Dispersion refers to the frequency dependence of the properties of a wave.

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Why grating is an essential part of a monochromator?

From looking at these two images, it appears that the dispersed "rays" of the reflected light could be manipulated just as well if the reflecting mirror would be turned to a fixed angle. So why is ...
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Why do dispersive waves get wider?

Consider the two waves $$y_1=Acos(\omega_1 t+k_1 x), \tag{1}$$ $$y_2=Acos(\omega_2 t+k_2 x), \tag{2}$$ where $\omega_i=k_iv(k_i)$ for $i=1,2$ so we have a dispersive medium. Then if we take their ...
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Is difference in wave number always small?

Over the last few days I have been looking at a derivation of group velocity. The derivation is the one shown in this question Deriving group velocity. I have seen this derivation in many places, and ...
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Why is it possible to choose an arbitrary zero energy level when dealing with frequencies of a wave function?

This is a followup of my previous Why don't the De Broglie dispersion relation contain a constant term? question. Answerers pointed out that only differences in energy matter I can understand ...
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Why don't the De Broglie dispersion relation contain a constant term?

Wikipedia says that the dispersion relation for a non-relativistic particle is: $$ \omega = \frac{\hbar k^2}{2m}. $$ But when I tried to calculate it myself, I seem to get a constant term in that ...
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Dispersion of electrons in conductive medium

Say you have a 1'x 1'x 1' cube of conductive metal. If you placed an electrode on the center of one of the sides, and quickly turned it on and off, how would the electrons disperse? Both initially ...
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83 views

How to minimize the wavepacket dispersion?

This is a final exam problem. Here is what I can remember: We know that if an electron's wavefunction starts out as a narrow wavepacket, and moving in a region of constant potential, then the ...
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Third-order dispersion of glass

When working with short laser pulses, it is important to compensate the dispersion of a pulse passing through a material because it changes the pulse's shape. The effect of dispersion can be described ...
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Deriving Graphene energy dispersion in tight binding model

I'm trying to get into graphene, in detail, I try to derive the elec. energy dispersion. Sadly, I am not that familiar with condensed matter QM by now, so I got some basic questions and I hope to find ...
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Linear vs. quadratic dispersion relation

In wave mechanics the dispersion relation between frequency $\omega$ and wave number $k$ is linear: $$\omega_n=c k_n$$ But in quantum mechanics, based on Schrödinger's equation, one can show that we ...
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Why does my wooden door disperse light into a rainbow color spectrum?

On a clear morning, light comes through this window (viewed from the inside) It then hits the door on the opposite side (so viewing from the outside the door straight on the other side) There is ...
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Density of States vs Dispersion

I have a rather naive question regarding DOS and dispersion. We showed the existence of a band gap in class for a small, periodic perturbation in class last week. When drawing this, the professor ...
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Wave Packets, Group velocity, and Phase velocity [duplicate]

Mathematically, you find that the wave function of a particle $\Psi (x,t)$ moves with the same velocity as the velocity of the particle ($v_{particle} = v_{group}$). Is there a reason why the ...
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Why does Snell's law not factor in wavelength?

If dispersion is caused due to different wavelengths bending with different angles, how is Snell's law right in generalizing it as $\sin(i) / \sin(r)$? Or am I missing something?
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The lineshape of a 2D photonic crystal dispersion diagram

Using simulation software (CST Studio), I calculated the dispersion of the eigenmodes of a photonic crystal, that is frequency vs wavenumber for the desired propagation direction. I wonder what kind ...
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How to calculate the dispersion relation for a wave equation with non-constant speed of wave propagation?

Specifically, it is a one-dimensional wave equation for waves on a string with a non-constant cross-section, i. e. $$S(x)=S_1+S_2 \cos{2x}; \qquad c(x)=\sqrt{F/\rho\, S(x)}.$$ Separating the variables ...
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Which electromagnetic radiation is faster in water, microwaves or light?

Well I've been asked this question, but I haven't been able to come with an answer yet using books and some web searches. The point is as the title says, to answer the question with the whole ...
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Dispersing ultrasound in a tube - patters

I am looking for patterns to efficiently disperse reflected ultrasound in the range of wavelengths 1mm to 4mm within the interior of a narrow tube (I do not want wall reflections). For various reasons ...
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28 views

Refractive index variation with colors [duplicate]

To explain the spectrum formation in the prism, my teacher said that different colors have different speeds in a medium, so, refractive index is different for all. So, angle is different. But I don't ...
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Why does the speed of the Electromagnetic wave in the material depend on the frequency of the wave where as they are constant in vacuum (freespace)? [duplicate]

I am confused on why would the propagation speed of any EM waves at ANY frequency is constant in the free space (vacuum) but they seem to disperse in any other materials as the propagation speed of EM ...
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Interpretation of dispersion relation

In my research, I found that my system has the following dissipation relation: $$\omega^2=k^2+k_0^2\ , $$ where $k_0^{-1}$ is an intrinsic lengthscale of the system and the units are chosen so that ...
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How does the color of fine dispersed metal particles change between silver and black?

Small dispersed particles of metals are often black, while a solid object of the same material would be some shade of silver. The most notable example is the use of metallic silver as the black color ...
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Does a man on the moon experience day?

Does a man on the moon (or any other similar body) experience daytime like we do? By daytime I mean looking upward and seeing a bright "sky," not dark space. If not, then what is the reason behind ...
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Expectation value and Dispersion of an Operator

Suppose we have an operator $Q$ with eigenvalue $q$. Expectation value is $\langle Q \rangle$ and dispersion $D(Q) = \sqrt{\langle \left( Q - \langle Q \rangle \right)^2 \rangle} $. I want to find ...
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Absorption of waves in a plasma

Suppose a plasma has characteristic frequency $\omega_p$. Since $$n = \sqrt{\left(1-\frac{\omega_p^2}{\omega^2}\right)} $$ For $\omega<\omega_p$, the refractive index will be imaginary - which ...
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Two-Dimensional Tight-Binding Dispersion Relation

As in my last post, I am doing out a calculation in Giamarchi's Many-Body text: http://dpmc.unige.ch/gr_giamarchi/Solides/Files/many-body.pdf. This time, I am going through the derivation of the ...
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Drawing the wave function for a wave packet

I have the following infotmation: Amplitude-Function: $U(k) = Ae^{-a|k-k_0|}$ Wave Function: $u(x,t) = \frac{A}{\sqrt{2\pi}} \frac{2a}{(x-vt)^2+a^2}e^{ik_0(x-vt)}$ Uncertainty in x: $\Delta x = 1$ ...
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What is the difference between dispersion and diffusion?

What is the difference between dispersion and diffusion? Currently I believe, that diffusion is the mixture of molecules due to Brownian motion. So I read everywhere, that it happens with magnitude of ...
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On what refractive index of medium depends ? [duplicate]

does the refractive index of a medium depends on wavelength of light passing through it ? If yes then why ?
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267 views

Dispersion relation for TE and TM waves in general anisotropic medium

I want to calculate the dispersion relation (the relation between $\bf k$ and permittivity and permeability tensors and $\omega$) for a TE and a TM wave with wave vector $\mathbf k=k_x\mathbf {\hat ...
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PDE from dispersion relation?

Suppose I have knowledge of a system's dispersion relation $f(\omega,k)$. Is it possible to recover the underlying PDE describing the system? Can I simply use the replacement $k=-i\nabla$, ...
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Dispersion Relation (e vs. k) clarification (crystal momentum or electron momentum)

If we get the dispersion relation from the Fourier transform of the lattice vectors then how do we get electrons information? Specifically, for the $k=0$ point of the graph, does this mean the ...
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What is the difference between Lehmann-Kallen and Dispersion relation?

I know that the Lehmann-Kallen (LK) form of an operator concerns just that, an operator. But the LK is very similar in form to dispersion relations found in analytic S-matrix theory.
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Phonon dispersion calculation based on velocity autocorrelation function in reciprocal space?

I would like to ask about the method of calculating phonon dispersion relation. Up to my knowledge, there are 2 methods to calculate the phonon dispersion: By diagonalizing the dynamics matrix. ...
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Splitting of degenerate states due to perturbation

In band structures we see avoided crossing when we have degenerate eigenstates (caused by perturbation due to potential energy). However along some direction in first Brillouin zone, even though the ...
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Dispersion relation of silicon

In the case of dispersion relation of silicon having crystal plane orientation 111; what is the Sellmeier's equation for refractive index $n$ of silicon orientation 111 & what it's extinction ...
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Why linear wave equation does not have solitonic solutions?

As many people define solitary waves they are localized pulses that propagate without changing the shape. As far as I know the same pulses exist in ordinary wave equation ! why should we look for ...
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Why do wave packets spread out over time?

Why do wave functions spread out over time? Where in the math does quantum mechanics state this? As far as I've seen, the waves are not required to spread, and what does this mean if they do?
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More extensions of the wave equation for dispersion

The Phys.SE question Minimal Extension of Wave Equation to Include Dispersion extended the wave equation for only a very simple form of dispersion. However, what about more complex dispersion ...
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Minimal Extension of Wave Equation to Include Dispersion

Let's say you are modeling some process with the wave equation $\frac{1}{c^{2}}\frac{\partial^{2}\psi}{\partial t^{2}} = \nabla^{2}\psi$. You wish to improve your model by including dispersive ...
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What are some problems with Hugyen's wave model of light? [closed]

In terms of the different light phenomenon (reflection, diffraction, rectilinear propagation and dispersion), what are some problems with Huygen's wave model of light?
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Equations of motion of displacement field

We have an action: $$S[\boldsymbol{u}] = \frac{1}{2} \int dt \int d^3x \left\{ \mu (\frac{\partial u_{i}}{\partial t})^{2} - \nu (u_{ii})^{2} - \rho(u_{ij})^{2}\right\} $$ Where $u_{ij} = ...
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Light dispersion in water

Simple question: Water is clearly not disspersive if we have it, for example, in a glass of water. We don't see the rainbow through a glass of water. However drops of water disperse light in the ...
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Mass frequency problem

For Dispersion relation , according to Gaussian profile, the author in the equation 3 wrote as $\omega= \left(k^2+\omega_{mass}^2\right)^{1/2}$ My question is what is mass frequency and how it arose ...
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antiferromagnetic spin wave

I have a hamiltonian that is derived from a spin wave energy dispersion calculation for a nearest neighbor interacting cubic antiferromagnet. After a Holstein-Primakoff transformation and making a ...
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Two different mediums can have equal index of refraction?

In other words: given a certain medium, is light's phase velocity unique?
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Dispersion-less media

As far as I know, vacuum is the only dispersion free medium for electromagnetic waves. This makes me wonder if there are any other dispersion free media for these waves? (Experimentally established or ...
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What is energy in $z \neq 1 $ theories?

In a critical theory with dynamical critical exponent $z \neq 1 $, which amongst frequency, $\omega$, and dispersion, $E(\vec{k})$, may be referred to as ''energy''? I'm confused about this since in ...
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Why do prisms work (why is refraction frequency dependent)?

It is well known that a prism can "split light" by separating different frequencies of light: Many sources state that the reason this happens is that the index of refraction is different for ...
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Definition of energy

What is the definition of energy $E$ given a dispersion relation $\omega=\omega(k)$ where $k=|\vec k|$ and $\omega$ is not necessarily linearly proportional to $k$? What about momentum $\vec p$? This ...