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On the non‐existence of maxima in variational computations containing non‐linear parameters
Author(s) -
Tal Yoram,
Katriel Jacob
Publication year - 1978
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.560130111
Subject(s) - maxima , homogeneity (statistics) , computation , kinetic energy , maxima and minima , energy minimization , energy (signal processing) , variational method , potential energy , mathematics , statistical physics , physics , computational chemistry , mathematical analysis , chemistry , classical mechanics , quantum mechanics , algorithm , statistics , art , performance art , art history
Abstract The homogeneity properties of the kinetic and potential energy operators are used to obtain expressions for the second derivatives of the energy expectation value. These are used to demonstrate that in atoms as well as in molecules in the neighborhood of the equilibrium geometry the variational energy cannot have maxima with respect to the non‐linear parameters.