Spectral projections

Mandelshtam, V.A. and Taylor, H.S. (1995) Spectral projection approach to the quantum scattering calculations, J. Chem. Phys. 102, 7390-7399. 

New Methods for Use in Scattering Calculations The Spectral Projection Method and the Stabilization Method... 

Note the similarity between the above equation and Eq. (25) originating from the spectral projection method of previous section. The symmetry of Eq. (49) which is due to the choice of Xp implies that the only integrals needed at each chosen energy are of the + or - form of... 

Acquiring spectral projections pertains to measuring linear cross sections in the time domain. This can be considered as a special case of a more general sampling scheme, where data points are sampled at any position of the time domain. The method is known as non-uniform or non-linear sampling (NUS or NLS). A historical perspective of this approach is well presented in Chap. 3. It was introduced almost a quarter of a century ago in a seminal publication by Laue and co-workers... 

Figure 23.7 Schematic representation of two-dimensional (2D) (spatial-spectral) projection in 2D EPRI experiment using a discretely changing gradient and the cone of missing angles. Adapted with permission from Ref [7] 2006, john Wiley, Sons.

Reagan, M.T., Najm, H.N., Ghanem, R.G., Knio, O.M. Uncertainty quantification in reacting-flow simulations through non-intrusive spectral projection. Combust Flame 132(3), 545-555 (2003)... 

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