Green operator

The dynamics of a scattering event can be described by the causal Green operator 287,288... 

Energy-Separable Polynomial Representation of the Time-Independent Full Green Operator with Application to Time-Independent Wavepacket Forms of Schrodinger and Lippmann-Schwinger Equations. 

The general expression for the Green operator G(TX) in equation (9) is then replaced by the Green operator G T ) for a general well p, for example, where... 

Using the projection operator from Eq. (8), we obtain the exact spectral representation of the Green operator and the Green function ... 

A demonstration has been given by Sanhueza et al. (1979). In our case we are using models in which the response of the medium is linear. Therefore the operator A is reduced to a Green operator. 

Equations (2.59)-(2.61) constitute a formal solution of the time-dependent Schrodinger equation, expressed in terms of the Green operator. We will later see how this fonnal solution can be applied. 

The matrix element of the Green operator (referred to as the Green function) over the initial state is then... 

Y. Huang, D. J. Kouri, and D. K. Hoffman, A general, energy-separable polynomial representation of the time-independent full Green operator with application to time-independent wavepacket forms of Schrodinger and Lippmann-Schwinger equations, Chem. Phys. Lett. 225 31 (1994). 

Instead of considering U t) it is useful to investigate its Fourier-Laplace transform, the resolvent or Green operator... 

To is the partial width of the zero-order resonances. The Green function [not to be confused with the Green operator (2)] was chosen in the form... 

Using the spectral representation of the Green operator E — H) in Eq. (12) within the Born-Oppenheimer approximation framework one gets ... 

A very recent technique allows the direct use of an ASC procedure without intermediate FEM steps or approximations of any sort. To arrive at this formulation the Green operator formalism generally in use in electrostatic formulations is replaced by the use of Calderon operators. It would be too long to give formal details here the corresponding computational procedure is now under development. ... 

The other form of T(E) in (17.22) is remarkable in that it is expressed as a trace of some operator over states defined on the scattering zone, that is, the molecular species S, only. The operator V(E)r(E)G E) is expressed in terms of the bridge s Green operator... 

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