Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [dispersion]

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

2
votes
1answer
56 views

Why don't the oscillator coherent states disperse in time?

A Gaussian wavepacket is made of a continuum of frequencies (or energies) and stretches in time due to the phenomenon of dispersion: the different plane wave components with different frequencies ...
0
votes
2answers
42 views

Time-of-flight spectroscopy and energy-time uncertainty

I am a bit confused about spectral and temporal filtering of light. I consider a single-photon source of a bandwidth of $1\,$nm at $1550$ nm. That means, that the wavelength of the emitted photons ...
0
votes
2answers
64 views

Dispersion relations in solid state physics

Could you please explain what exactly is the relevant information that is conveyed through a dispersion relation? Edit 1: Sorry about being vague. I am currently trying to understand the dispersion ...
0
votes
0answers
6 views

Number of allowed (phonon)wave vectors in a poliatomic-basis lattice?

Lets say that my crystal is of size $N=N_1N_2N_3$ , this is the typical textbook example and after that they say that the number of allowed wavevectors is N. But tbh I dont really know if they are ...
0
votes
1answer
37 views

How to find wavepacket time dependence from the $k$-wavefunction?

I am trying to code the time dependence of a gaussian wavepacket using the Fourier transform techniques. I began with constructing a wavepacket (real parts only at the moment) at $t=0$ by multiplying ...
0
votes
2answers
43 views

What does it mean to say that glass has refractive index 1.5?

The refractive index of a material depends on the wavelength of the light incident upon it which is why dispersion happens. When we say that glass has refractive index 1.5 which wavelength do we have ...
-1
votes
1answer
57 views

Speed of electromagnetic wave [closed]

On dispersion , speed of wave is inversely proportional to its wavelength . Therefore, gamma has max speed. But then in visible light , violet has least wavelength still it has least speed in visible ...
0
votes
0answers
42 views

Dispersion of light

I've been taking digital signal processing course. It's pretty interesting for me. One thought came to my mind while I've been practicing numerical problem on Fourier transform. So my question is ...
0
votes
1answer
21 views

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 ...
0
votes
0answers
30 views

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?
1
vote
4answers
90 views

$E=hf$ 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 ...
4
votes
2answers
96 views

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 ...
0
votes
0answers
47 views

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 = ...
2
votes
2answers
93 views

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) = ...
2
votes
0answers
18 views

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}\...
2
votes
2answers
82 views

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. ...
1
vote
1answer
33 views

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 ...
0
votes
1answer
50 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 ...
1
vote
0answers
24 views

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)$...
0
votes
2answers
51 views

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 ...
254
votes
2answers
20k views

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 ...
0
votes
3answers
99 views

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 ...
1
vote
0answers
43 views

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 ...
2
votes
0answers
37 views

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 ...
0
votes
0answers
54 views

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 < \...
2
votes
1answer
158 views

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 ...
2
votes
0answers
137 views

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 ...
2
votes
2answers
52 views

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? ...
1
vote
2answers
129 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 ...
2
votes
0answers
72 views

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(\...
0
votes
0answers
38 views

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 ...
1
vote
4answers
121 views

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.
0
votes
0answers
68 views

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=...
0
votes
0answers
25 views

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 ...
0
votes
1answer
208 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}\,...
1
vote
1answer
78 views

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, ...
1
vote
4answers
116 views

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 ...
0
votes
0answers
12 views

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.
1
vote
0answers
20 views

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{...
6
votes
1answer
111 views

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?
1
vote
0answers
52 views

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 ...
2
votes
2answers
200 views

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 ...
6
votes
2answers
162 views

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 ...
0
votes
1answer
822 views

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 ...
1
vote
0answers
255 views

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 ...
27
votes
4answers
5k views

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\...
0
votes
1answer
166 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 ...
4
votes
2answers
178 views

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 ...
0
votes
1answer
30 views

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, ...
1
vote
0answers
55 views

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 ...