Generalized sensitivity analysis in quantum collision theory

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Abstract
This paper considers the sensitivity of the scattering matrix with respect to variations of input parameters including those that persist asymptotically. The analysis shows that the first order sensitivity coefficients (i.e., the partial derivatives with respect to input parameters) of the scattering matrix may be expressed in terms of the available solution of the Schrödinger equation. This work encompasses earlier results which appear as special cases. As an application sensitivity with respect to the total energy is considered and the relevance of the result to the energy behavior of observables is discussed. In a second application, we show how sensitivity analysis may be used to estimate corrections to effective Hamiltonian results and also to examine their accuracy. The coupled states and infinite order sudden methods are chosen to illustrate the approach. Finally, the scope of sensitivity analysis in quantum collision theory is discussed.