Ok, let us suppose that, instead of matter waves, I speak of sound in a medium where phase and group velocities are different. Which one will go in the Doppler formula?
Short answer: No
Long answer: Kinetic energy is unlimited. But if you use really high speed you need to use the relativistic version:
\frac{{mc^2 }}{{\sqrt {1 - \frac{{v^2 }}{{c^2 }}} }} - mc^2
As you can see, if a massive particle travels at v=c, kinetic energy becomes ∞.
If I have a matter wave (for example, electron waves in a electronic microscope) at a given wavelength λ, and I move with respect (towards) them at speed v, I will measure a Doppler shift in the wave given by:
\frac{1}{{\lambda '}} = \frac{1}{{\lambda '}}\left( {1 + \frac{v}{{v_e }}} \right)...