The integration tag has no wiki summary.
-2
votes
1answer
27 views
How to take integral of a spherical function $f_{(t,r,\theta,\phi)}$? [closed]
I know that volume integral is possible for a function of $f_{(r,\theta,\phi)}$ but How to take integral of a spherical function of $r$, $\theta$, $\phi$, which depend on time too?
...
1
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0answers
84 views
Approximate solution for an ODE [migrated]
I've been working on a problem of Newton's gravity on different geometries. On a, physically meaningful, geometry I ended up with the following nasty first ODE:
...
-2
votes
0answers
120 views
A hard integral [closed]
It seems the "mathematicians" over at MathSE can only work out textbook integrals and the following is not one. Therefore I'll try my luck with you guys here to see if I can get any hints how to ...
3
votes
2answers
167 views
Help with Greens function/Fourier transformation to solve screened Poisson equation
I am having trouble getting from one line to the next from this wiki page. I am referring to the text line
Green's function in $r$ is therefore given by the inverse Fourier transform,
where
...
3
votes
2answers
69 views
Extension to continuous in proofs of rigid body mechanics
I'm studying rigid body mechanics and I've seen several proofs of properties related to total angular momentum, kinetic energy, etc. that all regard discrete set of points. For example, to show that ...
2
votes
1answer
232 views
Crazy Dirac Deltas
I'm not expecting any rigor in the following and the answers...since we're dealing with Dirac deltas in the context of QFT.
Consider the integral
$$
\int d^4q\ \Theta(q_0)\Theta(p_{3,0}+q_0)\ ...
0
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0answers
15 views
How can I calculate numerically an electrical potential distribution from an electric field distribution? [migrated]
I want to calculate the unknown electrical potential distribution $\phi(x)$ (notice this is a function of $x$) from a known electric field distribution $\boldsymbol{E}(x)$ using the Poisson equation,
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0
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0answers
58 views
Contour Integrals and Residues [closed]
I'm trying to figure out what it is all about, but my mind is blowing up. First of all, I have turned back and looked at the general definitions of integrals. Then I have looked to line integrals. ...
1
vote
1answer
73 views
the meaning of epsilon in this operator $ \epsilon $
Consider the dimensional regularized integral
$$ \int d^{d}k (k^{2}-m^{2}+i\epsilon)^{-\lambda} $$
For positive $ \lambda $ this integral has a pole at $ k=m $. Is this the reason we we insert the $ ...
0
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0answers
10 views
Is this an exact differential or not? [migrated]
I have the 1-form
$$dz=2xy\, dx+(x^{2}+2y)\, dy$$
And I want to integrate it from $(x_{1},y_{1})$, to $(x_{2},y_{2})$.
If I'm not drunk, checking mixed partials, I find that $dz$ is an exact ...
6
votes
4answers
147 views
Integrating radial free fall in Newtonian gravity
I thought this would be a simple question, but I'm having trouble figuring it out. Not a homework assignment btw. I am a physics student and am just genuinely interested in physics problems involving ...
7
votes
1answer
458 views
I reached a result concerning displacement with quantized time intervals. Am I on to something?
A few days ago, I realized a similarity between distance with constant acceleration, $d = v_i t + 1/2 a t^2$, and the sum of integers up to n, $(n^2 + n)/2$. This came up again today when I decided to ...
1
vote
2answers
73 views
Relation between the time, velocity and acceleration
This is question from I.E. Iredov's General Physics:
$1.22$ : The velocity of a particle moving in the positive direction of the $x-axis$ varies as $v = α \sqrt x$, where $α$ is a positive ...
1
vote
3answers
177 views
Integration by parts to derive relativistic kinetic energy
I have come across a weird integration during derivation of relativistic kinetic energy. Our professor states that i can get RHS out of LHS using integration by parts:
$$
\int\limits_0^x \! ...
4
votes
2answers
114 views
Twistor Function for Coulomb Field
In an article by Penrose in Hughston and Ward "Advances in Twistor Theory", it is claimed that the twistor function
$$ f(Z^\alpha) = \log{\frac{Z^1Z^2 - Z^0Z^3}{Z^2Z^3}}$$
produces an anti-self-dual ...
0
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1answer
86 views
4
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2answers
155 views
A four-dimensional integral in Peskin & Schroeder
The following identity is used in Peskin & Schroeder's book Eq.(19.43), page 660:
...
2
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1answer
103 views
Getting rid of double delta function in Feynman rules
[1]
A very simple example of feynman rule for scalar fields.
After computing the diagram i have got the following:
$$
-i(2\pi)^4g^2\int d^4q \frac{i}{q^2 -m^2c^2}\delta^{(4)}(p_1 - p_3 -q)
...
0
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2answers
160 views
Calculate the center of mass of a semicircle [closed]
How I determine the center of mass of a semicircle using the definition of center of mass? I only know solve this using the Pappus theorem. Consider that the semicircle is centered on the origin and a ...
-1
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3answers
138 views
What needs to be integrated to solve this problem?
An object is placed on a frictionless table with its one end attached to a cord which is connected to a pulley and the tension is maintained constant at 25 N. what is the change in kinetic energy ...
0
votes
1answer
77 views
Change of variables, Fermi Integral
This is a really basic question, but I'm kind of confused.
I have this integral
$$\int_{0}^{\infty}\frac{p^{2}dp}{e^{\alpha+\beta p^{2}/2m}+1}$$
where ...
0
votes
3answers
304 views
Deriving equations of motion using integration
Please refer to my school textbook pg48 (of the book, and not the pdf counter) here: http://ncertbooks.prashanthellina.com/class_11.Physics.PhysicsPartI/ch-3.pdf
My doubt is in this context: (right ...
0
votes
2answers
157 views
Getting position from an accelerometer on an Android phone
I know that integrating acceleration twice will give me position (acceleration-->velocity-->position) but how can I do all this when I all I have are a set of data points (ex: 1 second = some # ...
3
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0answers
123 views
Zeta regularization gone bad
This may sound as a mathematical question, but it should be very familiar to physicists. I am trying to perform an expansion of the function $$f(x) = \sum_{n=1}^{\infty} \frac{K_2(nx)}{n^2 x^2},$$ for ...
2
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2answers
54 views
Flux Over a Surface
I am teaching a multivariable calculus course and we are starting to go over surface integrals. I am a math professor with little knowledge of physics. At one point the book discusses fluid flow. ...
5
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0answers
125 views
Using $\frac{1}{A+i\epsilon} = PV\frac{1}{A}-i\pi\delta(A)$ in Feynman Integrals
Are the following operations O.K.? This is related to the Feynman parameter trick.
$$F:= \int_0^1 \mathrm{d}x\int_0^{1-x}\mathrm{d}y \frac{1}{f(x,y)+\mathrm{i}\epsilon}.$$ Now using
...
6
votes
1answer
300 views
Loop integral using Feynman's trick
I am trying to show for the one-loop integral with three propagators with different internal masses $m_1$, $m_2$, $m_3$, and all off-shell external momenta $p_1$, $p_2$, $p_3$ the following formula ...
7
votes
4answers
447 views
Possible ambiguity in using the Dirac Delta function
When doing integration over several variables with a constraint on the variables, one may (at least in some physics books) insert a $\delta\text{-function}$ term in the integral to account for this ...
1
vote
1answer
162 views
Shift operator (integral calculus involving Hermite polynomials) [closed]
I didn't know whether to pose this question on Physics.stackexchange or Math.stackexchange. But since this is the last step of a development involving the eigenfunctions of an Harmonic oscillator and ...
0
votes
2answers
111 views
Is air drag equation in term of momentum still valid?
This is the known equation of air drag:
$$m{\bf a}=mg-\mathcal D=mg-b{\bf v}.$$
Considering this, is air drag equation in term of momentum still valid?
$$m{\bf v}=mv_g-b{\bf r}.$$
2
votes
1answer
235 views
Ashcroft Mermin Solid State Physics Eq. 2.60ff
I'm trying to follow the steps in Eq. 2.60 of said book.
What I cant seem to figure out is how to change the integration variables from 'k' to 'E', as they state.
The equation is
$$\int ...
0
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0answers
265 views
Expectation value of a Gaussian wave packet [closed]
How can I compute the expectation value $\langle x\rangle_t$ of a Gaussian wave packet $$\psi(x,t) = \int_{-\infty}^\infty \mathrm dp \, \hat\psi(p) \exp{\frac{-\mathrm i(px - E_p t)}{\hbar}}? $$
...
4
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1answer
318 views
A confusion from Weinberg's QFT text (a vanishing term in Lippmann-Schwinger equation)
I was reviewing the first few chapters of Weinberg Vol I and found a hole in my understanding in page 112, where he tried to show in the asymptotic past $t=−∞$, the in states coincide with a free ...
13
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1answer
112 views
Monte Carlo integration over space of quantum states
I am currently facing the problem of calculating integrals that take the general form
$\int_{R} P(\sigma)d\sigma$
where $P(\sigma)$ is a probability density over the space of mixed quantum states, ...
1
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2answers
115 views
Are there general circuits that differentiate/integrate empirically?
Is it possible to construct simple circuits, that given a time-varying input, produce an output that represents the derivative or integral of the input with respect to time?
1
vote
1answer
144 views
Potential for charge distribution, finiteness
Consider a potential for charge distribution:
$$v_H(\mathbf{r}) ~=~ \int \frac{\rho(\mathbf{r'})}{|\mathbf{r}-\mathbf{r'}|}d\mathbf{r'}$$
where $\rho(\mathbf{r'})$ is the charge density.
This ...
3
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0answers
140 views
Should the Jacobian be negative in $\mathrm{d}^4 x$?
In page 24 of Srednicki's QFT textbook, he says that $\mathrm{d}^4x$ is a Lorentz scalar. I understand that the determinant of a Lorentz matrix is always $\pm 1$. So in an improper Lorentz ...
4
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4answers
627 views
How do you do an integral involving the derivative of a delta function?
I got an integral in solving Schrodinger equation with delta function potential. It looks like
$$\int \frac{y(x)}{x} \frac{\mathrm{d}\delta(x-x_0)}{\mathrm{d}x}$$
I'm trying to solve this by ...
1
vote
1answer
155 views
Integral in Peskin and Schroeder
I'm having a bit of a slow day, and can't see how to do the following integral in Peskin and Schroeder (page 107 for anyone with the book). We've derived in the centre of mass frame the integral over ...
14
votes
1answer
196 views
Why isn't the Gear predictor-corrector algorithm for integration of the equations of motion symplectic?
Okumura et al., J. Chem. Phys. 2007 states that the Gear predictor-corrector integration scheme, used in particular in some molecular dynamics packages for the dynamics of rigid bodies using ...
1
vote
1answer
106 views
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 ...
0
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0answers
89 views
Nicholas Kollerstrom article on the history of Calculus
Today, Newton´s birthday, I read an article posted in the arXiv by Nicholas Kollerstrom
http://www.arxiv.org/abs/1212.2666
That basically claims that Newton did not invent Calculus. The article does ...
2
votes
2answers
153 views
Gaussian type integral with negative power of variable in integrand
How can we compute the integral $\int_{-\infty}^\infty t^n e^{-t^2/2} dt$ when $n=-1$ or $-2$? It is a problem (1.11) in Prof James Nearing's course Mathematical Tools for Physics. Can a situation ...
1
vote
1answer
310 views
Derivation of the self gravitational potential energy of a sphere
I have been searching on the Internet but have not found a derivation of the formula for the self gravitational potential energy of a sphere. Can someone show how to do this? I assume it involved 6 ...
2
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1answer
252 views
Does the universe obey the holographic principle due to Stokes' theorem?
Does the universe obey the holographic principle due to Stokes' theorem?
\begin{equation}
\int\limits_{\partial\Omega}\omega = \int\limits_{\Omega}\mathrm{d}\omega.
\end{equation}
Can this ...
-1
votes
1answer
149 views
What will happen when measuring unmeasurable object?
There is a set called Vitali Set which is not Lebesgue measurable.
Analogously, there also exists a Vitali set $Y$ in $\mathbb R^3$ which is a subset of $[0,1]^3$ and $|Y\cap q|=1$ for all $q\in ...
5
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0answers
214 views
Gaussian Integrals : Functional determinant expressed as a trace
Be $A_{ij}$ a symmetric matrix. Then I can easily write
$$
\int \exp\left(-\frac{1}{2}\sum_{i,j}x_i A_{ij} x_j+\sum_{i} B_i x_i\right)\; d^nx=
\sqrt{(2\pi)^n}\exp\left\{-\frac{1}{2}\mathrm{Tr}\log ...
1
vote
1answer
128 views
What is the definition of density as a function?
(Before I start, I don't know which tag is suitable for this post. Please retag my post if it bothers you.)
Let's say there is a string on $[0,1]$ with a mass given by $m(x)$. ($m(x)$ means the mass ...
1
vote
1answer
102 views
Integration of constant: $\int dp = \Delta p$ in impulse formula
In University Physics, it has something like:
$$\int \sum F dt = \int \frac{dp}{dt} dt = \int dp = \underbrace{p_2 - p_1}_{\Delta p?}$$
But I thought $\int dp = p$? Though my maths is really rusty ...
3
votes
3answers
265 views
How to compute the expectation value $\langle x^2 \rangle$ in quantum mechanics?
$$\langle x^2 \rangle = \int_{-\infty}^\infty x^2 |\psi(x)|^2 \text d x$$
What is the meaning of $|\psi(x)|^2$? Does that just mean one has to multiply the wave function with itself?
