Use of a General Virial Theorem with Perturbation Theory
Abstract
If the Hamiltonian of a system is broken up into a series of homogeneous operators in the space coordinates, the sum of their mean values multiplied by the degree of homogeneity equals zero for a bound state. Assume that the Hamiltonian contains three groups of homogeneous terms: for example, kinetic energy, Coulomb energy, and a third interaction, U, which is small. By the "virial" theorem, the energy can be expressed in the mean values of any two of these terms. From perturbation theory, another relationship is derived which allows various orders of the energy to be obtained from the mean value of any one of the three terms of the Hamiltonian. The perturbation relation is Ū=ΣnE_{n}, where E_{n} is the nth order correction to the energy, defined by E=ΣE_{n}.
 Publication:

Physical Review
 Pub Date:
 May 1957
 DOI:
 10.1103/PhysRev.106.414
 Bibcode:
 1957PhRv..106..414C