Lippman-Schwinger equation

We mention that TKK and fKK are equivalent on the energy shell. The Mpller operator may be determined from the Lippman-Schwinger equation... 

Using the Lippman-Schwinger equation for the T operator, it follows that... 

Rates of non-adiabatic intramolecular electron transfer were calculated in Ref. [331] using a self-consistent perturbation method for the calculation of electron-transfer matrix elements based on Lippman-Schwinger equation for the effective scattering matrix. Iteration of this perturbation equation provides the data that show the competition between the through-bond and through-space coupling in bridge structures. 

The action of this operator on a function denotes the integration of this function with the kernel Gy(7, 7 E), and Eq. (4) may be rewritten in the canonical form of Lippman-Schwinger equation [5] ... 

The most comprehensive description of the tunneling problem is based either on a self-consistent solution of the Lippman-Schwinger equation [3] or on the non-equilibrium Green s function approach [4-8]. Inelastic effects within e.g. a molecule-surface interface can be included by considering multiple electron paths from the vacuum into the surface substrate [9], The current between two leads with the chemical potentials /ja and hb is given by the energy integral ... 

This approach lies in between the two presented multiscale approaches in which the RVE is discretized into several subdomains and the constitutive equations are estabhshed from a multiscale analysis performed on the discretized RVE. The term sequential refers to the fact that a series of analytical, for example, Eshelby solution, and numerical, for example, FEA, procedures are implemented to correlate the microconstituent and macroscopic constitutive relations. The transformation field analysis (TEA) sequential approach, developed by Dvorak et al. [74—77], discretizes the exact solution of the Lippman-Schwinger equation, while uniform mechanical fields are assumed for each of the subphases. 

Density functional methods provide a convenient framework for treating metallic interfaces [100]. Applications of this methodology to the problem of electron transport through atomic and molecular bridges have been advanced by several workers. In particular, Lang s approach [90, 159-165] is based on the density functional formalism [166,167] in which the single electron wave functions i/ o (r) and the electron density o(r) for two bare metal (jellium) electrodes is computed, then used in the Lippman-Schwinger equation... 

According to the Lippman-Schwinger equation the probability to change the vibrational state of the molecule from Xv R) to Xu> R) due to the collision process is given by,... 

Combining eqs. (2.243) and (2.248) gives the Lippman-Schwinger equation in Brillouin-Wigner form... 

Given an interaction potential V between the projectile A and the target B, the scattering cross sections may be obtained from the transition operator T which satisfies the Lippman-Schwinger equation... 

If we know the Green function of the non-perturbed problem, we can found a solution by using the Lippman-Schwinger integral equation ... 

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