Wavelength and relativityFrom de Broglie equation λ=h/p. But p=mv and velocity is a relativistic quantity so also wavelength is relative ? In other words does wavelength depends on the reference frame ?

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Gillian Kelly · Accepted Answer

Yes, but the variation of wavelength we&#039;re talking about here is not, as claimed in two other answers, the same as a standard Doppler effect. An electron, in its rest frame, has a wavelength of infinity, i.e., a wavenumber (  k  =  2  π      /    λ) of zero. There is no Doppler shift formula that is going to transform 0 to some finite wavenumber (or   ∞ to some finite wavelength). If you measure a wavenumber of 0 in some frame, then you have essentially no information, and you cannot find out the wavenumber in some other frame without knowing some additional information, such as the mass of the particle. (In more formal mathematical language, a tensor that is zero in one frame is zero in all frames.)For a sound wave or a light wave, there is an observable quantity that tells you the amplitude. You can tell where there are nodes (amplitude=0), and measure the wavelength by finding the distance between them. Therefore the wavelength must have some knowable transformation law when you go from one frame to another.Not so for a wavefunction. The wavefunction is not observable. The wavefunction of an electron moving at a definite velocity does not have nodes that are at detectable points in space (      e          i      k      x       is never zero). The wavelength does transform, but not according to any Doppler shift formulas. A particular wavetrain can be 3 wavelengths long according to one observer and 4 wavelengths long according to another (a situation that would be impossible with a sound or light wave).

hetriamhageh6k20 · Accepted Answer

Yes, the wavelength of a wave depends on the reference frame. This effect is generically known as the Doppler Effect. Note though that waves which propagate through a medium (e.g. sound waves that propagate through air) has a natural &quot;rest&quot; frame that coincides with the rest frame of the medium. Waves which don&#039;t propagate through a medium (e.g. electromagnetic waves) do not have such a natural rest frame.

Wavelength and relativity From de Broglie equation λ=h/p. But p=mv and

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