Questions tagged [fourier-transform]
A unitary linear operator which resolves a function on $\mathbb{R}^N$ into a linear superposition of "plane wave functions". Most often used in physics for calculating the response of a time shift invariant linear system as the sum of its response to time harmonic excitation or for transforming a quantum state in position co-ordinates into one in momentum co-ordinates and contrawise. There is also a discrete, fast Fourier transform for discretised data.
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Vibrating string at many frequencies at once [closed]
I understand standing waves . When it vibrates faster it pushes air faster higher frequency . What about a plucked string? Does different segments have their own standing wave as the string as a whole ...
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About the vector potential
I have a question that is probably trivial concerning the vector potential used in electromagnetism. When solving the wave equations for the vector potential $\mathbf{A}$, we are essentially ...
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Beating the uncertainty principle for musicians
https://www.phys.unsw.edu.au/jw/uncertainty.html
The musician's uncertainty principle as above states that tuning can be less precise in short notes. But when we have a string with knowing its ...
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In what sense is "momentum" flowing in Feynman diagrams?
Given a Lagrangian $\mathcal{L} = \mathcal{L}_0 + \mathcal{L}_I$, we can construct the Feynman diagrams for some process by writing out the Taylor series for our interaction term and judiciously ...
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Fourier Optics Relation with Signal Processing Pulse
In signal processing, a very short pulse in the time domain can be understood as a superposition of many frequency components in the frequency domain.
In imaging or Fourier optics, can we find an ...
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Solutions for massless scalar field vs massive scalar field
My question relates to the difference between the solutions for massless scalar field vs massive scalar field, as it appears in the book: Quantum Field Theory for the Gifted Amateur from Lancaster &...
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How to derive Fourier-Laplace transform of random walk master equation on 2D lattice (Part 2)?
This question is linked with this question and is related to this paper.
The Fourier-Laplace transform is given by:
$$P(q,r,s)=\sum_{t=0}^{\infty}\sum_{m,n=-\infty}^{\infty}\frac{e^{iqm+irn}}{(1 + s)^{...
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How to derive Fourier-Laplace transform of random walk master equation on 2D lattice (Part 1)?
I have certain gaps in clearly understanding the derivation given in this paper. Suppose a particle moves on a 2D lattice randomly. The probability of going in any one direction outb of four available ...
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Density matrix of particle on a circle
Consider a particle constrained to a ring of circumference $L$. Following this paper, the position eigenstate on a circle can be expressed in terms of the position eigenstates on the real line as
$$
\...
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”Heisenberg-like” uncertainty principle(s) for antennas?
In harmonic analysis, we have the (one-dimensional) uncertainty principle:
$$\left(\displaystyle\int\limits_{-\infty }^{\infty }x^{2}|f(x)|^{2} \, \mathrm dx\right)\left(\displaystyle\int\limits _{-\...
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Diffraction Modeling Question
I'm trying to implement a model for diffraction-limited imaging, following "Microlithography" by Sheats and Smith. You can skip to the bottom for my question, but I'll explain the setup ...
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Lorentz transformation of momentum space and position space simultaneously
When we consider Lorentz transformations, do we consider the transformations of the momentum space and the position space simultaneously? Or do we do it depending on the problem i.e. if we work in ...
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On the Separability of the Coulomb Interaction into Ionic and Electronic Components within the Ewald Summation
Background and Context:
In calculations for periodic systems, such as ab initio MD, the Ewald method is employed to compute the Coulomb interaction. A known issue with the Ewald method is the ...
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Scalar fields satisfying Klein-Gordon equation
If a scalar field satisfies the following equation known as Klein-Gordon equation
$$
\phi_{;\mu\nu}g^{\mu \nu} + m^2 \phi=(\Box+m^2) \phi=0
$$
Let’s apply seperation of variables as
$$\phi = T(t)X(x)Y(...
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Convergence of $E$ for a system of free fermions using Green's functions
I am following "Quantum Theory of Many-Particle Systems" by Fetter and Walecka. The expression for the total ground-state energy of a homogeneous system of fermions in a box of volume $V$ (...
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