Physical Significance of Frequency of matter waves So, in our book there was an additional exercise part and this question baffles me:-
Q. Answer the following questions:-
The energy and momentum of an electron are related to the frequency and wavelength of the associated matter wave by the relations:
E=hν ; p=h/λ ;
where E=energy, h=Planck's constant, ν=Frequency, p= momentum, λ=wavelength.
But while the value of λ is physically significant, the value of ν(and therefore, the value of the phase speed νλ) has no physical significance. Why?
Now there was an answer given too but I can neither understand the question neither the answer... Please someone explain.
Ok so as someone requested I am going to put the answer given too:-


 A: The wavelength $\lambda$ is physically significant in the sense that you can directly measure it. You can perform the double slit experiment and that will directly tell you the wavelength of the particle.
To see why the frequency is not "physically significant" I will compare it to potential energy because the reasoning is similar (I put this in quotes for a reason, I will explain this). The potential energy of gravity on earth is defined as $U(z)=mgz$. You can also add a constant to the potential energy and still have the same equations of motion: $U(z)=mgz+U_0$. This is because the force is defined as the derivative of the potential $F=-\frac{dU}{dz}$. Because of this, the precise value of $U$ is not significant; only differences in $U$ are in important. To say that $U$ is not physically significant might be a bit of a misnomer. $U$ is very important in physics, it's just that the precise value is arbitrary since you can always add a constant.
Similarly, you can always add a constant to frequency (in the context of matter waves!). The frequency is still a physically significant quantity, it's just defined up to an arbitrary constant. This carries over to phase velocity since it is just frequency times wavelength. The group velocity is "significant" though, since you can measure this directly.
A: I think you would do best to ignore this comment in your book; Personally, I even consider it wrong. We routinely talk about the energy of particles and that is a precisely defined quantity with no room for any arbitrariness or additive constant.
A: I think I got the answer after thinking a lot.
Our teacher had said that for electrons, E=hν was actually wrong, rather we should consider, E=0.5mv² , or, E=p²/2m so, this means if we use de Broglie's relation p=h/λ and put it in the energy of electron, we get
E=h²/(2mλ²) .
Thus we understand that for matter particles,ν has no physical significance while λ does have and since λ has physical significance, p also has... thus group speed=p/m and practically anything which can be related by momentum has physical significance as momentum can be related to wavelength.
(Like by the Davisson Germer experiment, we got to know about the wavelength of electron, which strikingly was in excellent agreement with the de Broglie hypothesis not its frequency! Right?)
