Questions tagged [dispersion]

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

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How to describe the unit vector for a complex wave vector?

In optics, we often come across complex wave vectors that describe absorption, dispersion, etc. given as: $\textbf{k} = \textbf{k}_{real} + i\textbf{k}_{imag}$ The electric field in phasor notation ...
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Color dispersion at the edge of a slanted mirror

When I look at the edge of a slanted mirror it looks like its affected by color dispersion which you can see by Image 1 but, when it reflects off the flat part of the mirror it looks normal, Image 2. ...
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If black color body absorbs all colors, why spectrum of light appears on black shoe?

Few days back in a 10 grade school practical, we were shown the dispersion of light by a prism to create spectrum. Then we went into the open sun and performed it under a linear building roof and ...
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Klein-Gordon/Maxwell Equation: dissipative or dispersive?

In Aspects of Symmetry, Coleman says (p. 185) ''Most of the simple field theories with which we are familiar have the property that all of their non-singular solutions of finite total energy are ...
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Why does the intensity of the scattered light vary when a monochromatic laser is shined into a transparent object?

When a laser is shined into a glass ball such as this video (link) or a bottle of water (link) the light is refracted through the whole transparent body. However, the intensity of the light scattered ...
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Why doesn’t a normal window produce an apparent rainbow?

When light refracts in a prism it creates a rainbow. My question is, why don’t all windows or transparent objects create this dispersion, i.e. why is the refractive index dependent on frequency in a ...
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Dispersion through Glass Slab

My questions related Dispersion through Glass Slab: Why does a parallel surface makes a difference? Why is that light do get disperse in a prism and a glass slab at surface one but at backs normal ...
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Physical Interpretation of Energy-wavenumber Graphs

Consider an energy-wavenumber graph, typical in solid state physics, like the one below. I can follow the mathematics in the derivations with a KP model. But I don't understand the physical ...
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Can dispersion relations be derived using Euler-Lagrange equations?

The question is long because of the demonstrations I give, but the problem is simple, so bear with me for a minute. I am trying to derive the dispersion relation of a semi-infinite system using Euler-...
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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 ...
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Wave packet in dispersive medium, how will the group velocity be affected? [closed]

A wave packet with center frequency ω is propagating in dispersive medium with phase velocity of 1.5 x 10^3 m/s. When the frequency ω is increased by 2%, the phase velocity is found to decrease by 3%. ...
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Dispersion relations in 2 atom and above

I am having a little trouble understanding this information of dispersion relations show below for a two atom basis. So it states that there should be in total 6 dispersion branches but there only 4. ...
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Where does dispersion actually take place?

Out of 1 & 2, which is most accurate? And, out of 3 & 4, which is most accurate? Do they both agree with each other? Please explain?
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Group and phase velocity for a superposition of 2 monochromatic waves

A wave packet in one dimension with a dispersion relation $\omega$ is a function of the form: $$f(x,t):=\sum_{i=1}^n\lambda_i\exp[i(k_i x+\omega[k_i] t)]\hspace{1cm}\forall i\leq n\colon\lambda_i,k_i\...
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What does the curve branch for $\omega > \omega_p$ mean for surface plasmon dispersion?

Consider a half-infinite metal (the other half is vacuum with $\varepsilon=1$). By solving Maxwell's equations and using boundary conditions at the interface, we get the dispersion: $$ \frac{\...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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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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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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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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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86 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, ...
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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 ...