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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 Schrodinger 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 Schrodinger 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.

Using simulated annealing algorithms to solve the Schrödinger equation in muonic atoms