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Amplitude coefficients are complex. The reflection and transmission coefficients must account for both amplitude change and phase change. In order to account for both of these, complex coefficients are required. These are the most general, and are needed for a complete description. In some special (and simple) cases, the phase shift is $0^\circ$ or ...


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The time evolution of wave function is dictated by the Schrödinger equation, as you surely well know. Let's take the simple free particle in $\mathbb{R}^d$ (with mass $1/2$ and $\hbar=1$): $$i\partial_t \psi(t,x)=-\Delta_x \psi(t,x)\; ;$$ where $\Delta$ is the Laplacian operator (i.e. $\partial_x^2$). Mathematically, this is a linear PDE (partial ...


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This is an extremely hard question to answer definitely; its answer is heavily dependent on three things (1) the makeup of the atmosphere in question (2) the density of the atmosphere in question and (3) the surface temperature, and therefore the spectrum of output light, of the star in question. If the atmopsphere's gasses are themselves are coloured (e.g. ...


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The most common colour for the sky on Earth is a white sky. Clouds cover around 70% of the Earth, and the nature by which they are scattering shortwave radiation makes them appear white or grey. This is because photons coming from the Sun are likely to be scattered multiple times, and because the dependence on wavelength is not strongly increasing or ...


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Probably too late now, but I have to answer this. There is indeed a way to predict the direction of a scattered Lyman $\alpha$ photon. The answer depends on whether the scattering takes place in the core or the wings of the line. In the core (i.e. closer to the line center than about 3 Doppler widths), we can use the dipole approximation, so the phase ...


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We know/assume that the mass of the particle is constant. Elastic scattering means no change in kinetic energy (in the center-of-mass frame). Since the mass of the particle is constant, this means there is no change in the speed (not velocity; speed) of the particle during an elastic collision. Torque is $\vec{\tau} = \vec{r} \times \vec{F}$. For a ...



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