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A New Approach for Scattering by Even‐Power Potentials
Author(s) -
Müller Harald J. W.
Publication year - 1968
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.19684760303
Subject(s) - eigenfunction , physics , formalism (music) , scattering , coupling constant , perturbation (astronomy) , s matrix , schrödinger equation , classical mechanics , mathematical physics , quantum mechanics , mathematical analysis , eigenvalues and eigenvectors , quantum electrodynamics , mathematics , art , musical , visual arts
The radial SCHRÖDINGER equation is considered in a more general form and is then transformed into another equation to permit straightforward application of the perturbation formalism used previously by the author. The potential considered is assumed to be expandable in ascending even powers of r . The potential (sinh r ) −2 emerges as a special case and is considered separately. For the general case, expansions are obtained for the eigenenergies and eigenfunctions valid in regions of small angular momenta and coupling constants. A simple analytic expression for the S ‐matrix is obtained. Finally several consequences are discussed.