Scattering theory, numerical

In this section we present several numerical teclmiques that are conmronly used to solve the Sclirodinger equation for scattering processes. Because the potential energy fiinctions used in many chemical physics problems are complicated (but known to reasonable precision), new numerical methods have played an important role in extending the domain of application of scattering theory. Indeed, although much of the fomial development of the previous sections was known 30 years ago, the numerical methods (and computers) needed to put this fomialism to work have only been developed since then. 

The depolarization of light scattered at 90° by PP and PS is treated according to RIS theory. Numerical calculations are carried out as functions of the statistical weight parameter to governing interactions of second order, of the locations of the rotational states, of the chain length expressed by the number x of repeat units, and of the stereochemical composition expressed by the fraction of racemic diads. 

Oberoi, R.S. and Nesbet, R.K. (1973). Numerical asymptotic functions in variational scattering theory, J. Comput. Phys. 12, 526-533. 

Le Fevre published an extensive article on the work done regarding molecular refractivity. To Shore is due a report on the scattering theory of absorption-line profiles and refiractivity. Theories of hypoduromism are reviewed in the artides of Rhodes and Chase and of Weissbluth. The papers on optical rotatory dispersion and circular dichroism have been reviewed by numerous authors for various substances. 

Use of the potential (7.35) in solving the coupled Lippmann—Schwinger equations (6.73,6.87) corresponding to (7.24) is a unique and numerically-valid description of the electron—atom scattering problem in the context of formal scattering theory. 

Kahnert FM Numerical methods in electromagnetic scattering theory, J Quant Spectrosc Radiat Transf79S0 775-S24, 2003. 

There have been numerous tests since the KPS study of the QCT approach, mostly based on comparisons of QCT results with those from quantum scattering theory (QST) calculations for the same potential-energy surface. These scattering calculations involve solving the... 

We devoted considerable time developing the general scattering theory for antennas, see Section 2.2. We showed that the total RCS of any antenna depends in general strongly on the load impedance Zi. We further demonstrated these concepts by numerous cases see, for example. Section 2.9. 

Nonrelativistic many-body scattering theories should continue to be carefully developed in order to learn how far traditional nonrelativistic theories can go in describing nuclear phenomena. Systematic discrepancies, if they occur, possibly indicate missing physics in the theory. Such discrepancies could provide evidence for the importance of Lorentz invariance, many-body forces, possible quark-gluon effects, etc. We must, of course, be careful to distinguish between failure of the nonrelativistic many-body approach itself, and inadequacy of some particular numerical application. 

We have provided a pedagogical derivation of the traditional, nonrelativistic form of multiple scattering theory based on the optical potential formalism. We have also discussed in detail each of the important advances made over the past ten years in the numerical application of the NR formalism. These include the full-folding calculation of the first-order optical potential, off-shell NN t-matrix contributions, relativistic kinematics and Lorentz boost of the NN t-matrix, electromagnetic effects, medium corrections arising from Pauli blocking and binding potentials in intermediate states, nucleon... 

The last fifteen years have seen considerable progress in the quantum-mechanical treatment of polymers, but the papers that contain the theoretical developments and their applications are scattered over numerous journals. This monograph therefore aims at presenting a unified approach in one volume to the quantum theory of polymers and its applications. 

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