Runge–Lenz operator in the momentum space

The fundamental quantum Coulomb problem in the momentum space is considered. A differential equation with $SO(4)$ symmetry has been obtained in the momentum space instead of the integral Fock equation. The corresponding equation in the coordinate space is the sum of the squares of the angular momentum and Runge–Lenz operators. This approach is unknown in the momentum space where the Runge–Lenz operator is not applied. The Runge–Lenz operator obtained in the momentum space is simpler than that in the coordinate space and allows one to effectively consider the Coulomb problem in the momentum space. A relation of new operator to the infinitesimal rotation operator of the three-dimensional Fock sphere has been determined.