# Internal Symmetries and Additional Quantum Numbers for Nanoparticles

Nanoscale Systems: Mathematical Modeling, Theory and Applications (2013)

- Volume: 2, page 96-106
- ISSN: 2299-3290

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topV.G. Yarzhemsky. "Internal Symmetries and Additional Quantum Numbers for Nanoparticles." Nanoscale Systems: Mathematical Modeling, Theory and Applications 2 (2013): 96-106. <http://eudml.org/doc/266766>.

@article{V2013,

abstract = {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.},

author = {V.G. Yarzhemsky},

journal = {Nanoscale Systems: Mathematical Modeling, Theory and Applications},

keywords = {nanoparticles; group theory; Mackey theorem; quantum numbers; electron structure},

language = {eng},

pages = {96-106},

title = {Internal Symmetries and Additional Quantum Numbers for Nanoparticles},

url = {http://eudml.org/doc/266766},

volume = {2},

year = {2013},

}

TY - JOUR

AU - V.G. Yarzhemsky

TI - Internal Symmetries and Additional Quantum Numbers for Nanoparticles

JO - Nanoscale Systems: Mathematical Modeling, Theory and Applications

PY - 2013

VL - 2

SP - 96

EP - 106

AB - 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.

LA - eng

KW - nanoparticles; group theory; Mackey theorem; quantum numbers; electron structure

UR - http://eudml.org/doc/266766

ER -

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