The quantum electrodynamical theory of the two-photon transitions in hydrogenlike ions is presented. The emission probability for 2s1/2 → 2γ(E1) + 1s1/2 transitions is calculated and compared to the results of the previous calculations. The emission probabilities 2p1/2 → γ(E1) + γ(E2) + 1s1/2 and 2p1/2 → γ(E1) + γ(M1) + 1s1/2 are also calculated for the nuclear charge Z values 1 ⩽ Z ⩽ 100. This is the first calculation of the two latter probabilities. The results are given in two different gauges.
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