Abstract
A method based on the B-spline basis set is developed that significantly simplifies the Bethe-logarithm calculations for the atomic hydrogen. Without any auxiliary optimization and extrapolation, this method not only can calculate the Bethe logarithms of low-lying states to high precision using relatively small basis sets, but can also calculate high-lying Rydberg states efficiently. For the ground state, the Bethe logarithm is calculated to 24 significant figures using 450 B-spline functions. For high-lying Rydberg states, we can reproduce all the results of Jentschura and Mohr [Phys. Rev. A 72, 012110 (2005)]. DOI: 10.1103/PhysRevA.87.022510
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