Delta function Definition and 379 Threads

Homework Statement Show that \int^{\infty}_{-\infty} e^{-ipt} dt = \delta(t). Homework Equations The Attempt at a Solution I know that I must Fourier transform \delta(t), but not sure how.

Homework Statement Prove that \displaystyle \int_{-\infty}^{\infty} \delta (at - t_0) \ dt = \frac{1}{ | a |} \int_{-\infty}^{\infty} \delta (t - \frac{t_0}{a}) \ dt For some constant a. The Attempt at a Solution Edit: Looking at this again, I really don't understand where this is coming...

Hi All, I'm trying to plot some DiscreteDelta functions in mathematica but unfortunately since the points are singular nothing shows up in the plot. Usually when this comes up I replace the delta functions with very narrow gaussians, graphically it looks even nicer (I'm plotting absorption...

Hello Again! My question: Find the bound energy spectrum of the potential that contains two delta-function wells: V(x) = -V_{0}\delta(x-\frac{a}{2}) -V_{0}\delta(x+\frac{a}{2}) under the assumption that the wells are located very far away from each other. Find and plot the associated stationary...

I have a question about delta functions. What I want to believe is the following \int_{-\infty}^{0} \, dt \, f(t) \delta(t) = \frac{1}{2} f(0). It even shows up on Wikipedia (so it must be true!) Here is an argument (I know it isn't a proof). If I use the "delta-sequence" approach and...

Anyone know where I can find a discourse on the dirac delta function in spherical or polar coordinates, in particular why it is the form it is with correction coefficients? Thank you.

Homework Statement Dear all, I have a problem when I using MATLAB to get the Fourier transform of dirac delta function. below is my code.Homework Equations clear all; clc; close all; % t=0:0.002:2; t=0:0.002:4; dt=t(2)-t(1); u=zeros(size(t)); pos0=find(t>=1,1); u(pos0)=1/dt...

i don't really understand the dirac delta function in 3D. is it right that integral of f(r)d3(r-a)dt = f(a) where a = constant ,r is like variable x in 1D dirac delta function? so why when i have f(r')d3(r-r') , it picks out f(r)? where r is now a constant and r' is a...

[PLAIN]http://img820.imageshack.us/img820/5817/img8968h.jpg Any hints please, just starting question. Haven't really done any questions like this before

Hello all, I joined this amazing forum just today.I hope that my question will get answered soon. So here it is.I am unable to understand a some steps in calculation. Please help me understand. Here is a linear homogeneous first order differential equation whose solution a research...

I understand that the Dirac delta function can be taken as a distribution. And that one can calculate the Shannon entropy or information content of any distribution. So what is the information content of the Dirac delta function? I think it is probably identically zero, but I'd like to see the...

Hi, I am looking for approximations to the delta functoin which I can use on a computer. Although I will never get an exact delta function, I can make an approximation that it can be improved as much as I like. Would you help me to find the approximation of the delta function so that I can...

Homework Statement a.) Given \delta_n=\frac{ne^{-{n^2}{x^2}}}{\pi} Show: x{\frac{d}{dt}\delta_n}=-\delta_n b.) For the finite interval (\pi,-\pi) expand the dirac delta function \delta(x-t) in sines and cosines, sinnx, cosnx, n=1,2,3... They are not orthogonal, they are normalized to...

Hopefully people are still prowling the forums this close to christmas :) I want to show that sin(ax)/x is a representation of a delta function in the limit a->infinty i.e 1) It equals 0 unless x=0 2) integrated from plus minus infinity it equals 1 and 3) multiplying by an arbitrary...

Homework Statement Let's say we have a wire of finite length L with total charge Q evenly spread along the wire so that lambda=Q/L, linear charge density, is constant. The wire is shaped in x-y plane in some well behaved curve y = f(x). Find the surface charge density sigma(x,y). Homework...

I don't understand in the first paragraph of the attached lecture notes. Could anyone help?

What is the way to show that \lim_{y\rightarrow0}\frac{y}{x^2+y^2}=\pi\delta(x) ?

Homework Statement I am new to FT and dirac delta function. Given the following signal: x\left(t\right)=cos\left(2\pi5t\right)+cos\left(2\pi10t\right)+cos\left(2\pi20t\right)+cos\left(2\pi50t\right) I use the online calculator to find me the FT of the signal, which is...

Hello, My question is about how dirac-delta function is derived by using this integral, \frac{1}{2\pi }\int_{-\infty}^{\infty}e^{ikx}dk=\delta (x) I couldn't solve this integral. Please help me. Thanks for all of your helps.

Homework Statement Pro #2 if you click on this link. http://s1104.photobucket.com/albums/h332/richard78931/?action=view&current=hw4.jpg Homework Equations , The Attempt at a Solution Click here http://s1104.photobucket.com/albums/h332/richard78931/?action=view&current=2a.jpg...

Hi there! I have a problem with one of the questions given to us in the signals and systems course. If anyone could help me I would greatly appreciate it! Homework Statement integral(from -infinity to +infinity) of u0(t) * cos(t) dt u(t) is a step function. Homework Equations...

Homework Statement Hi All. I am given this integral: \int_{-\infty}^{\infty}A\Theta e^{i\omega t}dt I need to show that it's equal to the following: =A(\pi \delta(\omega)+\frac{i}{\omega})Homework EquationsTheta is the Heavyside step function. The Attempt at a Solution The step function...

Homework Statement I want to plot the following function into Maple14. \vec{v}=frac{1}{\vec{r^{2}}} \hat{r} **In case the latex is screwed this says v=r^(-2) *r-hat The Attempt at a Solution My code for Maple is the following, but it doesn't seem to work.restart; with(LinearAlgebra)...

Hi Can somebody help me with this... Is is correct to say that, Integral(delta(0)) = 1 (limits are from -infinity to +infinity) I don't know latex and sorry for the inconvenience in readability. Thanks, VS

Hi, I hope this is the right place to ask this Is it possible to expand the Dirac delta function in a power series? \delta(x)=\sum a_n x^n If so, what's the radius of convergence or how can I find it? Thanks.

Suppose I wind up with the relation f(x)\delta (x-x')=g(x)\delta (x-x') true for all x'. Can I safely conclude that f(x) = g(x) (for all x)? Or am I overlooking something? this is a little too close to dividing both sides by zero for comfort.

I'm trying to evaluate the energy shift in a scalar field described by the Klein-Gordon equation caused by adding two time-independent point sources. In Zee's Quantum Field Theory in a Nutshell, he shows the derivation for a (3+1)-dimensional universe, and I'm trying to do the same for an...

I'm curious about the use of the Dirac Delta function. I am familiar with the function itself, but have never really seen in used in actual problems. The only problems I've worked with the function are those specifically about the function (ie. Evaluate the Dirac Delta function at x=3). My...

how do we apply dirac delta function?when do we apply?

r(x) = x if x \geq 0 and r(x) = 0 if x<0 I have to show that: 1-\[ \int_{- \infty}^{+ \infty} r(x) \varphi ''(x) dx = \varphi(0) \] And 2- that the second derivative of r is the Dirac delta. And I managed to do this by integrating by parts. Howver, I don't get why I can't just write: \[...

Hi, In Srednicki's chapter on cross sections, when he calculating the probability of a particular process from the overlap \langle f\mid i\rangle he comes across: [(2\pi)^4\delta^4(k_{in}-k_{out})]^2 He states this is can be equated as follows: [(2\pi)^4\delta^4(k_{in}-k_{out})]^2=...

Homework Statement show that the charge distribution (|\vec{r}|\equiv r ) \rho(r) = Z\delta^3(\vec{r})-\frac{Ze^{-r/R}}{4\pi R^2r} has zero net charge for any Z and R. Explain the meaning of Z. Homework Equations none given, but divergence (gauss) theorem and poisson's equation may...

Homework Statement Prove that \delta(at)=\frac{1}{abs(a)}\delta(t) Hint: Show that \int\phi(t)\delta(at)dt=\frac{1}{abs(a)}\phi(0) (the limits of integration are from -inf to +inf btw, I couldn't find how to put them in..) Homework Equations The Attempt at a Solution Ok. I...

Can someone tell me how to express a line of charge of charge per unit length \lambda as a delta function volume charge density in cylindrical coordinates?

I tried to calculate the volume of a simplex, but got an integral I couldn't do. For simplicity take a 2-simplex (the volume of a 2-simplex is 1/6) V=\int da \int dx \int dy \int dz \mbox{ } \delta(1-a-x-y-z) where the integration limits are over the 4-cube. My reasoning for this formula...

Homework Statement Using Dirac delta function in the appropriate coordinates, express the following charge distributions as three-dimensional charge densities p(x). (a) In spherical coordinates, a charge Q uniformly distributed over a spherical shell of radius a. (b) In cylindrical...

Homework Statement show x\frac{d}{dx}\delta(x)=-\delta)(x) using the gaussian delta sequence (\delta_n) and treating \delta(x) and its derivative as in eq. 1.151. Homework Equations the gaussian delta sequence given in the book is \delta_n=\frac{n}{\sqrt{\pi}}e^{-n^2x^2} and eq...

Homework Statement Distribution of matter is given in cylindrical coordinates: \rho(\vec{r})=\frac{1}{\rho}\delta(\rho^2-10\rho+9)\delta\left(\frac{z^2-a^2}{z^2+a^2}\right)\delta(\cot(\phi)) where a>0 is a constant. Find the complete mass of the object. Homework Equations The...

Hello, Dirac Delta Function is defined as the function that its amplitude is zero everywhere except at zero where its amplitude is infinitely large such that the area under the curve is unity. Sometimes it is used to describe a function consists of a sequence of samples such as...

Dirac delta function as the limit of a sequence Hi.. If I have a sequence which in some limit tends to infinity for x=0 and goes to zero for x\neq0, then can I call the limit as a dirac delta function? If not, what are the additional constraints to be satisfied?

Claim: \nabla \cdot \frac{\hat{e}_r}{r^2}=4\pi\delta^3(\vec{x}) Anyone know of a proof of this? (or a reference which covers it?) We need to show that \frac{1}{4\pi}\int_0^R{(\nabla \cdot \frac{\hat{e}_r}{r^2})f(r)dr=f(0). The claimed identity can be seen in the solution for...

Homework Statement Evaluate the following integrals: \int^{+\infty}_{-\infty}\delta[f(x)]dx and \int^{+\infty}_{-\infty}\delta[f(x)]g(x)dx Homework Equations \int^{+\infty}_{-\infty}\delta(x)dx=1 \int^{+\infty}_{-\infty}\delta(x)f(x)dx=f(0) \int^{+\infty}_{-\infty}\delta(x-a)f(x)dx=f(a)The...

I know I haven't entered the formulae with the proper syntax, but I'm extremely exhausted at the time of posting, so please just read it and give advice, forgiving me this once for not using proper form (it's basically in latex code format). Homework Statement Show...

I'm trying to understand the multiple limit processes involved with the Dirac delta function. Does it matter which process you do first the integral or the delta parameter that approaches zero? The closest theorem I found that addresses the order of taking limits is the Dominate Convergence...

We all know that \frac{1}{2\pi}\int{e^{ik(x-x')}dk=\delta(x-x'). i am working a problem which appears to depend on the statement \int e^{z^*(z-w)}dz^*\propto\delta(z-w) Does anyone know if this is valid? \delta(z-w) is defined in the usual way so that...

Claim: if \psi is a variable grassmann number, then \delta(\psi)=\psi is a Dirac delta function for integrals over \psi. I'm not seeing this. A general function of a grassmann number can be written f(\psi)=a+b\psi because anti-commutativity requires \psi^2=0. According to the wikipedia...

Hello, I have just integrated over one variable, x and have now got a delta function \delta(m) where m = constant * (s-s') now I have to integrate over either s or s' but I am a bit confused since if I integrate over say s then the delta function depends on s. Hope I have explained clearly...

I do not know how to execute the problem with the 2x in the problem. Evaluate the integral: \int_{-4}^{4} (x^2+2x+1) \delta(2x) dx

Homework Statement Given f(x,y) = DeltaFunction(y - x*tan(theta)) a) Plot function. b) Take Fourier transform. c) Plot resulting transform. Homework Equations Delta function condition non-zero condition DeltaFunction(0) = Infinity Sifting property of delta functions The...

First of all, let me copy the standard solution from Griffiths, section 2.5, just for the sake of clarity. PotentialV(x) = - \alpha \delta (x) The bound state eigenfunction: \psi (x) = \left\{ \begin{array}{l} B{e^{\kappa x}}{\rm{ (}}x \le 0{\rm{)}} \\ B{e^{ - \kappa x}}{\rm{...