Because waves are able to apply a force. Thus they must carry momentum to ensure momentum is conserved. Claude.
Is that the matter force we should consider only or smt another..Or do anyone can explain this with maths...
In a mathematical view, it's just a postulation proposed by de Broglie. Later physical experiment had proved that wave could interact with particle and de Broglie's postulation accords with the basic conservation principles. It then became one of the cornerstones of quantum mechanics and works fairly well in predicting further phenomena. In detail, according to the concept of wave-particle duality (mathematically this is justified by Fourier transformation), a wave should have momentum and energy which are the main properties of a particle, so that it can interact with particle like that in Compton scattering.
I thought this thread was about classical waves: water waves, sound waves, waves on a string, electromagnetic waves...
My point is that it's just mathematical postulation. But it works well in accounting for the real-world phenomena. Like in the sun, the "light pressure", which is from the exchange of light's momentum, prevents it from collapse due to gravitation.
De Broglie hypothesised than momentum was related to the wavelength of a particle. He was by no means the first to apply the concept of momentum to waves. Also, I don't know why you insist that it is "just mathematical postulation", the effect is quite physical and readily observable. Claude.
If my knowledge is correct, the de Broglie hypothesis is part of the foundation of Schrodinger's equation. Logically, it is the cause of those "physical effect" via the Schrodinger's equation, but I think the original question of this thread is for the cause of this hypothesis, and that is just mathematical postulation that is necessary for its conclusions. We believe it is true not because we understand its cause but we have seen that its derivations fit well with our experience and we have been quite satisfied and not too stringent.
1) Yes- it's a consequence of conventional quantum mechanics. It doesn't require an extra postulate. 2) It's really due to the invariance of the wave-function to overall translation which can be shown to require that there exists a conserved quantity (which turns out to be the momentum) related to the FT of the wave-function. 3) It's not intuitively obvious that the quantum expression for the momentum should reduce to the classical expression (e.g. as hbar->0), but the math tells us this is so. This isn't a complete answer. Maybe someone can come up with an intuitive (non mathematical) explanation connecting the classical and quantum expressions for momentum.
Waves carrying momentum is a classical phenomenon (in addition to a Quantum one). I can get the end of a yo-yo to jiggle around if I jiggle the string (i.e. transfer momentum via a wave) - and I can explain it all using Newtonian mechanics. In fact, this can be done for any classical wave by regarding change in momentum as the integral w.r.t time of impulse. Long story short, if a wave applies a force over some finite length of time, it must carry momentum. Invoking QM is therefore unnecessary in order to answer the OPs question and will only serve to confuse the issue. Claude.
Claude: reviewing the replies it seems that it's not clear whether the OP was talking about QM or CM. I'm still not sure! I don't think it helps much to criticize others answers for possibly missing the point. After all, we're here to have fun!
I agree, but then again most classical phenomena have a quantum equivalent, in most cases (especially if it is posted in the classical physics section) when someone posts a question about a phenomenon that can be discussed from a classical standpoint - Introducing QM into the picture is an unnecessary complication. I agree that undue criticism is unwarranted, but by the same token, if something is posted that is wrong or misleading - it ought to be challenged. And learn too! Claude.