Hyperfine structure in hydrogen

[victorvmotti]

Consider the Dirac equation for bounded electron in hydrogen atom.

I am trying to get a clear physical explanation for all mathematical terms that appear in the Hamiltonian and energy spectrum.

Kinetic and Coulombic potential and rest energies are the first terms and easy to identify.

Then we have mass variation term and spin-orbit interaction term.

The Darwin term is due to Zitterbewegung or oscillation about the mean position.

Also we need to add electron spin and proton spin interaction.

Another correction is due to fluctuations in radiation vacuum.

Yet another correction is that when electron wavefunction is inside proton and Coulombic potential does not apply.

The question is that should we consider any other contributing energy?

How about gravity? Or electron Coulombic potential on itself?

Also related is that when expanding a Taylor series of the square of fine structure constant to obtain energy eigenvalues should there be a physical meaning or interpretation for all mathematical terms in the series and not only the few beginning terms?

In brief where our approximation ends and the full exact eigen state is obtained without neglecting any source of energy?

 

[A. Neumaier]

In brief where our approximation ends and the full exact eigenstate is obtained without neglecting any source of energy?

Never. There are infinitely many terms that would be needed to account for everything exactly. You may find out the approximations that very high precision predictions of electronic properties require by searching scholar.google.com for papers on NRQED (nonrelativistic QED).