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Description
In this work, we first formulate the reduced radial Schrödinger equation for a two-leptons system by separating out the center of mass motion. Then, a neural networks technique is, initially, employed to model the numerical solution of the Schrödinger equation written in terms of the relative coordinate r of the two leptons. Next, for the optimization of the defined error function of the concrete leptonic system of Muonium (Mu), the BFGS and the trust-constr methods (as provided from the SciPy submodule optimize) are being utilized. Finally, the numerical solution is compared with the “analytic” wave function provided by the Schrödinger equation, in order to appreciate the confidential level of the designed algorithm. We conclude that our method provides fast and accurate numerical solutions a fact that encourages us to apply the same scheme to solve the corresponding Dirac equations.
