Bound states magnitude

As regards the magnitude of the moment on each atom, the analysis is similar to that of Section 7 for the moment on a single atom for a virtual bound state. However, we cannot now assume that the Fermi energy is not shifted when our equations are expanded to third order irt U. Unless N (E )=0, it is, and the moment becomes... 

Results. Figure 5.6 compares the classical and quantum profiles of the spectral function, VG (o), of He-Ar pairs at 295 K (light and heavy solid curves, respectively), over a wide frequency band. Whereas at the lowest frequencies the profiles are quite similar, at the higher frequencies we observe increasing differences which amount up to an order of magnitude. The induced dipole [278] and the potential function [12] are the same for both computations. Bound state contributions have been suppressed we have seen above that for He-Ar at 295 K, the spectroscopic effects involving van der Waals molecules amount to only 2% at the lowest frequencies, and to much less than that at higher frequencies. 

Thus, the stationary wavefunction becomes on resonance essentially a bound-state wavefunction with an amplitude which is proportional to the corresponding lifetime. The larger the survival time in the well region the larger is the magnitude of the stationary wavefunction. 

In the case of a scattering resonance, bound-free correlation is modified by a transient bound state of fV+1 electrons. In a finite matrix representation, the projected (fV+l)-electron Hamiltonian H has positive energy eigenvalues, which define possible scattering resonances if they interact sufficiently weakly with the scattering continuum. In resonance theory [270], this transient discrete state is multiplied by an energy-dependent coefficient whose magnitude is determined by that of the channel orbital in the resonant channel. Thus the normalization of the channel orbital establishes the absolute amplitude of the transient discrete state, and arbitrary normalization of the channel orbital cannot lead to an inconsistency. 

The band description ignores correlations between electrons that result from the electron-electron repulsive interaction. Alternatively stated, the band description ignores the attractive Coulomb interaction between electrons in the TT -band and holes in the ir-band. This attraction causes the formation of excitons i.e. neutral electron-hole bound states. One of the fundamental unresolved issues of the physics of semiconducting polymers is the magnitude of the exciton binding energy (see Section V-B). 

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