S-matrix version of the Hulthen-Kohn-variational principle

2 S-matrix version of the Hulthen-Kohn-variational principle 

1 Derivation in one dimension. To make the derivation simpler everything will now be formulated in one dimension. In order to derive the S-matrix version of the Hulthen-Kohn variational principle (HKVP) one uses trial functions with incoming and outgoing wave boundary conditions [15, 16, 22]  

The part within the parenthesis of the last equation in (2.24) is —2ik/v) and for the variation of the functional we obtain 

In order to simplify the time-consuming inversion of the complex matrix, it is better to separate out the real and imaginary part in (2.37). This has been done with Feshbach partitioning [23] and results in the following formulation  

In this formulation for the S-matrix there are no so-called Kohn-anomalies, which are found in the K-matrix version of the HKVP [15]. If the condition 

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