Diffraction wavelength of particles in moving frames?

[knowing]

Here's a question I cannot seem to comply with my understanding of Quantum Mechanics.
The characteristic wavelength of a particle is responsible for diffraction interference fringes, which is part of the wavefunction solution to the Schrödinger equation. But the wavelength of a particle is dependent on its momentum P. So if the whole diffraction experiment was carried out in a moving frame of reference, then by the unitary space-time translating operator G, which translates the velocity, the momentum is dependent on the frame of reference. So in the moving frame of reference, the particle would seem to have a different wavelength. So what wavelength would the diffraction pattern relate to, which I assume must give the same fringe pattern in both frames.

 

[The_Duck]

In the moving frame the diffraction grating or slit will also be moving, which will complicate the calculation of the diffraction pattern. Once you account for this, the result of the calculation will be the same diffraction pattern as you would calculate in the original frame.