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By Bancroft W. D.

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We denote this by x

There are now 12 group elements, the original 6 from D s , each multiplied both by the identity and by a h . This is what we mean by the notation D3h = D3 X SP. The elements of D3 and £P commute because it makes no difference whether the triangle is first rotated and then subjected to reflection in the plane, or vice versa. The multiplication table of SP is E E Oh E E The group is Abelian; so there are two classes and two one-dimensional Irreducible representations. Upon denoting the two representations P+ and I' for even and odd, the character table is simply y E r+ F- 1 1 1 -1 Multiplying this table by that for D s given in Sec.

This in fact is the case. As described in Appendix A, the direct product of two matrices A and B is a matrix A x B whose elements are all the products of an element of A and one of B. Each element bears a double set of subscripts. For example, the element obtained from ATJBKL is labeled (A x B)IK JL, the two initial indices being given before the comma. The fact that these directproduct matrices in fact have the requisite group-multiplication property 44 [Chap. 2 GROUP THEORY AND QUANTUM MECHANICS follows from the commutivity of ordinary matrix multiplication and the direct-product operation.

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Photochemical Temperature Coefficients by Bancroft W. D.


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