Scattering theory variational formalism

This part introduces variational principles relevant to the quantum mechanics of bound stationary states. Chapter 4 covers well-known variational theory that underlies modern computational methodology for electronic states of atoms and molecules. Extension to condensed matter is deferred until Part III, since continuum theory is part of the formal basis of the multiple scattering theory that has been developed for applications in this subfield. Chapter 5 develops the variational theory that underlies independent-electron models, now widely used to transcend the practical limitations of direct variational methods for large systems. This is extended in Chapter 6 to time-dependent variational theory in the context of independent-electron models, including linear-response theory and its relationship to excitation energies. 

We use in Chapter 2 the Kohn variational 5—matrix formalism to probe the sensitivity of H-fH2 cross sections to small changes in the PES, to help resolve a discrepancy between experiment and theory over a possible H3 collision complex. We find the reactive scattering calculations to be very robust, and thus trust their predictions. 

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