Numerical tensor methods for atomic, molecular and exotic three-body Coulomb systems

With high-precision experiments becoming more advanced, and probed systems becoming more complex, theory should remain a vital tool for interpreting and predicting chemical systems and phenomena. Three-body Coulomb systems are the simplest that capture the effects of electron correlation and nuclear motion and are therefore of interest for atomic and molecular theory, for systems containing various elementary particles such as muons and positrons, and as a testing ground for new method developments. We report on the recent development of pioneering, unified, all-particle, high-precision calculations of the ground state energies of a quantum mechanical, three-body atomic system, an exotic system and a molecular system using two different numerical tensor methods (NTM), namely the Lagrange-mesh NTM, and the Laguerre (series solution) NTM, both utilizing explicitly correlated wave functions.