By Professor Ingvar Lindgren, Dr. John Morrison (auth.)

This publication has built via a chain of lectures on atomic conception given those final 8 years at Chalmers college of expertise and several other oth er study facilities. those classes have been meant to make the fundamental components of atomic conception to be had to experimentalists operating with the hyperfine constitution and the optical homes of atoms and to supply a few perception into fresh advancements within the thought. the unique purpose of this ebook has steadily prolonged to incorporate quite a lot of themes. we have now attempted to supply an entire description of atomic conception, bridging the space among introductory books on quantum mechanics - comparable to the booklet through Merzbacher, for example - and current day learn within the box. Our presentation is restricted to static atomic prop erties, reminiscent of the powerful electron-electron interplay, however the formalism should be prolonged with out significant problems to incorporate dynamic homes, equivalent to transition chances and dynamic polarizabilities.

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**Example text**

Ji2 i2 -! j12 - M + 2i2 + 1 ~ iz - l.. 2 l.. 12. t(/1) 2 m , - 'V 21 + 1 'P - 2 , for j = /- i. 13. 1. 1. 1. 1. l 2 2 1 We have arranged the rows of the above matrix according to m and the columns according to m. + mi' The vector-coupling coefficients are zero, if m is not equal to m, + m l , since the basis functions in both schemes are eigenfunctions of Jz. So the nonzero elements of the transformation matrix appear in blocks-one for each value of m-along the main diagonal. 76) for the vector-coupling coefficients is quite unwieldy for manual work, is can easily be programmed for computers, and several standard routines are now available for calculating these coefficients.

85) that the sum of the angular momenta, I + k + 1', must be even. 18. 130) 46 2. 19. 131) where all the C tensors refer to the same coordinates. 126). 3. Angular-Momentum Graphs The techniques of dealing with angular momentum developed in the previous chapter are straightforward in principle, but they can become quite complicated when applied to real physical problems. The effort involved in practical applications can be reduced considerably by using graphical methods. Graphical methods of treating angular momenta were first introduced by Jucys et al.

The last constant is known as the Lande g factor. :iLl ~ M=J ~ =J-1 i~· I I I I I I I I • • M=-J )IBI Fig. 9. 116) splits the states having a definite value of J into (2J + I) equidistant levels as shown in Fig. 9. As long as the magnetic field is sufficiently weak, the separation of these sublevels is proportional to the field strength. In order to calculate the magnitude of the splitting, it is necessary to evaluate aL and as. l12a,b), these coefficients are related to the reduced matrix elements of Land S.