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Variational Matrix Padé Approximants in Two Body Scattering
Author(s) -
Turchetti G.
Publication year - 1978
Publication title -
fortschritte der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.19780260102
Subject(s) - padé approximant , matrix (chemical analysis) , series (stratigraphy) , variational principle , mathematical analysis , scattering , mathematics , convergence (economics) , amplitude , physics , variational method , mathematical physics , quantum mechanics , paleontology , materials science , economics , composite material , biology , economic growth
The convergence and bounding properties of the variational matrix Padé approximants are investigated for non relativistic two body interactions. Selecting L – 1 discrete values qi , i = 1, …, L – 1 and the physical momentum q 0 the off shell scattering amplitudes are L X L matrices. The [ N / N ] Padé approximants to the Born series of these matrices are the variational solution of the Schwinger principle and the corresponding physical amplitude has variational properties in the off shell momenta. For positive interactions the best approximants to the phase shift is an absolute minimum on the q i and monotonic convergence to the exact result for N → ∞ or L → ∞ ca be proved. Similar properties are shown for the bound states using the Ritz variational principle. The required mathematical background is extensively worked out, the extensions to non positive, singular and long range potentials are considered and some numerical examples are presented.