De broglie wavelength derived from relativity but used in non relativity?

phyky
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The question as stated in title, why?
 
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The deBroglie wavelength is introduced as λ = h/p. Here nothing is said about the momentum and whether we talk about rel. or non-rel. physics.

But b/c the rel. expression for p can be approximated with the non-rel. expression for v << c we also have a non-rel. approximation for the wavelength, namely λ = h / mv (m: rest mass).
 
and 1 more thing about the velocity of de broglie wavelength is the phase velocity from derivative, but the velocity of electron is group velocity, right? Or just like his pilot wave theory of a phase guides the electron in space?
 
last question make confuse i should ask in this way. phase velocity, vp=ω/k=fλ. With vp=c^2/vg where vg is group velocity is able to derive de broglie wavelength. So i do not understand the description is λ=h/mvg and since λ depend on vp and the equation show is related to vg. So my question is what exactly vp=c^2/vg mean? and λ is what exactly?wavelength of electron or the phase wavelength that guide the electron? and the phase velocity relate to the phase in wave packet? I m confuse...
 

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