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

The mean values of the potential $\left\langle \hat{\varPi}\right\rangle$ and kinetic $\left\langle \hat{\mathrm{T}}\right\rangle$ energy of an electron in a hydrogenlike atom are found. It is found by direct calculation that $\left\langle \hat{\varPi}\right\rangle =2E$ and $\left\langle \hat{\mathrm{T}}\right\rangle =\mid E\mid$ 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.