By Anatoli V. Andreev

** Atomic Spectroscopy **provides a finished dialogue at the normal method of the speculation of atomic spectra, in line with using the Lagrangian canonical formalism. This process 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 place to begin of basic method. The designated awareness is paid to the speculation of Lamb shift formation. The formulae for hydrogenic spectrum together with the account of Lamb shift are written in basic 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 contemporary atomic spectroscopy.

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**Additional resources for Atomic Spectroscopy: Introduction to the Theory of Hyperfine Structure**

**Example text**

In the vicinity of its bottom, thc potential energy of the atomic trap can be approximated by the parabolic potential well: U (R) = U (0) a ~ ~ . 55) are again the confluent hypergeometric functions. 53b) we get 38 Schrodinger equation where ,B = M a / & , and n R is the non-negative integer. 57) is degenerated with respect to the combination of the quantum numbers n R and I . In this case, the combination is the sum of doubled radial quantum number and orbital quantum number, p = 2 n ~2 . + Interaction of trapped atom with electromagnetic field Let us consider the interaction of the trapped atom with the electromagnetic field.

In the frame of the field theory formalism the wave function (r,t ) plays the role of the coordinate of the matter field. 1 Lagrange function The Lagrange function of the point particle depends in classical mechanics on the coordinate, velocity, and time. Similarly, the Lagrange function of the matter field depends on the wave function, its space and time derivatives, and time 6 where = d $ / a t . The appearance of the space derivative, in addition to time derivative, is quite understandable, because the wave function is the continuous function of coordinates.

21), the angular part of the wave function is given by exp (imcp). 3 Particle motion in the Coulomb field Let us consider the problem on a particle motion in the attracting Coulomb field. 12) became [-&($+ :$ 5) - - $1 qE( r ) = E$E (r) . 27) commutes with the operators of parity, angular momentum square, and projection of angular momentum. Therefore the wave function can be expressed in terms of the eigenfunctions of the parity, angular momentum, and projection of angular momentum operators. However, as we have seen, the parity of states in the spherically symmetric external field is unambiguously determined by the angular momentum, therefore to define the particle state we can use the following quantum numbers: energy E, angular momentum 1, and projection of angular momentum m.