By Professor Ingvar Lindgren, Dr. John Morrison (auth.)
This ebook has constructed via a chain of lectures on atomic idea given those final 8 years at Chalmers college of expertise and a number of other oth er learn facilities. those classes have been meant to make the elemental components of atomic thought on hand to experimentalists operating with the hyperfine constitution and the optical homes of atoms and to supply a few perception into fresh advancements within the idea. the unique goal of this booklet has progressively prolonged to incorporate a variety of issues. we now have attempted to supply an entire description of atomic conception, bridging the space among introductory books on quantum mechanics - equivalent to the e-book by way of Merzbacher, for example - and current day examine within the box. Our presentation is restricted to static atomic prop erties, akin to the powerful electron-electron interplay, however the formalism will be prolonged with out significant problems to incorporate dynamic houses, akin to transition chances and dynamic polarizabilities.
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Extra info for Atomic Many-Body Theory
Hence, this must be true also for arbitrary finite rotations. ,q(w) \. 46,47) imply that the angular-momentum eigenfunctions and the tensor operators from a basis for a representation of the rotation group. The representation is said to be "irreducible", because it is not possible to form any linear combinations of the basis functions which give a representation of lower dimensionality. 4 Tbe Orbital Angular Momentum. 3). 7). The operator 1'2 appearing here is the Laplacian operator. 49) which in spherical polar coordinates transforms into ",2 ,.
62) So in order to find the desired linear combination, it is necessary to evaluate matrix elements of the kind <1m' Iexp (-ielx ) 11m) . ;12 (0I 0I 0)1 , 010 and exp (-iel x ) is represented by the matrix exp (M), where ie M= - ";2 (01 01 0)1 . 010 It is easy to demonstrate that ~ ~) o J... 2 Rotations in Space 27 and 1 0) o 1 , 1 0 where n is a positive integer. Using the formulas exp (M) . sm () M M2 M3 = 1 + IT + 2T + 3T + ... (J3 = () - 3! ()2 ()S ()7 + 5! - 7! ()4 ()6 + ... cos () = 1 - 2!
Is the g value of the electron spin. According to Dirac's relativistic theory, g. is exactly equal to 2. When quantum-electrodynamic effects are taken into account, however, a value of g. is obtained, which is slightly larger than 2. Accurate calculations yield the value g. 002319, which is also in very good agreement with the experimental result. Since the magnetic field is assumed to be weak, we are interested in matrix elements of Hm between states I(SL)JM >having definite values of S, L, and J.
Atomic Many-Body Theory by Professor Ingvar Lindgren, Dr. John Morrison (auth.)