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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2answers
156 views

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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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....
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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 ...
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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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2answers
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Is the monochromatic solution of the free Schroedinger equation a travelling wave? [closed]

When we examine the monochromatic solution of the free Schroedinger equation: $$\psi(t,\mathbf r) = e^{-i\left(\frac{ħk^2}{2m}\right)t}\left(Ae^{i\mathbf{k\cdot r}} + Be^{-i\mathbf{k\cdot r}}\right).$...
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Why is there a “blue hour” after the “golden hour”?

There's a great story about why the sky is blue during the day, and turns golden during sunsets: Rayleigh scattering affects blue light more. During the day, blue light from the Sun is scattered ...
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Frame-independent probability amplitude for Compton scattering in scalar QED

In scalar QED, the matrix element for compton scattering is the sum of three diagrams: the s-channel, t-channel and the seagull diagram. After simplifcation, making use of the orthogonality between ...
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1answer
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Elimination of three gluon vertex

I am reading this paper by Dixon, where it is mentioned that one can diagrammatically compute the colour factor of certain Feynman graphs, such as shown in figure 1, where they expand a three gluon ...
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Difference in transition lifetimes for near-resonant v/s non-resonant Raman effect

I have read that a virtual state is created when Raman scattering occurs. Since this state is forbidden, the molecule upon absorbing a photon (not enough to take it to the next electronically excited ...
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S-matrix elements for Nucleon-Pion decay

I want to compute nucleon-pion decay rates. I am a bit confused how I can compute the S-matrix. Let's say we have a Nucleon Pion scattering and I want to compute their corresponding S matrix: \begin{...
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Combining a sine and cosine, with complex coefficients, into a single sine with a phase shift

In section 13.4 of Townsend's Modern Approach to Quantum Mechanics on the partial wave expansion for scattering, the author discusses the asymptotic expansion of the spherical Bessel functions. He ...
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Why do we analyse the step potential problem in quantum mechanics with non-normalizable solutions?

While reading Griffiths Introduction to Quantum mechanics and using MIT 8.04 QP-1 lectures by Adam Allans as a supplementary source to understand the topic of scattering of particles for step ...
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Photon-phonon scattering problem

I have to calculate the following: a) The speed of the acoustic phonons b) Which phonons(frequency and wavevector) can be observed for scattering angles between 0° and 180° and how much of the ...
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Fermi’s golden rule integral over energy states, time constraints

In perturbation theory, we can, to first-order, arrive at an expression for transition rates that looks like $$ \Gamma = \frac{2}{\hbar} |M_{if}|^2 \frac{\sin{\frac{E_f-E_i}{\hbar} t}}{E_f-E_i}. $$ ...
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Electron tunneling: transmission>1? [duplicate]

Assume a simple electron tunneling scheme from medium 1 into medium 2. By applying the boundary conditions (continuity of the wave function and its derivative at the interface), it is straightforward ...
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Quantum mechanics: bounded states and scattering states

So in quantum physics, we can solve solutions of the schroedinger equation and have that the eigenvalues are either positive or negative, which means it is either a scattering state or a bound state. ...
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Is there energy losses due to Screening /Shielding Effect?

Elastic scattering can be modeled by Mott cross-sections which include the screening factor. We assume there is not energy losses in elastic scattering events. I imagine that the free electron ...
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1answer
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Scattering cross section from sum of delta functions in 3D

we had the following question in our exam: I know basic scattering concepts like partial waves, born approximation etc. and the solution of common potentials like coulomb or hard spheres but have ...
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2answers
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Why is the probability density oscillating in region $x<0$ before the potential barrier?

My understanding was that the standing wave solution is that of a free particle in the region before it enters the classically forbidden region. Does multiplying the wave function by its complex ...
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1answer
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How is a horizontal sunset possible? [closed]

Source: @PHSXES/Reddit Normally, sunset moves vertically, from up to down in the sky. But in this photo, it appears to be moving horizontally, from left to right. It might be an instant of a ...
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2answers
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How can the sky be blue and transparent at the same time, from below and above?

The sky is blue, when looking from below. That's based on scattering, no problem with that: Why is the sky blue? But it is also colorless transparent from above. No problem with that either, we look ...
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Why is elastic scattering of photons (largely) non-isotropic, but inelastic scattering is isotropic?

I'm working on an experiment regarding Raman spectroscopy, and i'd like to fully understand the reasoning behind this fact. I assume it is related to the photons momentum. My apparatus has a '...
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Is my way for calculation of intermediate scattering function right?

I have a C++ code for below formula: $$F_{\text{s}} (\mathbf{k},t) = \frac{1}{N} \langle \sum_{j=1}^{N} exp\left( i \mathbf{k} \cdot \left[ \mathbf{r}_j (t) - \mathbf{r}_j (0) \right] \right) \...
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Reference request: Scattering from action

Consider a separable solution to a Hamilton-Jacobi equation of an $n$-dimensional autonomous system of the form $$W(\alpha_1,...,\alpha_n,x^1,...,x^n) = \sum_j \int_0^{x^j} w^j(\alpha_1,...,\alpha_n,x'...
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Probability current for a one dimensional step potential for a reflected wave [closed]

I've been following the step potential problem from my textbook and I've got the set of equations right which are: $$\psi_1 = A_1\left(e^{ik_{1}x} + \frac{k_{1} - k_{2}}{k_{1} + k_{2}}e^{-ik_{1}x}\...
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1answer
51 views

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....
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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....
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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 ...
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1answer
41 views

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 ...
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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 ...
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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 ...
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1answer
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$\alpha$-particles scattering at Al foil

I am currently reading myself into the topic of scattering experiments and (differential cross sections) and stumbled across the following problem which I really dont know how to solve (this is $\...
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The use of the Hartree-Fock Hamiltonian in the Moller operators

Consider the scattering of a particle with momentum $p$ and mass $m$ by any target. If $|\Psi \rangle$ is the scattering state, we can write it as $|\Psi \rangle = \Omega_{\pm} | \psi \rangle$, where ...
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Where can I learn about the reflection/refraction of sound waves and acoustic impedance in a way similar to quantum tunnelling? [duplicate]

I have learnt about the reflection and transmission of a particle at a potential barrier in quantum mechanics. I vaguely remember there is something similar in acoustics - things such as acoustic ...
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27 views

Derivation of unitarity condition for partial wave amplitudes

In Gribov's lectures "The Theory of Complex Angular Momentum," he states that the condition of unitary of the scattering matrix $$2 \text{ Im} A = A A^\dagger$$ can be restated, upon expanding out $...
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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 ...
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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 ...

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