By Houben J., Weyl T.
Methoden der Organischen Chemie (Methods of natural Chemistry, known as Houben-Weyl) is a customary reference paintings for chemists engaged in natural synthesis. In volumes on compound sessions, together with all Supplemental volumes, preparative equipment are handled comprehensively and significantly. Tables of examples evaluate an important tools and exhibit their scope. unique experimental techniques are given for the easiest equipment. The reactivity and additional reactions of every compound category also are awarded. The wide use of formulation schemes help in making the German-language volumes extra simply comprehensible to non-German readers.
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Extra info for Houben-Weyl Methods in Organic Chemistry: Organotellurium Compounds
4) and thus must commute. Introducing operator functions ˆ . ξn . ) = ψ(. bnf ϕfn (ξn ), nf 38 EXCITONS IN SECOND QUANTIZATION REPRESENTATION b†nf ϕ∗f n (ξn ), ψˆ† (. . ξn . 9) nf we obtain the transition from operators in the Schr¨ odinger representation into operators in the second-quantization representation. For example, the operator of the total number of crystal molecules can be put into the form b†nf bnf . ˆ . ξn . )dξ = ψˆ† (. . ξn . )ψ(. 10) nf The crystal energy operator without intermolecular interactions can be obtained from the transformation ˆ n (ξn ) → H ˆ0 , H n ψˆ† (.
Into irreducible representations (see, for example, (21), § 26, and also (20)). The corresponding coeﬃcients u ˜αμ (0), as mentioned previously, determine for k → 0 the s-independent wavefunctions of mechanical excitons and not those of Coulomb excitons. The coeﬃcients u ˜αμ (0) will coincide with the coeﬃcients uαμ (0) appropriate for wavefunctions of Coulomb excitons only for a special choice of the directions k, namely for the case when the group of the wavevector k for k → 0 coincides with the crystal class group.
Nnf . . (1 − Nnf ) . . 7) It follows from the above relations that the operator b†nf can be called the creation operator of the states nf , and bnf the annihilation operator for the same states. 7) that the operators obey the anticommutation rules bnf b†nf + b†nf bnf = 1, bnf bnf = b†nf b†nf = 0. 4) and thus must commute. Introducing operator functions ˆ . ξn . ) = ψ(. bnf ϕfn (ξn ), nf 38 EXCITONS IN SECOND QUANTIZATION REPRESENTATION b†nf ϕ∗f n (ξn ), ψˆ† (. . ξn . 9) nf we obtain the transition from operators in the Schr¨ odinger representation into operators in the second-quantization representation.