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- W2340693729 abstract "A single-step Eriksen transformation of~$1S_{1/2}$,~$2P_{1/2}$ and~$2P_{3/2}$ states of the relativistic hydrogen atom is performed exactly by expressing each transformed function (TF) as a linear combination of eigenstates of the Dirac Hamiltonian. The TFs are four-component spinors with vanishing two lower components, are calculated numerically and have the same symmetries as the initial states. For all nuclear charges~$Z in [1ldots 92]$ a contribution of the initial state to TFs exceeds 86% of the total probability density. Next large contribution to TFs comes from delocalized states with negative energies close to~$-m_0c^2-E_b$, where~$E_b$ is the binding energy of initial state. Contribution of other states to TFs is less than~$0.1%$ of the total probability density. Other components of TFs are nearly zero which confirms both validity of the Eriksen transformation and accuracy of the numerical calculations. The TFs of~$1S_{1/2}$ and~$2P_{1/2}$ states are close to~$1s$ and~$2p$ states of the nonrelativistic hydrogen atom, respectively, but the TF of~$2P_{3/2}$ state differs qualitatively from the~$2p$ state. Functions calculated with use of a linearized Eriksen transformation, being equivalent to the second order Foldy-Wouthuysen transformation, are compared with corresponding functions obtained by Eriksen transformation. A very good agreement between both results is obtained." @default.
- W2340693729 created "2016-06-24" @default.
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- W2340693729 date "2016-04-08" @default.
- W2340693729 modified "2023-09-27" @default.
- W2340693729 title "Transformation of localized states of relativistic hydrogen atom into two-component form" @default.
- W2340693729 hasPublicationYear "2016" @default.
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