# Tagged Questions

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 calcalating the response of a time shift invariant linear system as the sum of its response to time harmonic excitation or for transforming a ...

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### Wilsonian Renormalisation — Peskin & Schroder Sect. 12.1

I'm working my way through Peskin & Schroeder, but some of the details of the calculations done in their introduction to the renormalisation group are slipping past me. For concreteness, the ...
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### Particle density in k-space

Question: Given a many particle wave function $|\Psi\rangle$, how can I calculate the occupation numbers in k-space? Setup: I have a 1D chain of molecules which contains 4 sites per unit cell. Let'...
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### Replacing fermionic operators with their Fourier transform and boundary conditions

In the section 4.1 of Quantum Computation by Adiabatic Evolution, Farhi et al proposes a quantum adiabatic algorithm to solve the $2$-SAT problem on a ring. To compute the complexity of the algorithm ...
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### What is abbe's rule in optics?

I have read wikipedia but can't really understand what they mean to say. The usual explanations are given in terms of Fourier optics, which I don't yet have the background for. Can anyone explain it ...
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### Hamiltonian - Fourier transform of order parameter [closed]

I have a rather simple task, but it seems I can't move forward with the solution. I have a Hamiltonian as seen in the picture. I have to use the Fourier transform of the order parameter $\phi(x)$ and ...
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### Confused about the substitution of the fermionic operators with their Fourier transform in an adiabatic Hamiltonian

In the section 4.1 of Quantum Computation by Adiabatic Evolution, Farhi et al proposes a quantum adiabatic algorithm to solve the $2$-SAT problem on a ring. To compute the complexity of the algorithm ...
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### Anomaly, Ward identity [closed]

While studying notes on anomaly by Adel Bilal (http://arxiv.org/abs/0802.0634), I stuck in a calculation. Here it goes as follows: The three-current correlator in perturbation theory as a one-loop ...
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### Asymptotic behaviours from Fourier transforms [migrated]

I have completely forgotten how one derives the asymptotic behavior in frequency space, given the asymptotic behavior of the function in real space (e.g. time). As an example example, it is often said ...
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### Help with two dimensional polar axis Fourier transform

This is a problem that I met in real-life physics research. This question is related to Wick's theorem. The question is: 1. In two dimensional plane with polar axis, why do we have the following ...
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### What is the meaning of the Fourier Transform of the electric field of a well guided mode in a dielectric waveguide?

I have been studying waveguiding in dielectrics for a while now; however, I cannot understand the meaning of the Fourier transformed electric field. I will first give some background information. ...
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### Interpreting group velocity of free particle wave packet

I am trying to understand the concept of group velocity of a free particle wave packet: $$\Psi(x,t) = \frac{1}{\sqrt{2 \pi}}\int_{-\infty}^{\infty} \phi(k)e^{ikx}e^{-\frac{i \hbar k^2 t}{2m}}dk.$$ ...
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### Which information do we get from the phase spectrum about the wave?

Let a wave is represented by an equation $$y=f(t)=10\sin(\frac{2\pi f_1t}{T} + \pi/6)+5\cos(\frac{2\pi f_2t}{T} +\pi/3)$$. Here, let us take $f_1=10 ,f_2=5 ,T=100$ Then, from the Fourier transform ...