By Boca, Roman (Auth.)

ISBN-10: 012416014X

ISBN-13: 9780124160149

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Extra resources for A Handbook of Magnetochemical Formulae

Example text

53 4U 1U2U1 ð1:110Þ An analytical formula says dimðΓλ Þ 5 N! h2 ! . hr ! i,j ð1:111Þ with hi 5 r 1 λðiÞ 2 i ð1:112Þ where λðiÞ is the length of row i, and r is the number of rows in the Young diagram. The Young tableaux are useful for labelling IRs of various groups: a. The N-box Young diagrams label all IRs of the symmetric group SN. b. The standard tableaux of k-box Young diagrams with no more than n rows label the IRs of GLn, in particular they label the IRs of Un. c. The standard tableaux of k-box Young diagrams with no more than (n 21) rows label the IRs of SLn, in particular they label the IRs of SUn.

The spatial symmetry of the atomic coordinates within the point group G; 2. the symmetry of the angular momentum within the groups R3 and SU2S11; 3. the permutation symmetry that accounts for permutations of individual particles (spins) within the symmetry group SN. The most general formulation of the Pauli principle is based upon the fact that the only allowed states refer to the one-dimensional permutational states. There are only two one-dimensional representations in the group SN: the totally symmetric (Γ1) and the totally antisymmetric (Γ2).

5 fΓ6 1 Γ7 g 3 Γ5 5 fΓ6 1 Γ7 g 1 fΓ6 1 Γ7 g S 5 2 ! fΓ1 1 Γ3 1 Γ4 1 Γ5 g, fΓ1 1 Γ3 1 Γ4 1 Γ5 g 3 Γ5 Eg ! Γ5 5 fΓ5 g 1 fΓ5 g 1 fΓ5 g 1 fΓ1 1 Γ2 1 Γ3 1 Γ4 g S 5 1=2 ! Γ6 , B2g ! Γ4 Γ6 3 Γ4 5 Γ7 S 5 1 ! fΓ2 1 Γ5 g, A2g ! Γ2 fΓ2 1 Γ5 g 3 Γ2 5 fΓ1 g 1 fΓ5 g S 5 3=2 ! fΓ6 1 Γ7 g, fΓ6 1 Γ7 g 3 Γ2 5 fΓ6 g 1 fΓ7 g A2g ! Γ2 S 5 2 ! fΓ1 1 Γ3 1 Γ4 1 Γ5 g, fΓ1 1Γ3 1Γ4 1Γ5 g 3 Γ4 5 fΓ4 g1fΓ2 g1fΓ1 g1fΓ5 g B2g ! e. ^ γÞjΓ; γi 5 jΓ; γi PðΓ; ð1:91Þ and annihilates functions belonging to other representations, viz.

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A Handbook of Magnetochemical Formulae by Boca, Roman (Auth.)


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