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Differentiability of degenerate electronic wave functions with respect to parametric variables
Author(s) -
Yin Li,
Goscinski Osvaldo
Publication year - 1990
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.560370305
Subject(s) - differentiable function , degenerate energy levels , degeneracy (biology) , mathematical analysis , gravitational singularity , parametric statistics , wave function , function (biology) , mathematics , space (punctuation) , parameter space , pure mathematics , physics , quantum mechanics , geometry , computer science , bioinformatics , statistics , evolutionary biology , biology , operating system
The present paper is aimed at differentiability of electronic wave functions, with respect to parametric variables, in the presence of electronic degeneracy. An analysis is made of a wave function, constructed so that it has the largest domain of parameter space in which it is differentiable, with the help of Berry's formula for the geometric phase. In particular, the electronic wave functions, in presence of a double degeneracy in two‐ and three‐dimensional parameter spaces, are studied in detail. It was found that the three‐parameter‐dependent wave function is differentiable everywhere except along an axis starting from the degenerate point where it is discontinuous. The two‐parameter‐dependent wave function is differentiable everywhere except at the degenerate point where it is disocontinuous. These singularities are expected to have consequences on wave functions having parametric variables as arguments.