The Lamb Shift of Hydrogen and Low-energy Tests of Qed

Leading logarithmic corrections to the difference of Lamb shifts of s-states EL(1s) − 8EL(2s) and to the life time of 2p1/2 state are considered. The result of Sokolov and Yakovlev for the Lamb splitting of 2s1/2 and 2p1/2 is reevaluated and our new value is 1057.8576(21) MHz. Using value of EL(1s)− 8EL(2s) = -187.237(8) MHz, obtained here, a new value of the Hydrogen and Deuterium ground states using all recent measurements connected with 1s or 2s Lamb shifts. The highest precision value for the Hydrogen ground state is obtained from corrected result of Sokolov and Yakovlev experiment as 8172.934(22) MHz. The Deuterium result is EL(1s) − 8EL(2s) = -187.229(8) MHz, using it we obtain from the Garching experiment 8183.905(224) MHz. Some related topics are also considered. Taking into account nearest future result the fine structure constant problem are reviewed. Special attention is payed to Muonium hyperfine splitting, which it is done simillar to Lamb shift calculatuion for and to the neutron de Broglie’s wave length measurements which also could lead to some connection between the Deuterium mass and the fine structure constant.