# Tagged Questions

For questions about problems related to physics that involve evaluating integrals. Purely mathematical questions should be asked at math.SE.

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### What does it mean for an integral's differential to be raised to a power, like e.g. $d^3r$ or $d^3u$?

I was reading Zwelfel's book on reactor physics and saw the following notation: Notice that the differential of the integral is raised to the third power. What is the meaning of this notation? ...
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### Why we use differential element to get general form? [closed]

When we study any physical system we use differential element to get an equation then integrate over specific period to get a general form. Why we don't get directly a general form without ...
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### Integral over a product of two Green's functions

Need some help here on a frequently encountered integral in Green's function formalism. Forgive me since I am a junior student. I have an integral/summation as a product of a retarded and advanced ...
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### How is the two-point function of an operator dual to a scalar ADS field obtained in ADS/CFT?

The two point function of an operator dual to a scalar field in ADS/CFT can obtained directly from computation of the on-shell action in momentum space and then taking it back to position space. The ...
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### Area under the displacement-time graph giving time?

This is probably very stupid, but today at a lecture, our professor solved a problem where we had to find the time taken to travel from 0-5m, where $v = 3/x$ (velocity is a function of position.) ...
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### Why there is a $\frac{1}{2}$ in the distance formula $d=\frac{1}{2}at^2$?

I'm preparing for my exam, but I have difficulties in perceiving why there is a $\frac{1}{2}$ in the distance formula $d=\frac{1}{2}at^2$?
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### How to Solve this Integral

I am currently doing a problem in Quantum optics, specifically the problem of finding Wigner Function for Number states or Fock states. I am actually did the problem in a different way and found that ...
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### Explain $\Delta x = v_0t + \tfrac{1}{2}gt^2$ please? [duplicate]

$g = \Delta v/t$, so $\Delta v = gt$. $v = v_0 + \Delta v$, so $v = v_0 + gt$. So if $\Delta x = vt$, then $\Delta x$ should be $v_0t + gt$. Why the $\tfrac{1}{2}gt^2$? I'm really confused, so this ...
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### Area under and slope of the motion graphs

I wanted to ask in general what area under the graph means. Also which physical quantity is highlighted by area under distance vs time graph. I'm confused that area is a 2 dimensional concept and it ...
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### Gaussian integration and dimension argument

I made a mistake recently regarding the Gaussian density, by putting the determinant of the variance to the power $\frac{d}{2}$. Would the following argumentation be valid to highlight it should be to ...
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### Potential energy of a spherically symmetric charge density in a spherically symmetric electrostatic potential

I'm interested in calculating the potential energy of a spherically symmetric charge density in a spherically symmetric electrostatic potential. More specific, I'm currently trying to calculate the ...
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### Electrostatic energy integral for point charges

The electric energy stored in a system of two point charges $Q_1$ and $Q_2$ is simply $$W = \frac{1}{4\pi\epsilon_0}\frac{Q_1Q_2}{a}$$ where $a$ is the distance between them. However, the total ...
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### Energy stored in electric field [duplicate]

I know that energy stored in electric field / unit volume = $\frac{1}{2} \epsilon\,E^2$. so can I say that for any configuration calculating $\int \frac{1}{2} \epsilon\, E^2 \,d^3r$ over whole space -...
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