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TL;DR: The supersymmetric partner potential to OP's potential is the constant potential, which is clearly reflectionless. Define for later convenience the constant $\kappa:=\hbar/\sqrt{2m}$. The constant potential and OP's potential are just the two first cases ($\ell=0$ and $\ell=1$) in an infinite sequence of reflectionless attractive$^1$ potentials ...

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Refraction occurs when a large number of dipoles scatter coherently. Each individual dipole scatters light in response to the incident radiation in (almost) all directions, but when you have a large collection of scatterers, each one scattering in many directions, you have to sum the contributions of each one in order to arrive at the total field. Each ...

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I think this is an interesting question. Unfortunately, many hasty sketches of the history of physics, as they are taught, tend to draw somewhat biased conclusions for the sole purpose of avoiding delving into these types of questions (some people consider it to be a waste of time apparently). As far as I can tell, the classical scattering theory at the ...

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By definition, Thomson scattering is the elastic scattering of light by a free charged particle. Atoms cannot be described as such, but the electrons in an atom may approximate to free electrons if their binding energy is much lower than the photon energy. This might be true for X-ray wavelengths, although if the photon energy gets too high then elastic ...

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I consider the scattering process $A+B \to 1 + 2$. The differential cross-section is always given by \begin{split}\label{eq1} d\sigma &= \frac{1}{(2E_A)(2E_B)|v_A - v_B|} \frac{d^3p_1}{(2\pi)^3} \frac{1}{2E_1} \frac{d^3p_2}{(2\pi)^3} \frac{1}{2E_2} \left| {\cal M} \right|^2(2\pi)^4 \delta^4( p_A + p_B - p_1 - p_2) \end{split} ...

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You may visualize atom as nucleus surrounded by an electron cloud. Now imagine the incident plane wave is scattered by two parts of the electron cloud (front and back). If rays are going in forward direction (near 0 angle, low momentum transfer vector) then the path difference between two beams is less and you will have good constructive interference i.e. ...

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A clean metallic surface appears shiny because it is reflecting light. The interaction is due to the conductivity of the surface of the metal. When surface conditions change, the reflectivity is reduced. For example, a clean aluminum surface is very reflective, and aluminum coatings are used on the back side of mirrors; the glass protects the clean aluminum ...

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Yes, the Probability current is defined as $$J(x,t)=\frac{i\hbar}{2m}\bigg(\Psi\frac{\partial \Psi^*}{\partial x}-\frac{\partial \Psi}{\partial x}\Psi^*\bigg)$$ If the scattering matrix is defined as $$\begin{bmatrix} S_{11}&S_{12}\\ S_{21}&S_{22}\\ \end{bmatrix}$$ The transmission coefficient $T$ is given by $(S_{21})^2$, this is only true in ...

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Generally speaking, the first and main difference is that refraction happen upon transmission of the light, while scattering happen upon reflection of the light (namely, diffusive reflection, where the angle of reflection does not equal to the angle of incident).

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