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Questions tagged [dispersion]

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

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Principle of Energy Dispersive x-ray Spectroscopy

I have a question about the EDS I don't understand how the detector can differentiate the Energy of incident x-ray simultaneously. In my thought, the emitted x-ray from the sample have different ...
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How does refractive index increase in anomalous dispersion?

Refractive index generally increases with decrease in wavelength but in anomalous dispersion it decreases with decrease in wavelength. What causes it to be like that?
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$E=hf$ true for all implies $E=pv$ true for all?

In the answer to this question: Can I apply $E=hf$ to a particle having mass? It was stated that $E=hf$ is true for all particles. If so, doesn't this imply that $E=$momentum x velocity is true for ...
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What really is the speed of light in a medium/vacuum, group or phase velocity?

While reading about refractive index 2 terms popped up, group velocity which alway slows down in a medium and phase velocity which may exceed speed of light. Say in a complete vacuum and using laser ...
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Spring constant and dispersion relation

In order to calculate the dispersion relation (i.e $w(k)$) for the electrons and protons, I used the following relations: $ E = ℏω$, $p = ℏk$, and I substituted them in this formula for energy: $E = ...
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Higher-order dispersion in non-linear optics

In many cases, dispersion of an optical medium is presented by saying that the dependence of the wavenumber $k$ on the (angular) frequency $\omega$ can be expanded in Taylor series as: $$ k(\omega) = ...
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Relation of dispersion for a plasma

Assuming the electric field : $\vec{E} = E_{0}\,e^{i(kz-\omega t)}\vec{e_{z}}$ and the complex relation by doing $\vec{rot}\,(\vec{rot}\times\vec{E})$ with $\vec{rot}\times \vec{E}= i \vec{k}\...
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Why we do not use $v=f \lambda$ for the waves associated with particles?

As the waves travel with velocity $$v= f \lambda,$$ where $v$ is velocity, $f$ is frequency and $\lambda$ is wavelength. Here we can see that velocity of wave is directly proportional to wavelength. ...
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Physical significance of growth rate in plasma

Let us say that we have a dispersion relation curve and associated instability curve as shown below for a magnetised plasma, which have been formulated through kinetic theory. The frequencies and ...
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33 views

Phase velocity of optical branch of lattice vibration at zone center

In a 1-D diatomic lattice, the dispersion relation for lattice vibration is given by: $\omega =\surd( \beta (1/M + 1/m)+\beta(\surd(1/M + 1/m)^2 -4sin^2ka/Mm))$ $v = \omega/k$ gives the phase ...
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Why is the current in the nonrelativistic Dirac sea infinite?

Consider the model of a nonrelativistic noninteracting Dirac sea. I define the model as one with two infinite bands of single particle states: $$E_\pm (k) = \pm \biggr(\Delta + \frac{k^2}{2m}\biggr)$...
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Dispersion and wavelength

Why does dispersion increase with wavelength? If I understand correctly, refractive index is decreasing with wavelength. As a result, greater wavelengths are traveling faster. How does this cause the ...
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What is Chirped Pulse Amplification, and why is it important enough to warrant a Nobel Prize?

The 2018 Nobel Prize in Physics was awarded recently, with half going to Arthur Ashkin for his work on optical tweezers and half going to Gérard Mourou and Donna Strickland for developing a technique ...
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A question regarding the speed of light in a vacuum, specifically putting a 'color' in

I know that red and blue etc. lights are produced when 'white' light is put through mediums. I have learned that all light in a vacuum, all electromagnetic waves, travel at the same speed in a ...
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If the velocity of light is different in different medium is it wavelength changes or frequency changes?

We know that the velocity of light is equal to the product of it's wavelength and frequency. And when light goes from vacuum to any other medium it's velocity changes depending the mediums refractive ...
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Using convolution to simulate acoustic dispersion in shallow water

Background I'm a marine biologist who's trying to wrap my head around shallow water propagation. I'm interested in how acoustic dispersion (as described by Pekeris' waveguide) alters how sounds ...
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Density of states as a function of dimension: what happens between 3D and 4D?

Consider a parabolic dispersion $\varepsilon_{\boldsymbol q} = \frac{\boldsymbol |q|^2}{2m}$. The two-particle density of states $\rho_2(\boldsymbol k, \varepsilon)$ is zero for $\varepsilon < \...
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In refraction how does light interact with electrons if it is not absorbed? [duplicate]

What I (think I) understand: When light is refracted in a medium (say glass), the light interacts with the electrons in the medium and the electrons create new waves. Summing the waves with the ...
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Does an electron have a frequency (and hence an energy)?

The formulation is provocative, the question is similar to the question here. There I can follow the question, but not the answers, which for me imply that an electron in a momentum eigenstate does ...
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Finding dispersion relations

I was wondering if there is a general (theoretical, not experimental) method for finding the dispersion relation for waves in a medium, say given the equation governing purturbations in the medium? ...
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101 views

How come group and phase velocity can be different in a non-dispersive media?

I'm a (ex-)physicist working in the applied-physics world and was digging into group vs phase velocities. There is one thing that confuses me : when would that be the case where group and phase ...
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Perturbation theory with eigenvalue-dependent perturbation

Suppose I have an operator equation of the sort $$ [H_0 + H_1(\lambda)]\mathbf{v} = \lambda\mathbf{v}. $$ Here, $H_0$ defines unperturbed eigensolutions $\{\lambda_0, \mathbf{v}_0\}$, and $H_1(\...
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Analytic Microcavity Polariton Dispersion Relation

I feel like I have a good theoretical understanding of how one derives the microcavity polariton dispersion relation utilizing the rotating wave approximation, but when it comes to actually ...
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Why does the wavelength of a particle go down with higher velocity?

In mechanical waves, the wavelength increases with a higher velocity. λ = v / f. And the wavelength in particles lower with a higher velocity. λ = h / mv.
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Density of States General Formula

So I have this formula regarding the density of states in 3D and 2D respectively are given by a function of the dispersion relation: $N=\frac18 \frac{4\pi}{3}(V^{\frac13}\frac{k(\omega)}{\pi})^3$ $N=...
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Derivation of group velocity as a function of refractive index dispersion (solved) [duplicate]

How can I derive the expression $$v_g=\frac{c}{n-\lambda_0 \frac{dn}{d\lambda_0}}$$ in the wiki page? I know we need to use chain rule, but I can't quite get the terms of $dn/d\lambda$ in the ...
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160 views

Dispersion relation of wave packet from Schrödinger equation

I have a question regarding the derivation of the dispersion relation of a wave packet from the Schrödinger equation. The wave packet is given by $$\psi(x,t)=\int_{-\infty}^{\infty}\frac{dk}{2\pi}\,...
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Difference between advecton-dispersion equation and advection-diffusion equation?

Following is the advection-dispersion equation. \begin{equation*} \frac{\partial u}{\partial t}= d\frac{\partial^2 u}{\partial x^2} -\nu \frac{\partial u}{\partial x}+F(x,t), \end{equation*} here ...
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Matrix representation of spin-1/2 system

Problem 1.19 from Sakurai's Modern Quantum Mechanics asks you to find $\left< (\Delta S_x)^2 \right> = \left< s_x^2 \right> - (\left< s_x \right>)^2 $ in the $S_z +$ state. However, ...
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Is light dispersed over distance by flat mirrors?

Hello and thank you for your time: Let's assume I have a 100 squared meter circular flat mirror placed 1 AU from the sun, and let's assume my intention is to shine light on a circular area on another ...
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Dispersion coefficient in Er-doped fiber

We generally consider the dispersion coefficient $D(\lambda)$ in single-mode fibers is $17ps/nm/km$. Now what's the $D(\lambda)$ of Er-doped fiber? I only know it's less than zero.
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Theoretical constraints of relativity on dispersion relations

A wave has a dispersion relation $\omega=\omega(\vec{k})$. (The function has been made single valued usinng initial conditions.) A delta function in the origin at $t=0$ ( $\psi(\vec{x},0)=\delta(\vec{...
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Can I make a rainbow in shower?

As droplets of shower acts like rain, and say a light bulb will take place of sun. In this scenery, is it possible to make a rainbow?
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How dispersion relation is used when calculating the density of available states in a metal crystal? [duplicate]

found this question somewhere and still do not know how is it useful for calculation of density of state?
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What causes observed color differences in white LED's for near and far fields?

While running towards traffic early morning before sunrise I recently noticed that the new automobile LED (white) lights when viewed at a distance appear blueish, but when the light is viewed much ...
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Dispersion of a Gaussian wave packet- why does momentum become more certain?

So I understand from the equations, and considering the Fourier components of a Gaussian, how the wavefunction for a free particle spreads due to dispersion. However mathematically, and from the ...
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Understanding group velocity

Group velocity as a concept in Classical Waves confuse me. It's very easy to point out visually, like in this really helpful graphic here. Okay, it's the speed of the moving bulge, which, notably ...
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Refractive index and wavelength relation [duplicate]

In general, the refractive index of a certain medium tends to decrease with increasing wavelength. But are there any materials in which the opposite phenomenon occurs? That is, in which the ...
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Interpretation of antiferromagnetic magnons dispersion relation

The dispersion relation of magnons in a ferromagnetic 1d lattice is \begin{equation} \omega(k)=\omega_0\big[1-\cos(ka)\big] \end{equation} where $\omega_0$ is a constant and $a$ is the spacing ...
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Why is the speed of oceanic waves not a constant like sound?

I cant understand this, according to what I read here. The speed of a wave depends on its wavelength and its depth, through the relation $$ v=\sqrt{\frac{g\lambda}{2\pi}\tanh\left(2\pi \frac d\lambda\...
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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 ...
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Light dispersion in gravitational theories

GR predicts no Ricci curvature in vacuum (or at least when we can ignore the cosmological constant). Would theories that violate this lead to observable light dispersion in solar system tests of ...
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What are $A$ and $k_0$ in this effective mass equation?

I have the equation: $$E=A(k-k_0)^2$$ I am trying to find effective mass with the equation: $$m^*=\frac{h^2k^2}{2A(k-k_0)^2}$$ I know that $k$ is momentum, and I assume $k_0$ is minimum momentum, ...
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Experimental data on the speed of heat

I know about the speed-of-information problem tied with the solution of the heat equation (diffusion equation) for the propagation of heat via conduction. Due to the quantum-statistical nature of ...
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What would an intuitive explanation for the $E$-$k$ diagram?

In all of my solid state books they seem to plot the $E-k$ diagram. But I don't understand why ? What is the physical significance of the $E$-$k$ diagram? Please don't give answers like it shows ...
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Dispersion relation in string vibration

In case of a continuous,bounded string we know, the dispersion relation is linear, i.e, the restoring force is directly proportional with the wave propagation vector. In other words, $$w=ck$$ Where $...
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Is there a way to explain a rainbow in an almost-QM-correct way to a 5 year old child?

My toddler asked me "how does rainbow happen", and I would like to give a pedagogical explanation of the relation of photon frequency, its color, and the way different frequencies are bent in a drop ...
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66 views

Relation between Dispersion and radius of curvature [duplicate]

Is there any way to correlate radius of curvature with the possibility of dispersion?
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119 views

Group velocity for wave pack

I was reading about the derivation for group velocity on the wiki page here. As far as I understood, what's done here is based on these steps Get a basic solution for the wave equation, that is $exp(...
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Why do high frequencies have a larger deflection through a prism than smaller frequencies? [duplicate]

The following is a proof that higher (angular) frequencies have a greater deflection than lower frequencies through a glass prism: It was omitted in the image above, but $n_{\text{air}}$ is taken to ...