Hydrogen and muonic hydrogen atomic spectra in non-commutative space-time

Comparing electronic hydrogen with muonic hydrogen shows that the discrepancy in measurement of the Lamb shift in the both systems are relatively of order of (m(mu)/m(e))(4-5). We explore the spectrum of hydrogen atom in non-commutative QED to compare the non-commutative effects on the both bound states. We showthat in the Lorentzviolating non-commutative QED the ratio of NC-corrections is (m(mu)/m(e))(3) while in the Lorentz-conserving NCQED is (m(mu)/m(e))(5). An uncertainty about 1 Hz << 3 kHz in the Lamb shift of hydrogen atom leads to an NC correction of about 10 MHz in the Lorentz-violating non-commutative QED and about 400 GHz in the Lorentz-conserving non-commutative QED.