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