“…For mathematical simplicity, we shall also assume that the interaction has “compact support” (i.e., it is zero outside the range of r max ):
In general, however, our results will hold for interactions that are not too singular at r = 0 and that tend to zero faster than 1 / r 2 as r → ∞. Following Sams and Kouri and Kouri and Vijay, we rewrite eq 15 as
But
so we write eq 28 as
We recognize that the factor [1 +
+ i
], although unknown, is simply a constant normalization so that
where
Equation 32 for u lk ( r ) has the tremendous virtue, compared to the Lippmann−Schwinger equation for
( r ), of being a Volterra integral equation, , and under iteration, it converges absolutely and uniformly for all appropriately measurable interactions because the kernel, G̃ l 0k ( r , r ‘) V ( r ‘), is triangular, implying that the Fredholm determinant is identically one …”