Lecture_34_Chapter_12_Tables

Lecture_34_Chapter_12_Tables - Table 12.2 Multiplication...

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Unformatted text preview: Table 12.2 Multiplication Tablea for the Group C2v Operation B E C3 0'v 0'1, E E C; 0' v 0'; Operation A if g? f; (g; 52 “3 0", 0v C i E 3The table contains the products AB for the indicated operations. Note that each column and each row has each symmetry operation represented only once. _‘_——-——'___—_————_—_—_____ Example 12.4 The multiplication table of the representation is the same as that of the group Show that the representation given in equation 12.16 has the same multiplication table as the operations in the group sz (Table 12.2). From the multiplication table of the R’s of equation 12.16: RUE) R(C2) RM) ROTQ) R(E) 1 —1 1 -1 R(C2) -1 1 —1 1 Rm) 1 , —1 1 —1 Rm) —1 1 ~1 1 —_—————.—_.—____—___ If we compare these numbers with those we would obtain by replacing the operations in Table 12.2 by the R’s of equation 12.10, we see that they are identical. —-—————————__—_____________ Table 12.4 Character Table for the C2v Group Cgv E C2 0'V (xz) 03’, (yz) A1 1 1 1 1 z, zz, x2, y2 A; 1 1 -1 —1 xy B1 1 —1 1 ‘ —1 x,xz Bz 1 —1 —1 1 y, yz ...
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