Delta function Definition and 366 Threads

Using perturbation theory, I'm trying to solve the following problem \frac{\partial P}{\partial \tau} = \frac{1}{2}\varepsilon^2 \alpha^2 \frac{\partial^2 P}{\partial f^2} + \rho \varepsilon^2 \nu \alpha^2 \frac{\partial^2 P}{\partial f \partial \alpha} + \frac{1}{2}\varepsilon^2 \nu^2...

Homework Statement By using the substitution u=cosx obtain the value of the integral \int\delta(cosx-1/2)dx between 0 and pi Homework Equations I have no idea how to go any further with this apart from substituting in for u!? The Attempt at a Solution

that is 0 everywhere and 1 at 0. the code I wrote was this: n = -20:1:20; if n==0 imp = 1 else imp = 0; end >> stem (n, imp) ? Error using ==> stem at 40 X must be same length as Y. but i got that error. Using vectors and matrices is useless cause the delta...

Homework Statement How do you show that int[delta(t)]dt from negative infinity to infinity is 1? Homework Equations Dirac delta function defined as infinity if t = 0, 0 otherwise The Attempt at a Solution My teacher said that it has to do with m->infinity for the following...

1. The problem statement Show that: \int_{-\infty}^{\infty} f(x) \delta^{(n)}(x-a) dx = (-1)^n f^{(n)}(a) The Attempt at a Solution I am trying to understand how to prove: \int_{-\infty}^{\infty} f(x) \delta '(x) dx =- f'(x) I know that we need to use integration by parts, but I'm...

Homework Statement Justify the following expretion, in spherical coordinates; delta (vector r) = (1 / r^2 * sin (theta) ) * delta(r) * delta(theta) * delta(phi) Homework Equations The Attempt at a Solution I don't know what it means... please help?

Griffiths' section 1.5.3 states that the divergence of the vector function r/r^2 = 4*Pi*δ^3(r). Can someone show me how this is derived and what it means physically? Thanks in advance.

Homework Statement Starting with the definition of the Dirac delta function, show that \delta( \sqrt{x}) um... i have looked in my book and looked online for a problem like this and i really have no clue where to start. the only time i have used the dirac delta function is in an integral...

Hi I have been trying to learn dirac delta function. but its kind of confusing. I come across 2 contrasting definitions for it. The first one states that the function delta(x-xo) is infinite at x=x0 while the other states that delta(x-x0) tends to infinite as x tends to x0. Now both of them...

Let A, M be a commutative ring and a finitely generated A-module respectively. Let \phi be an A-module endomorphism of M such that \phi (M)\subseteq \alpha\ M where \alpha is an ideal of A. Let x_1,\dots,x_n be the generators of M. Then we know that \displaystyle{\phi(x_i)=\sum_{j=1}^{n}...

Hey there! I'm faced with this problem: http://img7.imageshack.us/img7/4381/25686658nz9.png It's a 1D nonhomogeneous wave equation with a "right hand side" equaling to the dirac delta function in x * a sinusoidal function in t. I have to find its general solution with the constraints...

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 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?

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.

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...

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...

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

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 ...

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} =...

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...

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...

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...

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 >...

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 ...

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...

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...

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)...

OK, so my basic understanding of Dirac Delta Function is that it shows the probability of finding a point at (p,q) at time t. Dirac Delta is 0 everywhere except for (p_{0},q_{0}). So my question comes Is it possible that a point enters the (p_{0},q_{0}) and stays there (for some period of...

is there a form to define the dirac delta function for complex values ? i mean \delta (x-a-bi) or \delta (-ix) using 'test functgions' i get that they converge nowhere (always infinite) which makes no sense at all, using scalling properties we could define \delta (ix) = \delta(x)...

Alright...so I've got a question about the convolution of a dirac delta function (or unit step). So, I know what my final answer is supposed to be but I cannot understand how to solve the last portion of it which involves the convolution of a dirac/unit step function. It looks like this: 10 *...

Alright, I'm in my first QM course right now, and one of the topics we've looked at is solving the one-dimensional time-independent Schrodinger equation for various potentials, such as the harmonic oscillators, infinite and finite square wells, free particles, and last, but not least, the dirac...

Homework Statement I would like to prove that \delta(ax)={\delta(x) \over {|a|}}. My problem is that I don't know how the absolute value brackets arise. Homework Equations \int_{-\infty}^{\infty} \delta(x)dx = 1The Attempt at a Solution I start from \int_{-\infty}^{\infty} \delta (ax) dx, and...

with limits from 0 to 1 \int delta(x) * cos(x) dx does this delta function integral even make sense from 0 to 1?

The Dirac delta function, \delta (x) has the property that: (1) \int_{-\infty}^{+\infty} f(x) \delta (x) dx = f(0) Will this same effect happen for the following bounds on the integral: (2) \int_{0}^{+\infty} f(x) \delta (x) dx = f(0)...