By Anatoli V. Andreev

** Atomic Spectroscopy **provides a finished dialogue at the common method of the idea of atomic spectra, according to using the Lagrangian canonical formalism. This method is constructed and utilized to give an explanation for the hydrogenic hyperfine constitution linked to the nucleus movement, its finite mass, and spin. The non-relativistic or relativistic, spin or spin-free particle approximations can be utilized as a kick off point of common strategy. The distinct cognizance is paid to the idea of Lamb shift formation. The formulae for hydrogenic spectrum together with the account of Lamb shift are written in easy analytical shape. The e-book is of curiosity to experts, graduate and postgraduate scholars, who're concerned into the experimental and theoretical examine within the box of recent atomic spectroscopy.

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**Sample text**

The electromagnetic field produced by a particle exists in the area outside of the particle localization point. ll),that the velocity of electromagnetic wave propagation is equal to the light velocity. The velocity of particle propagation is always smaller that the light velocity, therefore one can say that the particle has no opportunity to interact with its own field. 12) are completely determined by the symmetry properties of the physical system under consideration. e. the rotation of the coordinate frame around the symmetry axes should not affect on the quantum mechanical averages of the observable variables.

3 Spatial translation Let us consider now the spatial translation transformation. At the infinitesimal translation of reference frame, Sa, the particle coordinates are transformed in the following way By applying this transformation to the wave function we get $' (r') = 4 (r - Sa) = $ (r) - SaV$ (r) = (1 - 6aV) $ (r) . 23) T6a= 1 - SaV. 23)), we have TG' f' (r') gt ( r t )= TG' f ' ( r t )T 6 l g t ( r t ). 18) is the particular case of this general relationship. 14) we transform them into their initial unprimed form.

2 Space inversion and parity operator The space inversion transformation consists in the replacement r + -+ - r. The operator P generating this transformation is called by the parity operator P$ (4 = $ (4. 7). The generalized momentum p and vector potential A are both polar vectors, therefore at the space inversion transformation we have Pp = -p and PA = -A. Hence the kinetic energy remains invariable at the space inversion. e. 7) [P, H]= 0. The commuting operators have the common set of eigenfunctions.