New answers tagged fourier-transform
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Dependence of Klein-Gordon solution only on spatial coordinates
It does. The bold x notation represents the spacetime 4-vector components, so depends on time and space. The solution is not at all due to second quantization: you’re putting the cart before the horse....
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What is the physical meaning of the pressure of an acoustic point source being complex?
You have to view this as a time Fourier transform. In general, if your signal in time domain is real, the Fourier transform is complex. In fact, the Fourier transform acquires an imaginary part when ...
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Peskin and Schroeder path integral discretization
I think I figured it out. The key thing I forgot is the constraint on the field configuration at the initial and final time in the definition of the path integral. Once this is taken into account then ...
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Functional measure variable change
Question 1
First of all, a Jacobian is not a transformation, but a measure of how a transformation affects the volume or area elements. For example, if you have a function $f$ that maps $x$ to $y$, ...
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What defined the frequency of a pulse if not its periodicity?
An infinite long sinusoid, such as $A_x\cos(\omega_x t +\phi_x)$ is characterized by its frequency $\omega_x$ and amplitude $A_x$. The phase $\phi_x$ here just means a point in time referencing where ...
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What defined the frequency of a pulse if not its periodicity?
I have always understood that the frequency is the inverse of the period of repetition of a signal
That is the definition of the fundamental frequency.
IDK the proper name of the theorem, but it has ...
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What is the point of a reciprocal space?
As I understand it, we have a Brillouin zone in the primitive cell, in this primitive cell we only have one lattice point.
This already has a huge misunderstanding that makes it impossible to ...
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Field operators on vacuum
Your definitions/conventions trivially yield
$$\psi(\vec{x})|0\rangle = \int \frac{d^3p}{(2\pi)^{3}}\frac{1}{ 2E_p } e^{-i\vec p \cdot \vec x} |\vec p\rangle $$
and
$$\pi(\vec{x})|0\rangle = \...
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Why $w = 10/m$ is the single major Fourier component? (Statistical Mechanics: Entropy, Order Parameters and Complexity 2nd Edition)
Although I still have no idea what does the unit of $w = 10/m$ mean and if $U(w_x,t)$ represents the amplitude of the wiggle part, I now know how to solve the evolution equation of the wiggle part.
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Calculation about two-point correlation function in Fourier space
The delta function is an even distribution: i.e. $\delta(x)=\delta(-x)$ in general.
Also note that $\langle \delta(k) \delta^*(k') \rangle$ is an expectation value here, $\bf{not}$ an inner product (...
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What's the diffraction pattern for free-space propagation plus a thin lens at arbitrary distances?
The method is essentially the same as in a previous answer of mine Equation of light beam through a dielectric block, only the interface is treated differently. There are some mistakes in your formula ...
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Do these two separate light pulses (in sequence) interfere in this scenario? Why or why not?
From a purely mathematical point of view, if I take a function consisting of two distinct pulses, compute its spectrum and then filter out a portion of this spectrum, the inverse Fourier transform of ...
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