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- W2042022103 abstract "This work was written to clarify the use of a recently developed procedure to obtain approximate solutions of the one-particle Dirac equation directly and in response to a recent critique on its application to lowest order. The critique emphasized the fact that when the wave functions are determined only to zero order then a first order energy calculation contains significant errors of the order of α 4 , α being the fine structure constant, and a matrix element calculation error of order α 2 . Tomishima re-affirms that higher order solutions are required to obtain accuracy of these orders. In this work the hierarchy of equations occurring in the procedure is extended to first order and it is shown that exact solutions exist for hydrogen-like atoms. It is also shown that the energy in second order contains all of the contributions of order α 4 . In addition, we illustrate, in detail, that the procedure can be aplied in such a way as to isolate the individual components of the wave functions and energies as power series of α 2 . This analysis lays the basis for the determination of suitable numerical methods and hence for application to physical systems." @default.
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- W2042022103 date "1981-11-01" @default.
- W2042022103 modified "2023-09-24" @default.
- W2042022103 title "Reply to A remark on Moore's new method of obtaining approximate solutions of the Dirac equation" @default.
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- W2042022103 doi "https://doi.org/10.1139/p81-212" @default.
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