# Questions tagged [scattering]

Scattering is a general term for several physical processes in which radiation of some sort changes direction due to an interaction with a particle. Scattering can be classified by the type of radiation (ie, electromagnetic, x-ray, neutron), or by the relative sizes of the wave and the particle (ie, Rayleigh, Mie, geometric).

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### Are the matrix elements of $S$-matrix Lorentz invariant?

In quantum field theory, the $S$-matrix is defined as a time-ordered exponential $$S=T\Big[\exp\Big(-i\int d^4x \mathcal{H}_{\rm int}\Big)\Big].$$ Since $\mathcal{H}_{\rm int}$ is a combination of ...
1answer
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### What is difference between scattering matrix method and transfer matrix method?

I want to simulate light propagation into nanostructures, but I do not know which method should I use: Scattering method or Transfer method?
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### Anderson orthogonality theorem for anisotropic potential

The original paper by P.W. Anderson presents the infrared orthogonality catastrophe for the fermionic many-body system in the presence of local scattering potential, e.g. $V(r)=\delta(r)$. The ...
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### Relation between momentum and number of collisions

I was wondering there exists any mathematical relation between momentum of a photon (hence frequency) and the number of collisions it makes. Lets consider the case of the ionosphere where we have a ...
1answer
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### What is the difference between “Inverse source problem” and “inverse scattering problem”?

As above in the title. I know the inverse scattering problem problem in the context of recovering dielectric profile of imaging domain from scattered fields measured at certain locations. But, what is ...
1answer
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### Scattering into collection of bound states: relativistic vs non-relativistic case

As far as I understand, in non-relativistic quantum scattering problem there is a possibility (channel) of the following process. Several (in fact, at least 3) particles which are far apart approach ...
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### $e^{-}(p_1)+e^{+}(p_2) \longrightarrow H(k_1) + Z(k_2)$ propagator approximation

I'm considering the scattering: $$e^{-}(p_1)+e^{+}(p_2) \longrightarrow H(k_1) + Z(k_2)$$                   &...
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### Action of Moller operators on stable one particle states in QFT

In Weinberg's book "The QFT", vol. I, it is claimed that for theories with stable single particle states the $S$-matrix maps each such state to itself (see Section 4.3, p. 179). I am wondering if the ...
0answers
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### Differential cross-section derivation from S-matrix

I am trying to derive the usual expression for the differential scattering cross section: $\frac{d\sigma}{d\Omega} = \frac{q_f}{q_i}|f(\vec q_f,\vec q_i)|^2.$ I am familiar with the derivation which ...
0answers
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### What is responsible for colour of sky seen from ground vs space?

If short wavelength of light such as blue and violet scatters more by air molecules in our atmosphere at noon time along the equator but our eyes can only see the blue sky due to biology, then what ...
0answers
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### Scattering of unpolarized light

I am doing an experiment in which I want to get $\mathrm{I}$ intensity of light at an angle $\theta$, from the original path of unpolarized light of intensity $\mathrm{I}$ after scattering from a ...
4answers
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### Why is the sunset not bluer [duplicate]

My question is a duplicate of this; Clarification on Rayleigh scattering causing various sky colors. The accepted answer from the link above says that at sunset the scattering occurs farther away and ...
2answers
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### Usually, how much does a phonon travel without scattering?

Phonons propagate without problems in a lattice, until they scatter on something, like a defect, an electron, or other phonon. But in a typical solid at room temperature, how much (or how long) is the ...
1answer
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### Can you please explain me phenomenon of reflection at subatomic level? [duplicate]

When we see atoms under an electron microscope, what exactly are we seeing? I mean, these spheres that we know as atoms are electron clouds and that is what we are seeing, am I right? https://www....
1answer
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### How exactly does polarization by scattering work?

Consider an electron sitting at the origin of a coordinate system. Let an unpolarized light travelling in the $z$-direction excite the electron at the origin. The motion of the electron can be thought ...
0answers
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### Change of electric vector (and hence polarization) of photon after Compton scattering

I want to know how the electric vector (polarization) of individual photon changes after Compton scattering. Is that totally a random process, means the photon electric vector orientation change has ...
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1answer
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### Explicit form of S-matrix on the line

Consider the Hamiltonian $H$ on functions on the line with \begin{eqnarray} H=H_0+V,\\ H_0=-\frac{1}{2m}\frac{d^2}{dx^2} \end{eqnarray} where $V$ is a potential vanishing outside of a bounded interval....
3answers
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### Effect of layout on text visibility [closed]

My college recently switched to whiteboards. Though writing on a whiteboard with a black ink sounds similar to the conventional way of writing with white chalk on a blackboard, it feels very different....
0answers
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### When does transmittion coefficient be able to calculate directly from the probability amplitude?

It's been so long so I could not recall just in a second. Let the usual setting $Ae^{ikx}+Be^{-ikx}$ for incident and reflected beam and $Ce^{ikx}$ for transmitted beam. The probability of ...
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### Quantum scattering from delta potential Barrier and well

Scattering from delta potential potential at $x=0$ it is observed that for $E>0$ both for potential well and barrier the reflection and transmission coefficient becomes same.As, in both the context ...
1answer
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### WKB for $E > V(x)$

When we use the WKB method, at least when I learned it, all of our examples had $V(x) > E$ at some point, allowing for turning points. Say we have some $V(x) < E$ for all $x$. How would we ...
1answer
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### bombarding Electrons into the nucleus!

Recently, in a workshop on Electron microscopy, our professor asked us a question over the backscattering of electron. his question goes like this "Why doesn't this electron falls straight into the ...
1answer
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### “In” and “Out” states in the Heisenberg picture

When studying scattering in quantum mechanics, we define the "in" and "out" states as states that are eigenfunctions of the free Hamiltonian at ${t \rightarrow \mp\infty}$. This makes sense to me ...
1answer
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### Factorisation of tree level amplitudes from unitarity

Is there a simple argument to explain why tree level amplitudes must factorize on their pole into products of lower point tree level amplitudes, not by ispection of Feynman diagrams but as a ...
0answers
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### A relation for the state of a scatteing process

I am studying the article "A Formal Optical Model", of Bell and Squires (the article is here https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.3.96) where they proof that the self-energy of ...