Two-body Coulomb problem and $g^{(2)}$ algebra (once again about the Hydrogen atom)

Alexander V Turbiner, Adrian M Escobar Ruiz

Taking the Hydrogen atom as an example it is shown that if the symmetry of a three-dimensional system is $O(2)\oplus Z_2$, the variables $(r,\rho ,\phi )$ allow a separation of the vari…