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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65 views

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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Lorentz invariant interaction: why restrict attention to interactions built by integrating a Hamiltonian density?

In Weinberg's QFT book, Chapter 3, he shows that if the interaction term $V(t)$ is of the form $$V(t)=\int \mathcal{H}(t,\mathbf{x}) \ {\rm d^3}\mathbf{x},$$ where the operators $\mathcal{H}(x)$ are ...
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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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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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114 views

Some Rayleigh Scattering questions

Last week I've heard about Rayleigh scattering for the first time, when the classic 'why is the sky blue?' question has crossed my mind and I must admit that it is fascinating! However, I do have a ...
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Use my example to explain why loop diagram will not occur in classical equation of motion?

We always say that tree levels are classical but loop diagrams are quantum. Let's talk about a concrete example: $$\mathcal{L}=\partial_a \phi\partial^a \phi-\frac{g}{4}\phi^4+\phi J$$ where $J$ is ...
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X-ray diffraction analyisis: The angle of elastic x-ray scattering

What is the scattering angle distribution for x-rays (in the 8keV range) scattered elastically? I work with XRD analysis, which is fundamentally basede on these elastic scatterings of x-rays. I read ...
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Scattering from a delta function [closed]

Show that for a potential of type 𝑉 (𝑟⃗) = 𝑔𝛿 (𝑟⃗), where 𝑔 is a constant and 𝛿 (𝑟⃗) is the delta function of Dirac in 3D. Using the Born approximation, determine the scattering amplitude and ...
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167 views

Calculating the probability of transmission of a wave function between two delta distributions

Given is the potential :$V(x) = \frac{-\hbar^2}{m}D\delta(x+a) - \frac{-\hbar^2}{m} D\delta(x-a)$ with $a >0$ and $ D > 0$. A stream of particles from the positive $x$-axis are falling towards ...
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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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Møller scattering amplitute computation

I'm trying to compute the squared matrix element of these 2 diagrams in the high energy limit(ignoring the masses). Now I know that $|\mathcal{M}|^2=|\mathcal{M}_1-\mathcal{M}_2|^2$ since the 2 ...
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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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Normalized probability distribution from the Coulomb/Rutherford scattering amplitude?

My question appears elementary, but I have been pretty vexed trying to answer it precisely. Can one use the Rutherford/Coulomb scattering amplitude to get a finite, normalized momentum-space ...
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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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Can Rayleigh scattering explain the orange color of the Titan sky?

It is my understanding that Rayleigh scattering depends on both the length of the particle as well as the wavelength. Due to the similar lengths of molecular nitrogen and oxygen it is blue light that ...
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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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545 views

Difference between coherent scattering and elastic scattering

What is the difference between coherent and elastic scattering. Maybe the elastic scattering implies that there is not loss of energy, whereas the coherent scattering implies that the wavelength of a ...
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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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What exactly is a bound state and why does it have negative energy?

Could you give me an idea of what bound states mean and what is their importance in quantum-mechanics problems with a potential (e.g. a potential described by a delta function)? Why, when a stable ...
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How to prove the equivalence of two different definitions of $S$-operator?

I read there are two definitions about $S$-operator: The first one (e.g (8.49) in Greiner's Field Quantization) is: $$S_{fi}\equiv \langle \Psi_p^{-}| \Psi_k^{+}\rangle$$ where $|\Psi_p^{-}\rangle$ ...
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178 views

Scattering off of a bi-local potential

I am trying to figure out the scattering wave function for the following potential: $$V(x,x')=-A \phi(x)\phi^*(x')$$ Such that the SE can be written as $$[\frac{\hbar^2\partial^2_x}{2m}-E]\psi = A\...
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What is the difference between Raman scattering and fluorescence?

What is the difference between Raman scattering and fluorescence? Both phenomena involve the emission of photons shifted in frequency relative to the incident light, because of some energetic ...
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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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Photon-mirror collision

I'm trying to implement a simple simulation of a box of photons, to demonstrate mass-energy equivalence, and relativistic time dilation. I want to be able to push the box around interactively. As I ...
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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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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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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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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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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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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....
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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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Generic Rayleigh effect experiment - nothing happens for water

On youtube, a bunch of Rayleigh scattering experiments (e.g this one) are set up with some compound being added to water in order to invoke the effect. Why is there no Rayleigh effect for "pure" ...
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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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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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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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188 views

QM: Wave packet scattering in an infinitely growing potential

Say we are dealing with a 1-d non-relativistic quantum mechanics problem with a time independent potential $V\left(x\right)$. This satisfies the Schrodinger equation: $$ i \hbar \frac{\partial}{\...
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1answer
287 views

Asymptotic behavior of wave function in scattering of spin 1/2 particles against spin 0 target

I need a little hand here. My professor left me as homework to study the chapter VII of the Ref. [1]. Everything was going well until the section "Particle with spin". In Eq.(7.1), is given the ...
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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?

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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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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Scattering, Perturbation and asymptotic states in LSZ reduction formula

I was following Schwarz's book on quantum field theory. There he defines the asymptotic momentum eigenstates $|i\rangle\equiv |k_1 k_2\rangle$ and $|f\rangle\equiv |k_3 k_4\rangle$ in the S-matrix ...
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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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151 views

Why is there a difference in angles of deflection in Rutherford model?

In Rutherford's model why were the angles of deflection different from each other?why were the deflections of large angles so less in number and was there a difference in deflections from protons and ...
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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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Why does the scattering cross section equal to the sum over all differential cross section; including the incident angle?

According to Beer Lambert's law, the intensity of light passing through a homogeneous medium diminishes at a rate proportional to the incident intensity; i.e. $$ \frac{dI(s)}{ds} = -I(s)\sigma\, , $$ ...
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Explanation of why poles in the S-matrix corresponding to particle production/bound states?

I've frequently heard the statement that the only singularities of the S-matrix in QFT correspond to things like the existence of bound states and the possibility of multi-particle production. I'm ...
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414 views

How do I determine an unknown element if I know the diffraction lines?

I'm not quite sure if I fully understand x-ray diffraction yet. In a standard XRD experiment, if I'm given the $\theta$ values for the $K_{\alpha}$ and $K_{\beta}$ peaks, I can plug them into Bragg's ...