Abstract
We study the Klein-Gordon equation in a non-commutative space-time as applied to the Hydrogen atom to extract the energy levels, by considering the second-order corrections in the non-commutativity parameter. By comparing to the 2S – 1S transition energies we obtain an upper bound on the non-commutativity parameter. Phenomenologically we show that non-commutativity is the source of lamb shift corrections and spin of the electron.
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