Nonrelativistic calculation of the Lamb shift to order α5

It is demonstrated, for the first time to our knowledge, that the Lamb-shift calculation for all states of hydrogenic atoms can be carried out to order α5 by applying the methods of nonrelativistic quantum electrodynamics and without using the Dirac equation and the second quantization for the electron. The extremely small deviations from the standard relativistic results were calculated for different S- and non-S-states as well.