# Relativistic corrections to quantum mechanics of Coloumb potential

Systems of charged particles (such as atomic nuclei and electrons) can be described by nonrelativistic quantum mechanics with the Coloumb interaction potential. A fully relativistic description is given by quantum electrodynamics which is much more complex.

Is it possible to expand various quantities in QED as power series in 1/c i.e. around the nonrelativistic approximation? Examples of relevant quantities are:

• Ground state energy of a given set of charged particles
• Excited state energies
• Scattering cross sections of charged particles & their bound states (assuming we trace over the photons in the final state)
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Yes, it's possible. Look Breit equation, for example: en.wikipedia.org/wiki/Breit_equation –  Vladimir Kalitvianski Dec 23 '11 at 12:45
Valdimir, as your comment is providing an answer, could you post it as an answer? –  Piotr Migdal Dec 23 '11 at 15:17

Yes, it's possible. Look Breit equation, for example: http://en.wikipedia.org/wiki/Breit_equation

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Thx Vladimir, this is indeed relevant to my question. However this only provides the answer to second order in 1/c. What about higher orders? –  Squark Dec 23 '11 at 19:22
@Squark: Higher orders give radiation effects and cannot be reduced to non-relativistic potential terms depending solely on the inter-particle distances and velocities. They will include inevitably the propagating field variables. Do you want to include the radiated field too? –  Vladimir Kalitvianski Dec 23 '11 at 22:07
@Squark: Normally for slow motions it is the dipole filed approximation which is dominant. You may be interested in the filed multipole expansions known from Classical Electrodynamics. –  Vladimir Kalitvianski Dec 23 '11 at 22:20
well I want a computable expansion of the full QED. I didn't say it has to be reducible to potential terms –  Squark Dec 24 '11 at 18:40