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A minimum principle for atomic systems allowing the use of discontinuous wave functions
Author(s) -
Hall G. G.,
Hyslop J.,
Rees D.
Publication year - 1969
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.560030205
Subject(s) - classification of discontinuities , variational principle , cutoff , upper and lower bounds , wave function , free energy principle , energy (signal processing) , mathematics , variational method , jump , hydrogen atom , mathematical analysis , class (philosophy) , physics , quantum mechanics , computer science , statistics , group (periodic table) , artificial intelligence
In this paper a variational principle proposed by Hall [1] is shown to be a minimum principle for coulombic systems. Into this principle it is possible to admit a larger class of trial wave functions than is possible in the conventional variational treatment, including wave functions with discontinuities. It is further shown that the upper bounds given by this treatment are always at least as good as that given by the Rayleigh–Ritz method. The theory is then applied to the hydrogen atom and upper bounds to the energy are calculated for various “cutoff” wave functions. It is usually possible to define an optimum “cut off” distance which minimizes the upper bound.