Questions tagged [phase-velocity]

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3answers
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In superluminal phase velocities, what is it that is traveling faster than light?

I understand that information cannot be transmitted at a velocity greater than speed of light. I think of this in terms of the radio broadcast: the station sends out carrier frequencies $\omega_c$ but ...
2
votes
3answers
1k views

Derviation of group velocity

I am working thru a derivation of the group velocity formula and I get to this stage: $$y=2A\cos(x\frac{\Delta K}{2} -t\frac{\Delta \omega}{2})\sin( \bar k x-\bar \omega t)$$ Then all the derivations ...
4
votes
2answers
11k views

Group Velocity and Phase Velocity of Matter Wave?

In quantum mechanics, what is the difference between group velocity and phase velocity of matter wave? How can it also be that phase velocity of matter wave always exceeds the speed of light?
2
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2answers
7k views

Phase velocity greater then the speed of light?

It is my understanding the the phase velocity of a wave can be greater then the speed of light. So imagine we had a wave packet consisting of a single sinusoidal wave; $$y=\sin(\omega t-kx)$$ Then ...
6
votes
2answers
16k views

Deriving group velocity

At the introduction to quantum mechanic phase $v_p$ and group $v_g$ velocities are often presented. I know how to derive $v_p$ and get equation: $$ \scriptsize v_p=\frac{\omega}{k}. $$ What i dont ...
6
votes
7answers
967 views

Information relationship to Special Relativity

How do we write mathematically that "information" cannot go faster than light? And along a similar line of thought, how do we relate "information" with special relativity. Lastly, what is the ...
3
votes
1answer
129 views

Does phase velocity or group velocity change when light enters a new material? Contradictory sources

I'm so confused. I've read in this book (page 28) that group velocity of light can exceed $c$ in certain gases. However a lot of people online and in the forums say that phase velocity can exceed $c$. ...
2
votes
2answers
801 views

What does phase velocity physically represent, and why can it be superluminal? [duplicate]

Phase velocity is defined as $v_p=\frac{\omega}{k}$ and is described in various textbooks as being the speed at which the phase of a wave propagates. If you have a wave train that is modulated by an ...
1
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2answers
2k views

Phase Velocity Derivation

I spend few hours trying to derive phase velocity of sinusoidal wave $$\cos(kx - \omega t).$$ I know that it must be equal to $\omega \over k$ but after banging my head for few hours and trying to ...
8
votes
1answer
346 views

Seeming violation-wave travelling faster than speed of light

Consider the basic relation $$E=\sqrt{(pc)^2+(mc^2)^2}.$$ Every particle possesses a wave nature and it depends on the situation in which one among the two is perceptible... Consider a particle with ...
4
votes
3answers
3k views

Why is the phase velocity used in the definition of the refractive index?

I'm aware of the so-called group index but why is the phase velocity used in the standard definition of the index of refraction? What advantage does this offer?
2
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2answers
1k views

Wave group and phase velocities

When talking about phase velocity and group velocity they tend to be both expressed in terms of another $v$. From my understanding this $v$ comes from the wave equation, but what does it represent? ...
2
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0answers
62 views

Is the phase velocity of plane wave solutions of the Klein-Gordon equation larger than $c$?

The phase velocity is given by $$ v= \frac{\omega}{k} \, .$$ Using the usual dispersion relation $$ E^2 = p^2c^2+ m^2c^4 \leftrightarrow \omega^2 \hbar^2= k^2\hbar^2 c^2 + m^2c^4$$ yields $$ v= \frac{\...
1
vote
1answer
497 views

Is quantum velocity generally equal to group velocity?

It is often said that the velocity operator in quantum mechanics identifies the group velocity. Here's the argument: for the free particle, we have $\omega = \hbar k^2/2m$ and the (quantum) velocity ...
1
vote
2answers
1k views

Klein-Gordon equation and wave velocity

It looks like solutions of the KG eqn travel faster than light, because if $$\omega^2 - k^2 = m^2$$ then $$\mid\ \omega\mid \ > \ \mid k\ \mid$$ and I thought the wave velocity was $\omega / k$. ...
1
vote
1answer
434 views

Wavefronts and phase velocity faster than $c$

Lets assume we have parallel wavefronts in a glass of water: and we put an inclined rod on the water surface: related to a very small inclining, Vy velocity is greater or much greater then Vx (Vy ...
0
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1answer
683 views

Interpreting group velocity of free particle wave packet

I am trying to understand the concept of group velocity of a free particle wave packet: $$\Psi(x,t) = \frac{1}{\sqrt{2 \pi}}\int_{-\infty}^{\infty} \phi(k)e^{ikx}e^{-\frac{i \hbar k^2 t}{2m}}dk.$$ ...
0
votes
1answer
595 views

How can we calculate (relativisticly correct) ratio $\lambda_e/\lambda_p$ if proton and electron have same speeds

This question is about group/phase velocities and also De Brogilie wavelength. What I would like to know is how to derive ratio $\lambda_e/\lambda_p$ ($\lambda_e$ and $\lambda_p$ are De Broglie ...