# Tag Info

1

Your final expression is correct except that $V$ should be in front since it does not commute with $Θ_0$ in general. In potential scattering ${Θ_0}V$ is often a compact operator and for large positive imaginary part of $z=E+iℏε$ its norm becomes arbitrarily small so the series converges. In certain cases one can do things a little differently by ...

0

The electron doesn't absorb the photons, it scatters them. The energy absorbed by an interaction depends on the scattering angle - this can be determined using the Compton formula for the wavelength of the scattered photon. And the electron tends to scatter more at different angles (proportional to the Thomson differential cross section). From this I found ...

1

I don't know how accurate this video is about the colour of the sky, but it does provide interesting visuals: https://www.youtube.com/watch?v=ywvUTWPlBhM (If the sun was replaced by other stars.) Here are a few screenshots from the video: Sirius: Arcturus: Polaris:

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The answer depends in part on the Z of the material you are looking at. This is something you can easily verify by looking at the XCOM database To generate an example, I entered "single element, Z=25" (manganese) and selected plots for different types of interaction in the range up to 10 MeV. The result looks like this: As you can see, the photoelectric ...

4

Heuristically, one approach to justifying Weinberg's application of Cauchy's formula is to treat the nonanalytic integrand as the boundary behavior of a meromorphic function (kind of like Fourier series): perform all internal integrations until you are left with an integral over energy, solve the Cauchy-Riemann equations within the upper half plane ...

1

From the general properties of 2x2 matrices, if ${\underline u}_1$, ${\underline u}_2$ are the eigenvectors of $A_{2x2}$, then $${\underline u}_1 {\underline u}^{*T}_1 + {\underline u}_2 {\underline u}^{*T}_2 = I_{2x2}$$ As for the Chandrasekhar decomposition, perhaps the explanation on pgs.269-271 in "Direct and Inverse Methods in Radar Polarimetry" ...

0

With regard to your first question, the transmitted plane wave doesn't undergo any scattering from the potential. This is made explicit by the representation of the scattered wavefunction as a sum of an incident planewave and an outgoing spherical wave. As such, the transmitted wave doesn't have anything to tell us about the scattering event. All of that ...

2

You can obtain the trajectory starting from the conserved quantities, which are the total energy and the angular momentum. By parametrizing the motion using polar coordinates in the plane of the orbit (the orbit is in a plane owing to conservation of angular momentum) you get E=\frac{1}{2} m \dot{r}^2 + \frac{1}{2} m r^2 \dot{\theta}^2 ...

0

So I think I figured out what my problem is. After some reading transfer matrices are just convenient rearrangements of the same information contained within a scattering matrix such that you can easily cascade the matrices and make the math a bit nicer. However, for my purposes I can just write out the separate equations resulting from the 3x3 scattering ...

2

A model for the interaction of light with atoms and molecules treats the charge distribution as an electric dipole, because the particles consist af separate positively and negatively charged particles that can be polarised to have a non-zero electric dipole moment. Neutral particles where no (internal) charge separation is possible should not be affected by ...

1

I'm guessing this is related to your earlier question, Will neutral particles be affected by EM waves?, and you're puzzled that Rayleigh scattering by air and reflection/refraction by solids and liquids seem so very different. The answer is that in Rayleigh scattering each scattering object behaves as an independant scattering centre, so the scattering is ...

-1

Electromagnetic waves are produced whenever charged particles are accelerated, and these waves can subsequently interact with any charged particles, they dont interact with neutral particles.Though I do remember reading somewhere that neutral particles can lead to acoustic waves but I dont remember the concept or conditions involved or the equations.

-1

The solution for oscillating charges or plasmons has an evanescent field that exponential decays in the z direction (out into the "air"). This is currently being postulated as a way to subvert the diffraction limit. For more info regarding the lens : http://www.sciencemag.org/content/308/5721/534.

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I would argue that this is like saying that the main difference between roses and rosemaries is the smell, in the sense that they differ in many things while both being flowers, and you are arbitrarily selecting a difference to be the outstanding one. The differences between direct reaction (DR) and compound nucleus reaction (CNR) are: the time duration: ...

0

I think the point is that if you took the limits to infinity without doing anything else, you'd be implicitly redefining the matrix element in order to make the equations consistent. So he just calls the redefined matrix element $T_{ni}$ instead of $V_{ni}$. Later he solves for $T_{ni}$ in terms of $V_{nj}$ (see the section "Solving for the T matrix").

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