Delta Definition and 1000 Threads

how to find the second derivitive of delta function?

By definition of the Dirac delta function, we have: \int f(x) \delta(x-a) dx=f(a) This is fair enough. But in ym notes there is a step that goes like the following: \mathbf{\nabla} \wedge \mathbf{B}(\mathbf{r})=-\frac{\mu_0}{4 \pi} \int_V dV'...

Homework Statement Evaluate the integral: Homework Equations To integrate this, should one use a dummy variable to get the delta function only of t, then integrate, then substitute back in after integration?

Homework Statement This is problem 2.46 from Griffith's Electrodynamics. I've already solved the problem but there is one aspect of the solution which bothers me and I can't think of where it is originating. I have found that the potential given in the problem produces an electric field...

I am still very confused about the differences between all the d's and delta's used to represent infinitesimal elements and/or derivatives and never know when and where to use what: - du - \partial u - \delta u For instance what can be simplified exactly in the chain rule and also what to...

I cannot get the answer as from the solution manuel. Please tell me what am I assuming wrong. Thanks

In a book on QM are listed a few properties of the delta function, one of which is: x \delta^{-1}(x) = - \delta(x) I can't figure out how to interpret that? Putting the statement in integral form isn't particularily enlightening looking: f(x) = \int f(x-x') \delta(x') dx' = \int...

I'm posting this here because I'm asking about the mathematical properties of the Dirac delta function, delta(x) which is zero for all non-zero real values of x and infinite when x is zero. The integral (-inf to +inf) of this function is said to be 1. How is this derived?

There is an overhead door at work that will start to open but then stops. I don't know all the details because I haven't been out to the door yet, but the information has been given to me by one of my guys. The door is driven by a 3-phase 480 volt motor. I don't know anymore information...

Homework Statement Hi there, i am trying to do a proof that H'(t)= δ(t) Homework Equations We have been given the following: F is a smooth function such that lim (t-->±∞)F(t)=0 Therefore the integral between ±∞ of [H(t)F(t)]'=[H(t)F(t)]∞-∞=0 I understand it up until this point...

I'm studying limits now (for the first time) and though have understood the intuitive concept of limit, I didn't get at all the epsilon-delta concept. What is epsilon and delta? What is x-2? I didn't get anything at all. So please explain me these in detail. Thanking you in advanced...

No answer in the linear algebra section, so I'll try here. ("Calculus & analysis" would probably have been more appropriate than "linear algebra"). I have a question about the delta function. Link.

Hi everyone, I need help finding the Fourier transform of Cos(10t)sin(t) i know that i need to find the transform of cos and sin and then convolve them, but i m not sure how to convolve delta function. I would really appreciate any helps.

Anyone use sleep machines? My father is asking one for xmas. Are they really just cd players or is there more to it? For example this Brookstone one I am looking at has claims of delta wave technology. Is that bunk?

Hey everybody, One question that I've had for a week or so now is how the following integral can equal a Dirac delta function: \frac{1}{2\pi} \int_{-\infty}^{\infty}{dt} \:e^{i(\omega - \omega^{'})t}\: = \: \delta(\omega - \omega^{'}) A text that I was reading discusses Fourier transforms...

Homework Statement particle of mass m is subjected to antisymmetric delta-function potential V(x) =V'Delta(x+a)-V'Delta(x-a) where V'>0 Show that there is only one bound state, and find its energy Homework Equations Assuming free particle eqn for x<-a for particle incident from -ve...

When working with Fourier transforms in Quantum mechanics you get the result that \int_{-\infty}^{\infty}e^{-ikx}e^{ik'x} = \delta(k-k') I understand conceptually why this must be true, since you are taking the Fourier transform of a plane wave with a single frequency element. I have also...

Homework Statement I have to show that the delta function bound state energies can be derived from the finite square well potential. Homework Equations The wave functions in the three regions for the finite square well. (See wikipedia) The Attempt at a Solution 1. I start from the...

I don't know how yor format this, so: x3 + x2 +x +1 The limit of that function = 0 as x approaches -1 What's the greatest value of delta when epsilon = 0.1? This is what I tried to do: |x3 + x2 + x + 1| < 0.1 -0.1 < x3 + x2 + x + 1 < 0.1 -1.1 < x3 + x2 + x < -0.9 In my...

Hi. Recently day, I tried to solve quantum mechanics problem in liboff fourth version to prepare graduate school. But what make me be confused a lot is Dirac Delta Function. One of my confusing on Dirac Delta is what i wrote below. -One of the formula describing Dira Delta...

You see the variables in the kinematic equations expressed as different things sometimes such as t, delta t, dt; or d, delta x, dx; What are all the different forms of the kinematic equations with these different variables? Do you approach certain problems with certain forms or can they all...

How does one prove: limit xy = ab x-> a y -> b using the precise definition of a limit? My attempt: |xy-ab|<ϵ for: 0<|x-a|<δ/2 0<|y-b|<δ/2 it follows that: δ/2-a <x< δ/2+a δ/2-b <y< δ/2+b then: (δ/2-a)(δ/2-n) < xy < (δ/2+a)(δ/2+b) (δ^2/4-aδ/2-bδ/2 +ab)...

Homework Statement consider the scattering matrix for the potential 2m/hbar2 V(x) = λ/a δ(x-b) show that it has the form (2ika/(2ika-λ) , (e-2kib) λ/(2ika-λ) (e2kib) λ/(2ika-λ) , 2ika/(2ika-λ) (I've used commas just to separate terms in the matrix) prove...

Okay for a simple finite limit: e.g. lim (3x) = 3 x->1 in the end I say: "Therefore for every |x - 3| < delta, there exists an epsilon such that |3x-3| < epsilon" Hence I can make delta really really small and the y bounds of epsilon will constrain the limit. So let's come to...

hello every body i am a new M.S student and i can't understand the Dirac delta function can anyone simply describe it to me in order to simplify it. thank you

1. Why delta PE=-W? In gravitation’s case, If we look at it numerically, PE= mg (b-a), W=F (b-a), then they are the same, where does the negative sign come from? Maybe that has to do with against gravitation or not? Vba=-Wba/q has the same concept. But here is one question: What minimum work...

Homework Statement I want to measure this integral ( Sd(x)δ(χ-c) , where c is constant Thanks in advancE Homework Equations The Attempt at a Solution

where can I read about distributions and the delta function. esp. to solve singular integrals. I have seen that you could write 1/x = \delta (x) + P.V (1/x) and all that stuff.. where can i read about it ...

Find a distribution F in R^2 that satisfies (Dx) F(x,t) = t*Delta(x) It is apperantly not t*H(x) as in R. * is multiplication, D is dirac delta, H is Heavyside , (Dx) is derivation with respect to x (in the sense of distributions) Sorry for not using Latex. Indeed I am trying to...

Hello everyone Today in my QM class, a discussion arose on the definition of the delta function using the Heaviside step function \Theta(x) (= 0 for x < 0 and 1 for x > 0). Specifically, \Theta(x) = \int_{-\infty}^{x}\delta(t) dt which of course gives \frac{d\Theta(x)}{dx} =...

Derivative Using Dirac Delta Function Homework Statement Let \theta(x) be the step function: \theta(x) be equivalent to 1, if x > 0 0, if x \leq 0 Show that \frac{d \theta }{dx} = \delta(x) Homework Equations In the previous portion I was able to prove x \frac{d}{dx}...

Hi everyone, I was wondering how to deal with delta functions of functions that have double zeros. For instance, how does one compute an integral of the form \int_{-\infty}^{\infty}dx g(x)\delta(x^2) where g(x) is a well behaved continuous everywhere function? In general how does one find...

I've come across a proof for star-delta transformation which goes like this.(Refer to the diagram for notation. Pardon me for my bad drawing skills.) In the delta, he found the effective resistance between two vertices ( say a and c, which can found easily). Then he found the effective...

Which of the following are true in curved spacetime? \int d^4 x \delta^4(x - x_0) = 1 (1) \int d^4 x \sqrt{-g} \delta^4(x - x_0) = 1 (2) I think the first one is incorrect in curved spacetime, or in general when the metric is non-constant. I would argue this by saying that the delta...

Show that \stackrel{lim}{\alpha \rightarrow \infty} \int^{\infty}_{-\infty}g(x)\sqrt{\frac{\alpha}{\pi}}e^{-\alpha x^2} dx = g(0) where g(x) is continuous. To use the continuity of g(x) I started from \left|g(x)-g(0)\right|<\epsilon and tried to put it in into the integral...

So let's say we have a particle in the delta function potential, V = - \alpha \delta(x). I calculated that the reflection coefficient (scattering state) is R = \frac{1}{1 + (2 \hbar^2 E/m\alpha^2)} Now, clearly, the term 2 \hbar^2 E/m\alpha^2 is very small, as \hbar^2 has an order of magnitude...

Given: f(x)=\delta(x-a) Other than the standard definitions where f(x) equals zero everywhere except at a, where it's infinity, and that: \int_{-\infty}^{\infty} g(x)\delta(x-a)\,dx=g(a) Is there some kind of other definition involving exponentials, like: \int...

Hey everybody. I was studying Fourier transforms today, and I thought, what if you took the transform of an ordinary sine or cosine? Well, since they only have one frequency, shouldn't the transform have only one value? That is, a delta function centered at the angular frequency of the wave...

Is it true that \sum_x e^{i(k-k')x} = \delta_{k-k'} , where \delta is the Kronecker delta? I've come across a similar relation for the Dirac Delta (when the sum is an integral). I do not understand why k-k' \neq 0 implies the sum is zero. Edit: In fact, I'm really confused, since it seems...

Homework Statement Three-dimensional particle is placed in a Dirac delta potential: V = -aV_{0}\delta(r-a) Find energy states and eigenfunctions for the angular quantum number l = 0.[/ Homework Equations The Attempt at a Solution It's not clear to me what boundary...

Three-dimensional particle is placed in a Dirac delta potential: V = -aV_{0}\delta(r-a) Find energy states and eigenfunctions for the angular quantum number l = 0.

Hi, I need your help with a very standard proof, I'll be happy if you give me some detailed outline - the necessary steps I must follow with some extra clues so that I'm not lost the moment I start - and I'll hopefully finish it myself. I am disappointed that I can't proof this all by myself...

Can anyone give me a coordinate-independent definition of \delta^a_b on curved manifolds? Should it be defined as \delta^a_b = g^{ac}g_{bc} where abstract index notation has been used?

Homework Statement Find the bound state energy for a particle in a Dirac delta function potential. Homework Equations \newcommand{\pd}[3]{ \frac{ \partial^{#3}{#1} }{ \partial {#2}^{#3} } } - \frac{\hbar^2}{2 m} \ \pd{\psi}{x}{2} - \alpha \delta (x) \psi (x) = E\psi (x) where \alpha >...

Homework Statement Hey, the question is about delta function potentials V(x) = -g[... del(x + 3b/2) + del(x + b/2) + del(x - b/2) ...] going on out to a large x in either direction. a) sketch the ground-state wave fn, write the form of psi(x) for -b/2 to + b/2 b) show that e^z =...

Using Cauchy's integral theorem how could we compute \oint _{C}dz D^{r} \delta (z) z^{-m} since delta (z) is not strictly an analytic function and we have a pole of order 'm' here C is a closed contour in complex plane

in the .pdf article http://repository.dl.itc.u-tokyo.ac.jp/dspace/bitstream/2261/6027/1/jfs080104.pdf i have found the strange representation \delta (x) = -\frac{1}{2i \pi} [z^{-1}]_{z=x} and a similar formula for Heaviside function replacing 1/z by log(-z) , what is the meaning ...

[SOLVED] Epsilon Delta Proof Does this limit proof make total sense? Given : "Show that \lim_{x \rightarrow 2} x^{2} = 4." My attempt at it :0<|x^{2}-4|<\epsilon which can also be written as 0<|(x-2)(x+2)|<\epsilon. 0<|x-2|<\delta where \delta > 0. It appears that \delta = \frac...

in peskin-schroeder and http://www.hep.phy.cam.ac.uk/batley/particles/handout_04.pdf" the amplitude for e^-e^+\rightarrow \mu^- \mu^+ is written using feynman rules as follows -iM=[\bar{v}(p_2)(-ie\gamma^\mu )u(p_1)] \frac{-ig_{\mu\nu}}{q^2}[\bar{u}(k_1)(-ie\gamma^\nu )v(k_2)] but what...

hi,... i unfortunately couldn't find a solution to this problem although it seems like a classical textbook problem... how can i solve the (time independent) schroedingerequation for the following potential V(x) = \infty for x<=-1 V(x) = a\delta(x) for -1<x<1 V(x) = \infty for x>=1 so at x=0...