# Questions tagged [integration]

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

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### Best integration method for singular functions in Mathematica

I have a quantity, $f$, as a function of energy, $E$, that is generated in Mathematica (see figure below). The expression for f contains factors of the form 1/(EH-E+i*eta), where a small eta was added ...
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### Lorentz-invariant phase space integral

Consider the following Lorentz invariant integral associated to a $2\to 2$ scattering: \begin{equation*} I = \int \frac{d^3\mathbf{p_3}}{(2\pi)^3 2E_3} \int \frac{d^3\mathbf{p_4}}{(2\pi)^3 2E_4} \...
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### Some integrals in QED Renormalisation

I am currently leaning the renormalisation of QED and I have met some tricky integral that seems unsolvable. The integrals are shown in Quantum Field Theory and the Standard Model by Schwartz, page ...
1 vote
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### How to derive the magnetic field at a distance $x$ (in the same plane) from the centre of a circular loop with current $I$ and radius $R$? [closed]

how to get the expression for magnetic field at any point in a circular loop (plane) with current $I$ and radius $R$, I can't seems to find it anywhere and all I'm getting is the derivation for ...
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### Density of States, Photoemission and Integrating the Number of States

I'm reading Fowler's theory on photoemission. I'm stuck on a part which Fowler helpfully identifies as "obvious". Fowler sets up the free electron model, suggesting that electrons need a ...
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### Integration over the complex plane and the completeness relation of the coherent states [duplicate]

I am studying some of the properties of coherent states using the book "Introductory Quantum Optics" by C. Gerry & L. Knight. (C. Gerry & L. Knight, Chapter 3, Section 5) And when I ...
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### Fermi-Dirac integrals [closed]

I accounted a problem when deriving the Fermi-Dirac integrals shown below Could someone point me out why the lower limit of integtal could subsitutite from $Ec$ to $0$? 20240410 edit I have derived ...
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### Integration by parts to switch sign on anti-Hermitian Louivillian

I am self studying non-equilibrium stat mech and a common theme is that I am unable to reproduce the "this follow from integration by parts" parts of derivations. Here is the most recent: In ...
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### Electric field at a point created by a charged object (derivation/integration process)

I was hoping someone can help me understand the math behind the electric field (electrostatics). I have gaps in my knowledge about integrals and derivatives (university moves very quickly and it has ...
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### Movement of a mass on a spring in damped SHM

Suppose a ball is connected to a spring attached to a wall, and they are in space, i.e. assume no gravity. The ball is put into a fluid with Stoke's drag and oscillates backwards and forwards relative ...
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### Integral Quantity Interpretation

Is there any natural interpretation for the following quantity? $$\int_{\vec{r}(t)} \nabla(\vec{v} \cdot \vec{A})dt \ .$$ Where: $$\vec{v} = \frac{d \vec{r}(t)}{dt} \ ,$$ is the velocity of the path ...
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### Why is the differential form of Gauss's Law equivalent to the integral form?

I can understand the Differential form of Gauss's Law ∇⋅𝐄= $\frac{ρ}{ɛ_0}$ as saying that the source of electric field vectors or flow disperse(The divergence of the electric field) is equal to the ...
1 vote
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### Problem with Deriving work done by gravitational force and gravitational potential energy from the first principles

Suppose we have a system with Two point masses of mass $M$ and mass $m$. And we want to derive Work done. Lets say M is fixed or $M>>m$. Initially assume mass m is at rest at a distance of $a$ ...
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### Integral from Feynman & Hibbs Appendix - solvable with Cauchy principal value [migrated]

In Appendix "Some Useful Definite Integrals" of Feynman & Hibbs "Quantum Mechanics and Path Integrals" they use some integral formulas that I'm struggling to derive. The ...
1 vote
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### Sign Problem When Calculating the Potential of an Infinite Line Charge [duplicate]

Similar questions have been asked before in the forum regarding the sign problems when integrating the electric field, but they do not fully clarify the problem for me, so I just want to ask for some ...
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### What's the path of charged particle around a circular magnetic field?

I'm trying to simulate electromagnetic fields. At the moment I'm exploring only magnetic fields (I know you can't have it without electric charge). Anyway, I created a current carrying wire (just a ...
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### Problem with understanding the definition of electric potential [closed]

Here is the definition I know: $V(\vec r)-V(\vec r_0)=\int_{\vec r_0}^{\vec r} -\vec E \cdot\vec dr$ I have lots of problems with this topic. How can I choose the starting point? and does it matter ...
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### Physical meaning of line integral involving force

I'm curious about the physical meaning of the following equation: $$\oint \mathbf{F} \cdot d \mathbf{s} = 0$$ What does this physically mean? I think is has something to do ...
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### Second-order variation of an integral

I was reading the paper SISAR Imaging for Space Debris based on Nanosatellites, in which the Fresnel-Kirchoff diffraction formula is applied for a scenario in which the receiver, transmitter and ...
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### Sign choice for line element while finding potential due to point charge [closed]

The canonical derivation for the $1/r$ potential due to a point charge is as follows: We consider an electric field of the form $$\mathbf{E}=\frac{q}{4\pi\epsilon_0 r^2}\hat{\mathbf{r}},$$ and ...
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### Why does taking average pressure and multiplying with area given total hydrostatic force

I am not able to wrap my head around this. Why does taking average pressure and multiplying it with the area given total hydrostatic force? In many books, the reason was because pressure is linearly ...
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### Difference between general formula for cosmological comoving distance compared to Carroll's one

I came across two different formulas for the transverse comoving distance in cosmology from GR based on Friedmann's solution in the FLRW metric for an expanding space homogenoeus and isotropic: a) .....
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### Another Fourier transformation but with a $\sqrt{\mathbf{q}^2 + m^2}$ term now

Just as the title proclaims, I have a Fourier transformation I am trying to determine. Here is the Fourier transformation in its full form: \int\frac{d^3q}{(2\pi)^3}e^{i\mathbf{q}\...
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### Integration to find force exerted by liquid on a tube

I was browsing PhysicsForums and I came across an interesting fluids question. I understood the method suggested to solve it, but I wanted to see if I could solve it through integral calculus. [...
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### (Not a flat-earther) The mathematics of an infinite flat earth using gauss' law for gravity

On the flat earth website, they prove that the gravitational pull of an infinite flat earth is finite. Is their proof correct?. I'm not that good at physics and can't determine if they're correct ...
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### Where does the absolute value sign come from for this integral on Peskin&Schroeder page 14?

On page 14 of Peskin&Schroeder, the authors are calculating the amplitute of a free particle propagating between states $|\vec{x_0}\rangle$ and $|\vec{x}\rangle$ using relativistic quantum ...
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### Derivation of conserved current

Can someone give me some steps on showing the last line. From the line, $$-\int d^3x \space \epsilon_{abc} \space [ (\nabla^2\phi_b) \phi_c - m^2\phi_b\phi_c ]$$ I cannot actually see how could this ...
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