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Energy stored in space/frequency electric field
I've come across a problem with finding the energy stored in time/frequency electric field. In space/time we have (taking $\epsilon = 1$)
$$ Energy = \frac{1}{2} \int_V |\mathbf{E}(\mathbf{x},t)|^2 ...
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1answer
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What's the average position of oscillating particles in a box with periodic boundary conditions?
Imagine an open box repeating itself in a way that a if a particle crossing one of the box boundary is "teleported" on the opposite boundary (typical periodic boundary position in 3D).
Now put a ...
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Why pulse waves results in wave packets?
I was doing experiments of measuring sonic velocity and I generate pulse waves from sensor 1, but when they are received by sensor 2, I saw wave packets on the oscilloscope, can you explain why?
I was ...
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Discrete sum over an exponential with imaginary argument, considering only every second lattice site?
Let's say I sum an exponential function $e^{\imath \left(k-k^{\prime}\right) x_{i}}$ over a chain system where every member of the chain is of the same type, e.g.,
A-A-A-...-A-A (total of N sites)
...
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Fourier Transform of ribbon's beam Electric Field
I have a monochromatic ribbon beam with $E(x)e^{i(kz-\omega t)}$ being the electric field's amplitude. I want to show that the lowest order approximation in terms of plane waves is
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Splitting light into colors, mathematical expression (fourier transforms)
I am trying to solve a problem that includes a function of the light hitting a certain area. My question is, how would I change a function $G(x)$ of photons hitting a certain area to include just ...
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51 views
Definition of frequency domain coordinates
I am using the Fourier Transform in Optics to perform differentiation with a filter by making use of the relation
$\frac {\partial}{\partial x} f(x)=2\pi i \int^{\infty}_{-\infty} u F(u) \exp (2i\pi ...
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How to solve following equation (Yukawa field)?
By using Lagrangian for Yukawa interaction,
$$
L = -\frac{1}{c}A_{\alpha}j^{\alpha} + \frac{1}{8 \pi c}(\partial_{\alpha}A_{\beta})(\partial^{\alpha}A^{\beta}) + ...
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What should the amplitude be when plotting 1-sided Amplitude Spectrum?
I have a continuous signal $x(t)$ such that
$$x(t)=12\cos(6\pi t)+6\cos(24\pi t)+3\cos(30 \pi t)$$
and is asked to sketch a 1-sided Amplitude Spectrum of the signal $x(t)$ if sampled above the ...
