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Localized functions on a circle
Author(s) -
Rees D.,
Hall G. G.
Publication year - 1995
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/qua.560540604
Subject(s) - eigenfunction , basis (linear algebra) , basis function , complex plane , transformation (genetics) , plane (geometry) , exponential function , alias , mathematics , position (finance) , mathematical analysis , analytic function , pure mathematics , physics , eigenvalues and eigenvectors , geometry , quantum mechanics , computer science , chemistry , biochemistry , finance , database , economics , gene
The derivation of hybrids as localized equivalent functions in the plane is discussed using the simultaneous eigenfunctions of the x and y position operators, as represented in a finite basis. It proves helpful, initially, to use complex exponentials as basis functions, but the transformation to a real basis is made later. The introduction of alias functions to produce commuting matrices is described. Full results are obtained for any number of functions in the plane. © 1995 John Wiley & Sons, Inc.