Using simulated annealing algorithms to solve the Schr?dinger equation in muonic atoms

3rd International Conference on Mathematical Modeling in Physical Sciences

物理学;数学

Kardaras, I.S.^1 ; Kosmas, O.T.^2

Theoretical Physics Section, University of Ioannina, Ioannina

GR-45110, Greece^1

Chr. of Applied Dynamics, University of Erlangen-Nuremberg, Germany^2

关键词: Dinger equation;    Dirac equations;    Nuclear systems;    Numerical techniques;    Parametric expressions;    Physical application;    Simulated annealing algorithms;    Simulated annealing method;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/574/1/012168/pdf
DOI  :  10.1088/1742-6596/574/1/012168

来源: IOP

【 摘 要 】

In many physical problems, the computation of exact wave functions for muons (particles about two hundred times heavier than electrons), bound in the extended Coulomb field created by the atomic nucleus, is required. Even though the problem is trivial under the assumption of point-like nuclear systems, the consideration of the nuclear finite-size necessitates the use of advantageous numerical techniques. In the case of non-relativistic bound muons, the solution of the Schrödinger equation is reliable, but for a relativistic description the solution of the Dirac equations for the bound muon is needed. In the present contribution, as a first step, we attempt to derive a method for solving the Schrödinger equation on the basis of simulated annealing algorithms. To this end, one may optimize appropriate parametric expressions for the wave function of a muon orbiting around complex nuclei by employing the simulated annealing method recently constructed to minimize multi parametric expressions in several physical applications.