Questions tagged [phase-velocity]
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Second derivative of energy with $k$
In solid-state physics, we often encounter the velocity operator (e.g. this post) which the eigenvalues can be written as
$$
V^\mu(\vec{k}) = \frac{1}{\hbar} \frac{\partial E}{\partial k^\mu} \biggr|_{...
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Group velocity, phase velocity and signal velocity for axion like particles
In dark matter models of axion-like particles (ALPs), sometimes we get the field
$$\phi=2\phi_0\sin(m_\phi c^2 t/\hbar)\cos(k_\phi x)$$
This is like an stationary field with amplitude $\phi_0$ (in m/s ...
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The velocity of a quantum mechanical plane wave of a photon
There is a famous "derivation" or "demonstration" that is often presented in introductory classes in quantum mechanics. I find it deeply unsettling and I feel like key information ...
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Phase difference in Michelson Interferometer
I'm currently taking a quantum mechanics course in university and our professor introduced us to the Michelson Interferometer (or at least what I believe is an apparatus based on it), where a light ...
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What does "non-dispersive" mean in terms of waves and group velocity?
I'm confused about the term wave group velocity: It is usually explained in terms of a superposition of harmonic waves with very closely spaced wave vectors and frequencies. It is then easily shown, ...
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Why the phase velocity of X-rays inside glass is faster than $c$?
For hard X-rays the refraction index of glass becomes slightly $n<1$ which means that the phase velocity (not group velocity) of X-rays inside glass is larger than $c$ the group velocity speed ...
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Can radiative transfer theory be used to calculate an effective index of refraction?
As I understand it, the (real) index of refraction is given by the ratio of speed of a monochromatic light wave in vacuo versus speed in medium. When it comes to the question of propagation of a light ...
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Coupled microstrip waveguide: Why do the even and odd modes have different wave velocities?
Why do the odd and even modes in a coupled microstrip waveguide have different phase velocities? Is this also the case for a coplanar strips waveguide?
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How to calculate the phase velocity of a partial standing wave
Partial Standing Waves
Partially Reflected Wave
A traveling wave encountering an impedance change will be partially reflected and transmitted. It can be represented as the sum of the incident (...
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Why is the velocity of a wave given by $v=\lambda{}f$ different than differentiation?
As obvious from the nature of this question, I am a first-year physics student (with an absent lecturer), and I am having trouble grasping the concept of wave velocity. I've read these answers (1,2) ...
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Confused about the Kelvin wake pattern
What are the $v_{\text{phase}}$ and the $v_{\text{group}}$ in Kelvin wakes? Additionally there are tons of water waves combined to form the kelvin wake. How is it possible for the $v_{\text{group}}$ ...
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Is the observed speed of an infinite set of perfect ocean waves of constant amplitude and frequency independent of an observer's motion?
I am asking this question because it occurred to me that wave propagation has some generally under considered properties regardless and independent of the medium in which the waves are propagating. ...
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Why Klein-Gordon and Dirac's waves have a phase velocity of $c$?
From De Broglie’s relations and the energy-momentum dispersion relation one finds:
$$v_p=\frac{w}{k}=\frac{E}{p}=\frac{\gamma mc^2}{\gamma mv}=\frac{c^2}{v} \tag{1}$$
Where, $v_p$ is the phase speed ...
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Integration constants in geodesic equation for wave equation
I am stuck at a following "hello world problem". Let us consider the most common (d'Alembertian) wave equation:
$$
\frac{\partial^2 \psi}{\partial^2 x} - \frac{1}{c_0^2}\frac{\partial^2 \psi}...
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Guided waves: showing geometrically that $v_p v_g = c^2$
In griffith's introduction to electrodynamics p.430 there's a Figure 9.25 of the wavefronts. I'm wondering if we can show geometrically $v_p v_g = c^2$ using this kind of figure. I think so, but I can'...
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