The Green’s function method of sensitivity analysis in quantum dynamics

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Abstract
The paper considers the sensitivity of quantum dynamics systems with respect to parameters or features in the underlying Hamiltonians. The analysis allows for the calculation of the gradient of the wave function with respect to any well defined system parameters in the Hamiltonian. Differential sensitivity equations are derived from the Schrödinger equation and their solution is expressed in terms of a Green’s function. For scattering problems the necessary asymptotic Green’s function can be exclusively expressed in terms of the available solution to the original Schrödinger equation. Also considered are problems from time‐dependent quantum mechanics. In this latter situation sensitivity theory allows for the calculation of gradients of the time evolution operator with respect to system parameters. The scattering formalism is illustrated with a study of the anisotropy coefficient sensitivity in the collision of an atom and a ridgid rotor. The time‐dependent theory was applied to a collision‐free molecular beam translating through a region of space containing electric and magnetic fields. This case examined the sensitivity of the molecular transition probabilities to field parameters. These brief examples serve to illustrate the potential usefulness of sensitivity analysis in quantum dynamics.

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