By Anatoli V. Andreev

Atomic Spectroscopy presents a finished dialogue at the normal method of the speculation of atomic spectra, in response to using the Lagrangian canonical formalism. This strategy is built 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 common procedure. The designated recognition 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 publication is of curiosity to experts, graduate and postgraduate scholars, who're concerned into the experimental and theoretical learn within the box of recent atomic spectroscopy.

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**Sample text**

One of them depends on the relative position coordinate, r, another term depends on the center-of-mass coordinate, R. 52). Hence, both angular momenta are the integrals of motion. e. 51). Hence without any additional analysis, we can easily write the equation for the energy spectrum of the hydrogenlike atom, when q, = - lei and qb = Z [el where me is the electron mass, and m, is the nucleus mass. 53b) are the plain waves $ (R) = CKexp ( i K R ) . To find the wave function $ (R) in the case of trapped atom, we need in the profile of the potential well of atomic trap.

As already mentioned, the angular momenta hll = [rp] and hl2 = = [RP]are both the integrals of motion. 57), The probability amplitude for the transition between the trapped hydrogen atom states of energy E = El E2 and El = Ei Ea is defined, in the frame of the first order approximation, by the following equation + + It is convenient to express the matrix elements of the momentum operator in terms of the matrix elements of the coordinate operator. 53a) and operator r is 40 Schrodinger equation Hence Now, we can use the matrix elements of the coordinate operator, that were calculated in the previous section.

E. 52) is the sum of two terms. One of them depends on the relative position coordinate, r, another term depends on the center-of-mass coordinate, R. 52). Hence, both angular momenta are the integrals of motion. e. 51). Hence without any additional analysis, we can easily write the equation for the energy spectrum of the hydrogenlike atom, when q, = - lei and qb = Z [el where me is the electron mass, and m, is the nucleus mass. 53b) are the plain waves $ (R) = CKexp ( i K R ) . To find the wave function $ (R) in the case of trapped atom, we need in the profile of the potential well of atomic trap.