APPLICATION OF THE QUANTUM-MECHANICAL HYPERVIRIAL THEOREMS TO EVEN-POWER SERIES POTENTIALS

The class of the even-power series potentials, V(r) = -D + Sigma(k=0)( infinity) V-k lambda(k)r(2k+2), V-0 = omega(2) > 0, is studied with th e aim of obtaining approximate analytic expressions for the nonrelativ istic energy eigenvalues, the expectation values for the potential and kinetic energy operators, and the mean square radii of the orbits of a particle in its ground and excited states. We use the hypervirial th eorems (HVT) in conjunction with the Hellmann-Feynman theorem (HFT), w hich provide a very powerful scheme for the treatment of the above and other types of potentials, as previous studies have shown. The formal ism is reviewed and the expressions of the above-mentioned quantities are subsequently given in a convenient way in terms of the potential p arameters, the mass of the particle, and the corresponding quantum num bers, and are then applied to the case of the Gaussian potential and t o the potential V(r) = -D/cosh(2)(r/R). These expressions are given in the form of series expansions, the first terms of which yield, in qui te a number of cases, values of very satisfactory accuracy.