Scattering many-electron treatment

Infrared, Raman, microwave, and double resonance techniques turn out to offer nicely complementary tools, which usually can and have to be complemented by quantum chemical calculations. In both experiment and theory, progress over the last 10 years has been enormous. The relationship between theory and experiment is symbiotic, as the elementary systems represent benchmarks for rigorous quantum treatments of clear-cut observables. Even the simplest cases such as methanol dimer still present challenges, which can only be met by high-level electron correlation and nuclear motion approaches in many dimensions. On the experimental side, infrared spectroscopy is most powerful for the O—H stretching dynamics, whereas double resonance techniques offer selectivity and Raman scattering profits from other selection rules. A few challenges for accurate theoretical treatments in this field are listed in Table I. 

In cases where both the system under consideration and the observable to be calculated have an obvious classical analog (e.g., the translational-energy distribution after a scattering event), a classical description is a rather straightforward matter. It is less clear, however, how to incorporate discrete quantum-mechanical DoF that do not possess an obvious classical counterpart into a classical theory. For example, consider the well-known spin-boson problem—that is, an electronic two-state system (the spin) coupled to one or many vibrational DoF (the bosons) [5]. Exhibiting nonadiabatic transitions between discrete quantum states, the problem apparently defies a straightforward classical treatment. 

J. M. Cowley, Diffraction Physics , 3rd edition, North Holland, 1990. The book was written by a pioneer in electron diffraction for graduate students learning diffraction physics. It contains many insights of diffraction, including the author s unique approach to diffraction. The discussions, especially the treatment of diffuse scattering, are indispensable for practioners of diffraction. 

Fourth, the predominantly one lectron nature of the phenomena lends Itself to theoretical treatment sy realistic. Independent-electron methods (2,4-9), with the concomitant flexibility In terms of complexity of molecular systems, energy ranges, and alternative physical processes. This has been a major factor In the rapid exploration In this area. Continuing development of computational schemes also holds the promise of elevating the level of theoretical work on molecular Ionization and scattering and. In so doing, to test and quantify many of the Independent-electron results and to proceed to other circumstances such as weak channels, multiply-excited states, etc. where the slimier schemes become Invalid. 

In classical mechanics, positions and momenta are treated on an equal footing in the Hamiltonian picture. In quantum mechanics, they become operators, but it is true that the position r and momentum p of a particle are appropriate conjugate variables that can entirely equivalently describe a state of a system under the commutation relation [r, p] = i (Dirac, 1958). This equivalence is usually demonstrated by the example of the onedimensional harmonic oscillator. The choice of the most appropriate representation depends on convenient description of the phenomenon considered. Generally, the position representation is useful for most bound-state problems such as atomic and molecular electronic structures as well as for many scattering problems. The momentum-space treatment... 

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