Internal Symmetries and Additional Quantum Numbers for Nanoparticles

Wavefunctions of symmetrical nanoparticles are considered making use of induced representation method. It is shown that when, at the same total symmetry, the order of local symmetry group decreases, additional quantum numbers are required for complete labelling of electron states. It is shown that t...

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Bibliographic Details
Published inNanoscale systems mathematical modeling, theory and applications Vol. 2; pp. 96 - 106
Main Author Yarzhemsky, V.G.
Format Journal Article
LanguageEnglish
Published Versita 06.05.2013
Subjects
02.20.Bd
05C
20C
61.46-w
71.10-m
81C
electron structure
group theory
Mackey theorem
nanoparticles
quantum numbers
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ISSN2299-3290
2299-3290
DOI10.2478/nsmmt-2013-0006

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Summary:Wavefunctions of symmetrical nanoparticles are considered making use of induced representation method. It is shown that when, at the same total symmetry, the order of local symmetry group decreases, additional quantum numbers are required for complete labelling of electron states. It is shown that the labels of irreducible representations of intermediate subgroups can be used for complete classification of states in the case of repeating IRs in symmetry adapted linear combinations. The intermediate symmetry approach is extended to singlet and triplet two-electron states making use of Mackey theorem on symmetrized squares of induced representations.
ISSN:2299-3290
2299-3290
DOI:10.2478/nsmmt-2013-0006