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I know that for spin 0 bosons, the Klein Gordon equation gives solutions that are similar to the solutions of the Schrodinger equation for a non-relativistic free particle, the only difference being that the energy used when calculating the wave frequency (E/h-bar) is the relativistic energy m*c-square*gamma.

I don't know how the wavefunctions look for spin 1 or spin 1/2 particles. What I would like to know is if there is any kind of particle for which one gets a wavefunction where the frequency is different then m*c-square*gamma/h-bar? Also, is it possible to verify these things experimentaly? I mean, can an experiment get an eigenstate and measure both the energy and the wave frequency? Has that been done for relativistic particles? Have any discrepancies been found? Where could I find such data?

Thanks!