By Peter A. Jansson
The Literature on deconvolution is wealthy with the contributions of many investigations. those contributions are, even if, scattered between journals dedicated to a number of specialties. No unmarried quantity has been on hand that offers either an summary and element wanted by means of a newcomer to this box.
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Extra info for Deconvolution: With Applications in Spectroscopy
The Schrödinger equation for relative motion of two unstructured particles in free space is − 2 2μ ∇ 2 + V (r) Ψ(r) = EΨ(r). 13) It is usually convenient to take E = 0 to be the energy of the separated particles, so that V (r) → 0 as r → ∞. 15) where the centrifugally corrected potential VL (r) is VL (r) = V (r) + + 1) . 8. 15 that are regular at the origin (usually ψL → 0 as r → 0 provided VL (r) 0 at r = 0). 1. 1 Effective potential for single-channel scattering, showing centrifugal barrier and typical wavefunctions for bound and scattering states.
The most important effect of an applied electric or magnetic field is that the energy levels of the colliding monomers split and shift by amounts that can be quite large © 2009 by Taylor and Francis Group, LLC Theory of Cold Atomic and Molecular Collisions 27 compared to the kinetic energy. The shifts in the positions of scattering thresholds have profound effects on collision properties, as will be seen below. Another effect of an applied field is that it breaks the isotropic character of space, so that the total angular momentum is no longer a good quantum number.
2009 by Taylor and Francis Group, LLC 10 Cold Molecules: Theory, Experiment, Applications motion of noninteracting particles. At very long range, where the centrifugal potential is negligible, the solutions may be written r→∞ ψL (r) ∼ sin(kr − Lπ/2 + δL ). , if V (r) is zero. The scattering amplitude may be written in terms of phase shifts as f (Θ) = 1 2ik ∞ (2L + 1)(e2iδL − 1)PL (cos Θ). 20) L=0 The differential cross-section is and thus involves a double sum over partial waves. Structure in the differential crosssection arises from interference between the contributions of different partial waves.
Deconvolution: With Applications in Spectroscopy by Peter A. Jansson
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