No abstract

Perturbation theory is derived in such a way that the wave function renormalization terms appear automatically. The derivation is based on the Feynman theorem for the rate of change of an eigenvalue with respect to a parameter, and a corresponding theorem for the rate of change of an eigenfunction.

The techn -j i hies involved in some of the recut developments in low r order perturbation theory are discussed in detail. 'these include: the close two-gjay relationship between the perturbation solutions-and the

The well-known relationship between gauge invariance and current conservation is exhibited within the usual quantum mechanical formalism. It is then shown that the use of Gauge Invariant Atomic Orbitals does not necessarily lead to the expected current conservation. The reason is found to lie in the constrained nature of the gauge invariance which is provided by the use of GIAO's. It is concluded that this invariance is, of itself, no argument in favor of their use.

Hypervirial theorems are used to compute various average values for the nonrelativistic hydrogenic atom, the isotropic harmonic oscillator, and the relativistic hydrogenic atom. In the latter case many new results are found.