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Sinc collocation in quantum chemistry: Solving the planar coulomb Schrödinger equation
Author(s) -
Koures Vasilios G.,
Harris Frank E.
Publication year - 1996
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/(sici)1097-461x(1996)60:7<1311::aid-qua12>3.0.co;2-7
Subject(s) - sinc function , eigenfunction , eigenvalues and eigenvectors , schrödinger equation , quantization (signal processing) , mathematics , completeness (order theory) , quantum mechanics , computation , mathematical analysis , basis function , physics , mathematical physics , algorithm
Dirac bra‐ket notation is introduced for the Whittaker cardinal (Sinc) functions and a previously unreported completeness relation for these quantities is presented and derived. With the use of this completeness relation it becomes simple to transform to a Sinc‐basis the eigenvalue equations arising from a light‐cone quantization of field theory or the similar equations occurring in nonrelativistic quantum mechanics. The simplicity and power of Sinc‐function expansions is illustrated by computation of the eigenvalues and eigenfunctions of the position‐space planar Coulomb equation, a problem for which convergence has not been achieved by a variety of other computational methods. © 1996 John Wiley & Sons, Inc.