H. Bachau, E. Cormier, P. Decleva, J. E. Hansen and F. Martin, Rep. Prog. Phys. 64, 1815 (2001)

[3] M. Dondera, V. Florescu and H. Bachau, Phys. Rev. A 95, 023417 (2017)



Acknowledgement:
This work has been supported partially by the Project 29/2016 ELI RO financed by the Institute of Atomic Physics.