Density matrix treatment amplitudes

INTRODUCTION DENSITY MATRIX TREATMENT Equation of motion for the density operator Variational method for the density amplitudes THE EIKONAL REPRESENTATION The eikonal representation for nuclear motions... 

Many apparent anomalies in the spectra produced by double resonance experiments can be resolved by a density matrix treatment. Thus in A- X experiments with a reduced amplitude of the irradiated field the normal effect of the NOE upon the intensities of the transitions may be severely modified and both emission and absorption may be observed. (58) It turns out that the overall behaviour depends upon... 

In the case of coherent laser light, the pulses are characterized by well-defined phase relationships and slowly varying amplitudes (Haken, 1970). Such quasi-classical light pulses have spectral and temporal distributions that are also strictly related by a Fourier transformation, and are hence usually refered to as Fourier-transform-limited. They are required in the typical experiments of coherent optical spectroscopy, such as optical nutation, free induction decay, or photon echoes (Brewer, 1977). Here, the theoretical treatments generally adopt a semiclassical procedure, using a density matrix or Bloch formalism to describe the molecular system subject to a pulsed or continuous classical optical field, which generates a macroscopic sample polarization. In principle, a fully quantal description is possible if one represents the state of the field by the coherent or quasi-classical state vectors (Glauber, 1965 Freed and Villaeys, 1978). For our purpose, however. 

Propagators have the advantage of giving direct information about transition energies and amplitudes from a reference state, but like density matrices, they suffer from a lack of simple ways generally to ensure so-called A-representability or correspondence to proper many-electron state vectors. Nevertheless, the propagator approach to semi-empirical many-electron theory appears to have certain advantages over other methods. Such treatment has led to useful relations between matrix elements in the PPP-model P... 

---