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, ...

learn more… | top users | synonyms

8
votes
2answers
650 views

Are all scattering states un-normalizable?

I am an undergraduate studying quantum physics with the book of Griffiths. in 1-D problems, it said a free particle has un-normalizable states but normalizable states can be obtained by sum up the ...
41
votes
5answers
4k views

Scattering of light by light: experimental status

Scattering of light by light does not occur in the solutions of Maxwell's equations (since they are linear and EM waves obey superposition), but it is a prediction of QED (the most significant Feynman ...
28
votes
4answers
4k views

Why does the sky change color? Why the sky is blue during the day, red during sunrise/set and black during the night?

Why does the sky change color? Why the sky is blue during the day, red during sunrise/set and black during the night?
22
votes
6answers
2k views

Why can we treat quantum scattering problems as time-independent?

From what I remember in my undergraduate quantum mechanics class, we treated scattering of non-relativistic particles from a static potential like this: Solve the time-independent Schrodinger ...
24
votes
3answers
111k views

Why does the moon sometimes appear giant and a orange red color near the horizon?

I've read various ideas about why the moon looks larger on the horizon. The most reasonable one in my opinion is that it is due to how our brain calculates (perceives) distance, with objects high ...
16
votes
1answer
8k views

Phase shifts in scattering theory

I have been studying scattering theory in Sakurai's quantum mechanics. The phase shift in scattering theory has been a major conceptual and computational stumbling block for me. How (if at all) does ...
5
votes
2answers
3k views

Why are scattering matrices unitary?

In Griffith's QM book, he introduces scattering matrices as an end-of-the-chapter Problem 2.52. For a Dirac-Delta potential $V(x) = \alpha \delta (x - x_0)$, I've derived the scattering matrix and ...
4
votes
2answers
467 views

Why can't gravitons be created in traditional particle accelerators?

I've heard that it is incredibly difficult to detect a graviton, but I don't quite understand why. With all of the knowledge I have at the present time it seems like it should be possible to create a ...
37
votes
9answers
12k views

Why can't we see gases?

I am not sure what causes gas molecules to be invisible.This question may look silly but I really want to know the story behind it.
6
votes
4answers
13k views

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 ...
2
votes
1answer
3k views

Quark Radius Upper Bound

If quarks had internal structure (contradicting current beliefs), what is the lowest upper bound on their "radius" based on current experimental results? If possible, I'd prefer to only consider ...
1
vote
1answer
392 views

Specific electron energy gap values $E_{i+1}-E_i$ vs. photons with arbitrary energy $\hbar \omega$

The energy levels of electrons in an atom are quantized $E_i$. A photon of a specific momentum $\vec p$ and energy $$\omega=(E_{i+1}-E_i)/\hbar$$ hits an atom and gets absorbed. Okay now say the ...
12
votes
2answers
961 views

Why can the Euler beta function be interpreted as a scattering amplitude?

The Wikipedia article on the Veneziano Amplitude claims that the Euler beta function can be interpretted as a scattering amplitude. Why is this? In another word, when the Euler beta function is ...
8
votes
4answers
517 views

Different kinds of S-matrices?

It seems to me that the notion of an "S-matrix" refers to several different objects One construction you can find in the literature is allowing the coupling constant to adiabatically approach 0 in ...
2
votes
3answers
1k views

Scalar Field Redefinition and Scattering Amplitude

Consider a field redefinition $$ \phi \rightarrow \phi' = \phi+\lambda \phi^2 $$ Find the Feynman rules for this theory and work out the $2\rightarrow 2$ scattering amplitude at tree level (The result ...
12
votes
3answers
2k views

What is the capture cross-section of a black hole region for ultra-relativistic particles?

What is the capture cross-section of a black hole region for ultra-relativistic particles? I have read that it is $$\sigma ~=~ \frac{27}{4}\pi R^{2}_{s}$$ for a Schwarzschild BH in the geometric ...
7
votes
2answers
627 views

Scattering states of Hydrogen atom in non-relativistic perturbation theory

In doing second order time-independent perturbation theory in non-relativistic quantum mechanics one has to calculate the overlap between states $$E^{(2)}_n ~=~ \sum_{m \neq n}\frac{|\langle m | H' |...
6
votes
5answers
6k views

Why is the sky of the moon always dark?

Why is the sky of the moon always dark compared to the sky of the earth, doesn't it have day and night like earth?
5
votes
3answers
2k views

What exactly is a bound state and why does it have negative energy?

Our professor hasn't explained what bound states are. Could you give me an idea of what they mean and their importance in quantum-mechanics problems with potential (e.g. a potential described by a ...
4
votes
1answer
1k views

Scattering Processes in Scalar Yukawa Theory

I'm trying to compute nucleon-nucleon scattering in scalar Yukawa theory. Here we view a nucleon as a complex scalar field $\psi$ and a meson as a real scalar field $\phi$. They interact through $H_I=...
21
votes
2answers
761 views

Covariant Description of Light Scattering at a fastly rotating Cylinder

Let us consider the following Gedankenexperiment: A cylinder rotates symmetric around the $z$ axis with angular velocity $\Omega$ and a plane wave with $\mathbf{E}\text{, }\mathbf{B} \propto e^{\...
19
votes
4answers
2k views

Tree level QFT and classical fields/particles

It is well known that scattering cross-sections computed at tree level correspond to cross-sections in the classical theory. For example the tree level cross-section for electron-electron scaterring ...
10
votes
1answer
3k views

Proof of Yang's theorem

Yang's theorem states that a massive spin-1 particle cannot decay into a pair of identical massless spin-1 particles. The proof starts by going to the rest frame of the decaying particle, and relies ...
8
votes
1answer
381 views

Setting of renormalization scale in field theory calculations

In dimensional regularization an arbitrary mass parameter $\mu$ must be introduced in going to $4-\epsilon$ dimensions. I am trying to understand to what extent this parameter can be eliminated from ...
3
votes
1answer
4k views

Plane wave expansion in cylindrical coordinates

I am trying to solve scattering problem in 2D and got to expand the wave function in cylindrical system which comes out to be Hankel function. Can you tell me how to expand the plane wave $\exp(i {\...
12
votes
1answer
1k views

When we define the S-matrix, what are “in” and “out” states?

I have seen the scattering matrix defined using initial ("in") and final ("out") eigenstates of the free hamiltonian, with $$\left| \vec{p}_1 \cdots \vec{p}_n \; \text{out} \right\rangle = S^{-1} \...
7
votes
3answers
275 views

Contradictory result for scalar-field propagator from Feynman rules and LSZ formula

I am trying to learn how to calculate scattering amplitudes in a Klein-Gordon theory. I am getting stuck with the simplest of the examples: $\phi\to\phi$ in a free scalar-field theory. If I calculate ...
5
votes
1answer
839 views

Connected and strongly connected Feynman diagrams

Recently I read, that only connected Feynman diagrams give contribution of nonzero values into the scattering amplitude. Why it is so and what is the physical sense of connected diagrams (due to their ...
6
votes
1answer
778 views

Scattering amplitude and LSZ formula

I'm arriving at a contradiction. To calculate the scattering amplitude, one usually follows the prescription given by the Feynman rules that you only consider fully connected diagrams with the ...
6
votes
1answer
159 views

Reflectionless potentials in quantum mechanics

Scattering on potential $$V(x) = -\frac{(\hbar a)^2}{m}\text{sech}^2(ax)$$ with 1D equation of Schrodinger is famous problem. It is dealt with in Problem 2.48 of Griffiths book or online here. It is ...
12
votes
3answers
5k views

Why is it necessary for an object to have a bigger size than the wavelength of light in order for us to see it?

I keep hearing this rule that an object must have a bigger size than the wavelength of light in order for us to see it, and though I don't have any professional relationship with physics, I want to ...
9
votes
2answers
1k views

Optical theorem and conservation of particle current

The optical theorem $$ \sigma_{tot} = \frac{4\pi}{k} \text{Im}(f(0)) $$ links the total cross section with the imaginary part of the scattering amplitude. My lecture notes say that this is a ...
7
votes
1answer
207 views

Do small-angle coherent scattering experiments really see coherent effects over arbitrarily large distances?

Short version After integrating over all possible outgoing angles, the total cross-section of coherent elastic scattering from a fixed target of characteristic length $L$ scales like $L^4$. Does ...
6
votes
4answers
657 views

Far-field intensity from scattering of small particles

Howdy, I'm building a simulation for looking at the light field underwater. In order to verify my simulation, I'm looking for some data showing the far-field intensity that comes from single ...
5
votes
1answer
924 views

What is the range of validity of Fermi's Golden Rule?

It is well known that to calculate the probability of transition in the scattering processes, as a first approximation, we use the Fermi golden rule. This rule is obtained considering the initial ...
5
votes
1answer
467 views

What's the relation or difference between Lippmann-Schwinger equation and Dyson equation?

In quantum scattering theory, Green's Function is defined as [1] $$G_0(z)=(z-H_0)^{-1},$$ $$G(z)=(z-H)^{-1},$$ where $H_0$ and $H=H_0+V$ are separately non-interacting and interacting Hamiltonian. $V$ ...
7
votes
1answer
361 views

Are the Møller wave operators $\Omega_\pm$ related to $\lim_{t\rightarrow\infty}U(t)$ from field theory?

When we want to compute correlation functions $\langle\Omega|\,T\hat{\phi}(x_1)\ldots|\Omega\rangle$ in an interacting quantum field theory, we relate it to the free-field objects $|0\rangle$ and $\...
4
votes
1answer
82 views

Scattering Theory

In non-relativistic quantum mechanical scattering theory you can derive an expression for the differential scattering cross section under the first order Born approximation as $$\frac{d\sigma}{d\Omega}...
3
votes
1answer
349 views

How is Lippmann-Schwinger equation derived?

I'd like to know the derivation of Lippmann-Schwinger equation (LSE) in operator formalism and on what assumptions it is based. I consulted the Ballentine book as advised in this Phys.SE post, but I ...
3
votes
2answers
444 views

Lippmann-Schwinger Equation with Outgoing Solutions

I'm reading about Green's functions and how the Lippmann-Schwinger equation eventually leads to the textbook expression for the form of wavefunctions in the far radiation zone after scattering by a ...
2
votes
1answer
1k views

Feynman Rules for massive vector boson interactions

I am stuck at the beginning of a problem where I am given an interaction term that modifies the regular QED Lagrangian. It involves the interaction between a photon field and a massive vector boson: $\...
1
vote
1answer
359 views

Boundary Conditions in a Step Potential

I'm trying to solve problem 2.35 in Griffith's Introduction to Quantum Mechanics (2nd edition), but it left me rather confused, so I hope you can help me to understand this a little bit better. The ...
7
votes
4answers
1k views

Is forward scattering = no scattering?

What is forward scattering? If it is equivalent to no scattering, then why not call it "no scattering"?
6
votes
2answers
609 views

Blue-shifting as opposed to violet-shifting

A recent XKCD comic implies that the sky is blue as opposed to violet due to human physiology, and that animals more sensitive to shorter wavelengths will perceive the Earth's sky as the shortest ...
5
votes
2answers
1k views

How did Lord Rayleigh derive/determine the phase function for his scattering model?

I've been researching the question for quite some time, as I understand it the phase function is actually an approximation due to the particle-wave duality inherent in participating media such as the ...
4
votes
0answers
220 views

Scattering amplitude, link between quantum mechanics and QFT

In quantum mechanics, we can define the scattering amplitude $f_k(\theta)$ for two particles as the magnitude of an outgoing spherical wave. More precisely, the asymptotic behaviour (when $r\...
4
votes
1answer
297 views

What causes these rainbow effects using a polarizing filter on an airplane?

I know that light reflected from a surface at 45° is polarized and that for a similar reason skylight arriving from a direction orthogonal to the sun is polarized too. Photographers make use of this ...
2
votes
2answers
460 views

Classical Rutherford scattering (partial) derivation

I am having trouble answering the following question, please could you help! Thank you in advance for any assistance you can give. Consider classical Rutherford scattering of a particle with mass $m$ ...
2
votes
1answer
421 views

Alternative methods to derive the static potential in the NR limit of QED

In QED, one can relate the two-particle scattering amplitude to a static potential in the non-relativistic limit using the Born approximation. E.g. in Peskin and Schroeder pg. 125, the tree-level ...
2
votes
1answer
227 views

Materials about S-matrix and S-matrix theory

What is the best book or paper to learn about analytical structures of S-matrix and S-matrix theory? I already know books as The Analytic S-matrix by RJ Eden, PV Landshoff, DI Olive, JC P and Quantum ...