Abstract
AbstractThe Titchmarsh–Weyl theory for a singular second‐order differential equation is presented. The equations, however, are arranged such that the theory is immediately applicable to the multichannel formulation. The mathematical basis of the Titchmarsh–Weyl theory (TWT) is outlined and the Titchmarsh–Weyl m function is presented. Relations to the associated Green's function and the spectral function are given. It is shown how some quantities common in scattering theory can be expressed in terms of the TWT. The method of complex rotation is then applied to the TWT to create a complex rotated analog of the Titchmarsh–Weyl theory. This is then extended as exterior complex scaling is introduced. An outline of a proof for the method of exterior complex scaling is presented and some numerical results of the complete theory are given.
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