Calculation of Matrix Elements in the Foldy-Wouthuysen Representation

Details Calculation of Matrix Elements in the Foldy-Wouthuysen Representation Calculation of Matrix Elements in the Foldy-Wouthuysen Representation

2010-03-25

arxiv.org/abs/1003.5138v1

Physics

General Physics

13 pages

Scientific paper

The paper compares the methods used to calculate matrix elements of the operator of radail electron coordinates in an arbitrary order in the Foldy-Wouthuysen representation and with the use of the Dirac equation for 1s-states of the hydrogen-like and helium-like ions of transuranic elements. The obtained analytical and numerical results for 1s-states of the hydrogen-like and helium-like ions proves that the wave function reduction requirement is met with transformation to the Foldy-Wouthuysen representation and confirms that matrix elements can be calculated using only one component (either upper, or lower) of the Dirac bispinor wave function.

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