Algebraic and numerical manipulation of the even-power-seriescentral potentials by means of the hypervirial theorems technique Original Research Article

A combination of two programs is described for the study of the class of central potentials V(r)=−D+σk=0∞ Vkbkr2k+2, V0=w2>0, which is of special interest in theoretical physics. The first program uses the Hypervirial Theorems (HVT) and the Hellmann-Feynman Theorem (HFT) to calculate approximate analytic expressions for the non-relativistic energy eigenvalues, the expectation values of the potential and the kinetic energy operator, and the expectation values of the even powers of the position coordinate. The second program implements the expressions obtained to yield numerical results.