By Peter R. Fontana (Auth.)
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T>tj+T, j9 = i 2 J The Fourier transform of a sinusoidal pulse is given by Eq. 46). F r o m Eq. 78) The integrand has poles at ω = — ω +ω — ω , + ω . The integral is best evaluated by using the method of residues. Since the poles are on the real axis, we displace them by adding to them a term + is or — is depending on whether the factor β in exp(ißco) is positive or negative. The contour is closed by an infinite semicircle in the upper half-plane if β is positive and in the lower half-plane if β is negative.
Plenum, New York, 1974. R. " Taylor and Francis, London, 1974. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 1 COUPLING O F ANGULAR M O M E N T A The theory of angular m o m e n t u m is central in many applications of atomic radiative processes. It allows us to m a k e use of the symmetry p r o p erties of the eigenstates of the system under rotation, and it leads to some powerful theorems that simplify the calculations of matrix elements and selection rules. An extension of the theory to irreducible tensors yields methods that m a k e it possible to express the Hamiltonian in terms of such tensors.
This integral appears frequently in the calculation of matrix elements of radiative transitions. The angular m o m e n t u m q u a n t u m numbers of the initial and final atomic states are l m and / m , respectively, and the spherical h a r m o n i c Y comes from the interaction Hamiltonian. F r o m the first C coefficient we get the selection rule m = m + ra and from the parity C coefficient we k n o w that l + l + / = 2n (n = 1, 2 , . ) and that the triangle rule must be satisfied. Thus, we already k n o w under what conditions a transition can take place.
Atomic Radiative Processes by Peter R. Fontana (Auth.)