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Bertrand theorem permits closed orbits in 3d Euclidean space only for 2 typesof central potentials. These are of Kepler-Coulomb and harmonic oscillatortype. Volker Perlick recently designed new static spherically symmetric(Bertrand) spacetimes obeying Einstein's equations and supporting closedorbits. In this work we demonstrate that the topology and geometry of thesespacetimes permits us to solve quantum many-body problem for any atom ofperiodic system exactly. The computations of spectrum for any atom areanalogous to that for hydrogen atom. Initially, the exact solution of theSchr\"odinger equation for any multielectron atom (without reference toBertrand theorem) was obtained by Tietz in 1956. We recalculated Tietz resultsby applying the methodology consistent with new (different from that developedby Fock in 1936) way of solving Schr\"odinger's equation for hydrogen atom. Byusing this new methodology it had become possible to demonstrate that theTietz-type Schr\"odinger's equation is in fact describing the quantum motion inBertrand spacetimes. As a bonus, we solved analytically the L\"owdin'schallenge problem. Obtained solution is not universal though since there areexceptions of the Madelung rule in transition metals and among lanthanides andactinides. Quantum mechanically these exceptions as well as the rule itself aretreated thus far with help of relativistic Hartree-Fock calculations. Theobtained results do not describe the exceptions in detail yet. However, studiesoutlined in this paper indicate that developed methods are capable ofdescribing exceptions as well. The paper ends with some remarks aboutusefulness of problems of atomic physics for development of quantum mechanics,quantum field theory and (teleparallel) gravity.

How the Modified Bertrand Theorem Explains Regularities and Anomalies of the Periodic Table of Elements