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5

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 ...


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 ...


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 ...


2

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 ...


1

Yes, you should start by assuming the wavelength used, $\lambda$, as known. The information you have is just sufficient to extract $\lambda$ in terms of the relative shift $\eta = \Delta \lambda / \lambda$ and the scattering angle $\theta$. All you have to do is maximize $\lambda$ in terms of $\eta$, $\theta$.


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

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" ...


1

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 ...


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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