Delta Definition and 1000 Threads

when using delta function \delta(r) in cordinates othe then cartesian when does it needs to be divided by the jacobian for example in spherical coordinates \delta(x)=\frac{1}{r^2sin(\vartheta)}\delta(r-r_{0})\delta(\vartheta-\vartheta_{0})\delta(\phi-\phi_{0}) but if you want a delta...

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

Meanwhile, somewhere in a backyard in Europa, a tiny TV station, RTL4 did something not seen before. It admitted that climate issues had been greatly exagarated to pursue a political project. Obviously, The Netherlands being mostly a river delta below sea level should be very keen to keep...

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...

Homework Statement write the radial equation for a particle with mass m and angular momentum l=0 which is under the influence of the following potential: V(r)=-a*delta(r-R) a,R>0 write all the conditions for the solution of the problem.Homework Equations Schroedinger's equation: Hu=Eu...

Homework Statement Consider the double delts-function potential V(x)=-\alpha[\delta(x+a)+\delta(x-a)] How many bound states does this possess? Find the allowed energies for \alpha=\frac{\hbar^{2}}{ma^{2}}and\alpha=\frac{\hbar^{2}}{4ma^{2}}Homework Equations The Attempt at a Solution I divided...

[SOLVED] Dirac delta function Homework Statement Prove that \delta(cx)=\frac{1}{|c|}\delta(x) Homework Equations The Attempt at a Solution For any function f(x), \int_{-\infty}^{\infty}f(x)\delta(cx) dx = \frac{1}{c}\int_{-\infty}^{\infty}f(t/c)\delta(t) dt where I have...

I can't get my head around the epsilon-delta definition of a limit. Unfortunately I don't have a teacher to ask (I'm teaching this to myself as a self interest) so this forum is my last resort -- google hasn't been kind to me. From what I've seen, I don't really understand how the definition...

This is probably a silly question to some, but I've been struggling to understand how the delta function behaves when given a complex argument, that is \delta(z), z \in C. I guess the basic definition is the same that the integral over all space is 1, but I'm looking for a more detailed guide on...

[SOLVED] Dirac delta function and Heaviside step function In Levine's Quantum Chemistry textbook the Heaviside step function is defined as: H(x-a)=1,x>a H(x-a)=0,x<a H(x-a)=\frac{1}{2},x=a Dirac delta function is: \delta (x-a)=dH(x-a) / dx Now, the integral: \int...

[SOLVED] Fourier transform of a function such that it gives a delta function. ok say, if you Fourier transform a delta function G(x- a), the transform will give you something like ∫[-∞ ∞]G(x-a) e^ikx dx a is a constant to calculate, which gives you e^ka (transformed into k space)...

Trying to solve the ODE mx''(t) + bx'(t) + kx(t) = F(t) with m measured in Kg, b in Kg/s and Kg/s^2, F(t) in Kgm/s^2 and x(t) in m with initial conditions x(0) = 0 and x'(0) = 0, i got the following Green's function G(t,t') = \frac{1}{m\omega} e^{-\omega_1(t-t')}\sinh\left[\omega(t-t')\right]...