On the Mean Value of the Potential and Kinetic Energy of an Electron in a Hydrogenlike Atom

The mean values of the potential $⟨\hat{\Pi }⟩$ and kinetic $⟨\hat{T}⟩$ energy of an electron in a hydrogenlike atom are found. It is found by direct calculation that $⟨\hat{\Pi }⟩=2E$ and $⟨\hat{T}⟩=\mid E\mid$ for arbitrary states with set of quantum numbers {n,l,m} . Such relations for the ground state {n = 1, l = m = 0} are well known and are a particular case of this general result. Thus, this work can have methodological value as a helpful supplement to the traditional university course in quantum mechanics. Moreover, on the scientific plane, it is possible to apply these results to a calculation of the energy of a two-electron atom by the variational method in spaces with number of dimensions D = 3,2, and 1.