A new basis set method for quantum scattering calculations

TLDR: In this article, a new basis set approach for quantum scattering calculations is described and tested on model problems of elastic and inelastic collisions, which is essentially the Kohn variational method, but applied to the S or T matrix directly rather than to the K matrix as is normally done.

Abstract: A new basis set approach for quantum scattering calculations is described and tested on model problems of elastic and inelastic collisions. The approach is essentially the Kohn variational method, but applied to the S or T matrix directly rather than to the K matrix as is normally done; it is seen that the result of the present approach is not equivalent to the usual Kohn method (i.e., for the K matrix) and is indeed preferable to it. The present approach is seen to have the same structure as the complex scaling/coordinate rotation expressions for the T matrix (but with some added features). Its potential advantage over the Schwinger variational method, another useful basis set technique, is that matrix elements of the Green’s function for some reference Hamiltonian are not required; the present method requires only matrix elements of the Hamiltonian itself between the basis functions. The essential reason for all of these desirable features is that the basis set which is used incorporates the correct sca...