Dirac delta Definition and 323 Threads

[FONT="Arial"][FONT="Arial"]Hello, What is the dirac delta function and how is it different from a probability distribution?

Suppose that we take the delta function \delta(x) and a function f(x). We know that \int_{-\infty}^{\infty} f(x)\delta(x-a)\,dx = f(a). However, does the following have any meaning? \int_{-\infty}^{\infty} f(x)\delta(x-a)\delta(x-b)dx, for some constants -\infty<a,b<\infty.

Let be the exponential: e^{inx}=cos(nx)+isin(nx) n\rightarrow \infty Using the definition (approximate ) for the delta function when n-->oo \delta (x) \sim \frac{sin(nx)}{\pi x} then differentiating.. \delta ' (x) \sim \frac{ncos(nx)}{\pi x}- \frac{\delta (x)}{\pi x}...

Hi, After reading DJGriffiths sections on the DDF I have a question about evaluating it in regards Prob. 1.46 (a), to wit: "Write an expression for the electric charge density \rho(\vec{r}) of a point charge q at \vec{r}'. Make sure that the volume integral of \rho equals q." This is easily...

Just have a question about the dirac delta function. I understand how you would write it if you want to shift it but how would you scale it assuming we are using discrete time. Would you write 2*diracdelta[n] or diracdelta[2n]. Also, would that increase it or reduce it by 2 meaning that...

I've recently come across this function in one of my science classes and am wondering were this identity comes from: \displaystyle{\int{\delta(t-\tau)f(\tau)d\tau}=f(t)} Where \delta(t) is the dirac delta function and f(t) is any (continuous?) function.

How can I prove that no continuous function exists that satisfies the property of the dirac delta function? I thought it should be pretty easy, but it's actually giving me quite a hard time! I know that the integral of such a function must be 1, and that it must also be even (symmetric about the...

Hey everyone, a quick question: what is the Fourier space representation of the dirac delta function in minkowski space? It should be some integral over e^{ikx} (with some normalization with 2*pi's). I'm curious if the "kx" is a dot product in the minkowski or euclidean sense, and how one...

I'm trying to show that \int \delta \prime(x-x')f(x') dx = f\prime(x) can I differentiate delta with respect to x' instead (giving me a minus sign), and then integrate by parts and note that the delta function is zero at the boundaries? this will give me an integral involving f' and delta...

If I had a function g(x) defined by g(x) = \int_{-\infty}^{\infty} f(x) \delta(x) dx where \delta(x) is the dirac delta function, what would dg(x)/dx be? The fundamental theorem of calculus requires that f(x) \delta(x) needs to be a continuous and differentiable function before I can...

I want to prove coulomb's low for a single charge point from the general form of coulomb's low: E→=1/(4∏€) ∫∫∫ ρv(ŕ) * (r→- ŕ→)/│(r→- ŕ→)│^3 dŕ using Dirac Delta function where r→ is the field point vector ŕ→ is the source point vector ρv(ŕ) is the volume charge density I really don't...

hello again, i have an integral to solve and not sure how to approach this: \int f(q+T)\delta (t-q)dq and the boundaries of integral are -inf +inf couldn't figure it out with latex. what I know about this is that if delta function is integrated like this, it would be just the value of...

just curiosity, if you integrate dirac-delta from exactly zero to infinity, will you get one or a-half? since it is symmetrical about zero, i think it is a half. is it? i mean: \int_{0}^{\infty} \delta(x) dx=\frac{1}{2} or is it 1? thanks.

Can someone help me understand the transition between these two steps? <x> = \iint \Phi^* (p',t) \delta (p - p') \left( - \frac{\hbar}{i} \frac{\partial}{\partial p} \Phi (p,t) \right) dp' dp = <x> = \int \Phi^* (p,t) \left( - \frac{\hbar}{i} \frac{\partial}{\partial p} \Phi (p,t)...

i can't solve there problem, please help me 1) delta(y^2-a^2) = 1/absolute 2a[delta(y-a)+delta(y+a)] 2) f(y)delta(y-a) = f(a)delta(y-a)

NOTE: I actually found the correct answer while I was typing this :rolleyes: and since I already had it typed, I figured i would post anyway. mods you can do with it as you please or leave it for reference. thanks Here's the problem: A uniform beam of length L carries a concentrated...

1. INTRODUCTION Many students become frustrated when they first meet the Dirac Delta function, typically in a course involving electrostatics, or Laplace transforms. As it is commonly presented, the Dirac function seems totally meaningless: Either, it is "defined" as...

I have a test in Diff Eq. tommorow and part of the test is inovling the Dirac Delta function. I have no clue as to what it is at all. More specifically its Laplace and Inverse Laplace. If anyone could explain to me what the delta function is and how to use in in diff eq and what are its...

Can someone explain me the Dirac Delta function for the function: \vec A = \frac{\hat r}{r^2}

let S be the Unit Step function for a function with a finite jump at t0 we have: (*) L{F'(t)}=s f(s)-F(0)-[F(t0+0)-F(t0-0)]*exp(-s t0)] so: L{S'(t-k)}=s exp(-s k)/s-0-[1-0]*exp(-s k) = 0 & k>0 but S'(t-k)=deltadirac(t-k) and we know that L{deltadirac(t-k)}=exp(-s k) so...

Okay...so here's the thing. I have been researching the dirac Delta properties. The sights I've visited, thus far, are moderately helpful. I'm looking to tackle this question I'm about to propose, so for you Brains out there (the truly remarkable :rolleyes:) please don't post a solution...

in the attatch file there is the dd function. what i want to know is: when x doesn't equal 0 the function equals 0 and the inegral is the integral of the number 0 which is any constant therefore i think the integral should be equal 0. can someone show me how this integral equals 1? for...

Supposedly, &int; ez*(z - z0)f(z) dz*dz is proportional to f(z0) much in the same way that (1/2&pi;)&int; eiy(x - x0)f(x) dxdy = &int; &delta;(x - x0)f(x) dx = f(x0) Is this true? Could someone help convince me of it, or point me to a text? I would say that even if true, it...