Scattering calculations Schrodinger equation

Tsoucaris, decided to treat by Fourier transformation, not the Schrodinger equation itself, but one of its most popular approximate forms for electron systems, namely the Hartree-Fock equations. The form of these equations was known before, in connection with electron-scattering problems [13], but their advantage for Quantum Chemistry calculations was not yet recognized. 

Discrete Fourier transform (DFT), non-adiabatic coupling, Longuet-Higgins phase-based treatment, two-dimensional two-surface system, scattering calculation, 153-155 Discrete variable representation (DVR) direct molecular dynamics, nuclear motion Schrodinger equation, 364-373 non-adiabatic coupling, quantum dressed classical mechanics, 177-183 formulation, 181-183... 

Schrodinger Equation with Absorbing Potential for Quantum Scattering Calculations. 

The quantum theory of molecular collisions in external fields described in this chapter is based on the solutions of the time-independent Schrodinger equation. The scattering formalism considered here can be used to calculate the collision properties of molecules in the presence of static electric or magnetic fields as well as in nonresonant AC fields. In the latter case, the time-dependent problem can be reduced to the time-independent one by means of the Floquet theory, discussed in the previous section. We will consider elastic or inelastic but chemically nonreac-tive collisions of molecules in an external field. The extension of the formalism to reactive scattering problems for molecules in external fields has been described in Ref. [12]. 

The procedure for calculating energy level diagrams by the self-consistent field Xa scattered wave (SCF-Xa-SW) method is as follows (Sherman, 1984, 1991). An octahedral cluster such as [FeO6]10 is partitioned into a set of (overlapping) spheres centred about divalent iron and each oxygen atom, and these are surrounded by an outer sphere. Within each atomic sphere the one-electron Schrodinger equation... 

In the exact quantum calculation of the dynamics of a reaction on a particular potential-energy surface, it is necessary to solve the Schrodinger equation for the scattering from all occupied internal states of the reagents to all possible internal states of the products as a function of the relative collision energy. This is a multichannel process in that many final product vibrational and rotational states may be populated from a... 

Variational formulations can also be developed for the Schrodinger equation in the continuum. However, certain modifications in the construction of functionals are necessary in order to ensure convergence of the integrals. Discussions of the historical development of variational calculations and applications to single- and multi-channel scattering can be found in Refs. 232 and 233. 

Quantum reactive scattering calculations arc based on the integration of the time-dependent Schrodinger equation... 

The eventual goal in scattering calculations is essentially to obtain the scattering matrix, S (see Section A3.11 and equation (B3.4.4) below). The scattering matrix can be obtained by reference to the solution of the time-independent Schrodinger equation, fulfilling... 

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