  We present a new perturbation theory for quantum mechanical energy
eigenstates when the potential equals the sum of two localized, but not
necessarily weak potentials $V_{1}(\vec{r})$ and $V_{2}(\vec{r})$, with the
distance $L$ between the respective centers of the two taken to be quite large.
It is assumed that complete eigenfunctions of the local Hamiltonians (i.e., in
the presence of $V_{1}(\vec{r})$ or $V_{2}(\vec{r})$ only) are available as
inputs to our perturbation theory. If the two local Hamiltonians have
degenerate bound-state energy levels, a systematic extension of the molecular
orbital theory (or the tight-binding approximation) follows from our formalism.
Our approach can be viewed as a systematic adaptation of the multiple
scattering theory to the problem of bound states.
