Download e-book for iPad: Angular Momentum Theory Applied to Interactions in Solids by Clyde A. Morrison

By Clyde A. Morrison

ISBN-10: 3540189904

ISBN-13: 9783540189909

ISBN-10: 3642933769

ISBN-13: 9783642933769

From December 1985 via March 1986 the textual content of this ebook shaped the root of an in-hours direction taught by way of the writer at Harry Diamond Laborato­ ries. enormous suggestions in revising and organizing the 1st draft used to be given via John Bruno. the unique draft of those notes was once in accordance with a set of lectures brought on the Universidade Federal de Pernambuco, Recife, Brazil, among 2 November 1981 and a pair of December 1981. The stopover at to Recife was once a reaction to an invi tation of Professor Gilberto F. de Sa of the Physics division. within the guidance of those notes I made many requests of my coworkers for past resul ts and memories of our early paintings. between these consul ted have been Donald Wortman, Nick Karayianis, and Richard Leavitt. extra, a couple of .suggestions from my Brazilian colleagues helped make the lectures extra transparent. specific between those have been Professor Oscar Malta and Professor Alfredo A. da Gama either one of whom I desire to thank for his or her support. Encouragement and information with investment for far of this paintings got here from Leon Esterowitz of the Naval learn Laboratory and Rudolph Buser and Albert Pinto of the heart for evening imaginative and prescient and Electro-Optics.

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Extra resources for Angular Momentum Theory Applied to Interactions in Solids

Example text

A q-a (a) where + Tkq = in which, by the properties of the C-G coefficient, k is restricted to 0 ~ k ~ 2. The Tk~ thus constructed is patently a spherical tensor of rank k, projection q. 1» gives (b) with m' = m + q. 1. I. IIR. and the C-G coefficient requires mil = m' - a. Substituting these results into (d) gives where we have used the same technique used in (e) on the second matrix element in (d). (m'» Comparing this result to (b) we obtain (h) 1. l 13 <1

Coefficients can be found on page 225 of Rose, 1957). You will need <1mlc2011m> = <1(m)2(0)11(m» <1(0)2(0)11(0» <11Ic2211-1> = <1(-0)2(2)11(1» <1(0)2(0)11(0» =~ , <1(0)2(0)1 1(0» <1(±1)2(0) IH±1» = <1(1)2(2)11(1» = _1_ , 110 ~ The answer can be obtained from <10IHI10> = 2 5 <1±1IHI1±1> = <11IHI1-1> B20 1 5 B20 16 B 5 22 = - -- 32 ' ' , , (The C-G 4. 3 Annotated Bibliography and References Ballhausen, C. J. (1962), IntroductIon to Ligand Field Theory, McGraw-Hill, New York, NY. Brink, D. , and G.

Ha)O(O) IHa» 13 a lI. J.. ; 63 In section 6 we have shown that ~ + = 1/2 [+2 j ~·s - t2 +2] s - therefore ~ - _1- [j(j+1) - 1(1+1) - s(s+1)] iSm'miSj'j 213 and in equation (0), j = 1 ± s 1 ± 1/2, 2j D (q) 21 ± 1; therefore, (-1)2j = -1 so that the result given in equation (0) agrees with equation (q) but is much more difficult to obtain. We have an interaction between two electrons given by Tk q - L = L <1(~)1(M-~)IL(M» 11~;1>11M-~;2> ~ where the last index in the angled brackets refers to the individual electrons.

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Angular Momentum Theory Applied to Interactions in Solids by Clyde A. Morrison


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