Delta Definition and 1000 Threads

This problem is a symmetric delta potential problem that I was given a few days ago and I can't seem to get the gist of it. Question: Find the spectrum and wave functions of a particle in the potential V(x)=G[d(x-a)+d(x-a)] Calculate the transmission and reflection amplitude. Where G can be...

the question is , can a delta function /distribution \delta (x-a) solve a NOnlinear problem of the form F(y,y',y'',x) the question is that in many cases you can NOT multiply a distribution by itself so you could not deal with Nonlinear terms such as (y)^{3} or yy'

Find the value of delta that corresponds to 0.75. Give your value of delta where delta or any positive number will satisfy the conditions . give the answer correct to 3 decimal places, round down if necessary. lim (4+x-3x^3)=2 x-->1

I need to show that: \delta(g(x)) = \sum_k \frac{\delta(x-x_k)}{|g'(x_k)|} where the set {x_k} are the zeros of g(x) and g'(x_k) \neq 0 I'm not really sure where to start for this problem, any clues would be much appreciated!

Given f(x) = x2, L = 4, xo = -2, e = 0.5 find delta. -0.5 < x2 - 4 < 0.5 3.5 < x2 < 4.5 (3.5)1/2 - (-2) < x - (-2) < (4.5)1/2 - (-2) =>|x - xo| < (3.5)1/2 - (-2) ~ 3.87 My text says the answer is 0.12 ? I was convinced that I have been doing these right. Am I?

I know that this question was posted before but I just couldn't get it using another way around. So your comments are highly appreciated. In the textbook, \nabla\bullet\left(\widehat{r}/r^{2}\right)=4\pi\delta^{3}\left(r\right). But when I want to calculate the divergence using Catesian...

Let f(X)=\frac{\sin(2x)}{x} and use a graphing utility to conjecture the value of L = \lim_{x->0}f(x) \mbox{ then let } \epsilon =.1 and use the graphing utility and its trace feature to find a positive number \delta such that |f(x)-l|< \epsilon \mbox{ if } 0 < |x| < \delta . My...

Homework Statement This is Example 5 in Chapter 2.3 of the above mentioned text: Problem: Prove that the \lim_{x\rightarrow2}f(x)=4 if f(x)= x^2 \text{ for }x\ne2\text{ and }f(x)=1\text{ for }x=2 Solution Step 1 Solve the inequality |f(x)-4|<\epsilon to find an open interval...

Homework Statement Evaluate the following sums, implied according to the Einstein Summation Convention. \begin{array}{l} \delta _{ii} = \\ \varepsilon _{12j} \delta _{j3} = \\ \varepsilon _{12k} \delta _{1k} = \\ \varepsilon _{1jj} = \\ \end{array} The Attempt at a...

A positive number epsilon (e) and a limit L of a function f at a are given. Find delta such that |f(x)-L|< epsilon if 0 < |x-a| < delta. \lim_{x->5}, 1/x= 1/5, \epsilon=.05. That implies the following |\frac{1}{x}-\frac{1}{5}|< \epsilon \mbox{ if }|x-5|<\delta. Which implies...

45. A gas sample expands from Vo to 4.0Vo while its pressure decreases from po to po/4.0. If Vo = 1.0m^3 and po = 40 Pa, how much work is done by the gas if its pressure changes with volume via (a) path A, (b) path B, and (c) path C? The p-V diagram can be found at the following addrs on...

I have started studying maths on my own using a University maths book that may not lend itself to self study. So I was hoping someone could help me with the following.abs{sqrt{x}-2} < .05 if 0 < abs{x-4} < delta. I rewrite this as abs{sqrt{x}-2} < .05 if abs{(sqrt{x}+2)(sqrt{x}-2)} < delta...

Find the delta for the given epsilon. lim (1/x) =1 epsilon=.07 x->1 Homework Equations The Attempt at a Solution I got to here .07526 >x-1> -.06542 so what one is me delta??

since dirac delta function is not a literally a function but a limit of function,does it mean that dirac delta function is continuous and differentiable through out the infinity? is there any example of dirac delta function if yes then give meeeeeeee?

I have an example bit I can't quite follow it...? Use epsilon -delta definition of continuity to prove f(x) = 3x^2 - x is continuous at x=2 Ep > 0 and delta > 0 in terms of Ep f(x) -f(2) = 3x^2 - x -(3*2^2 -2) f(x) - f(2) = 3x^2 -x - 10 f(x) - f(2) = (3x + 5)(x - 2) So far so...

Homework Statement I had to do a curve fit on some data and got an equation to the form:Homework Equations F(t) = a_0 + a_1 t + a_2 t^2The Attempt at a Solution Each parameter has an associated uncertainty. I need to integrate F(t) over a range to get I. How do I find the the uncertainty in...

Like many people on this forum, i am seemingly having a lot of trouble grasping the concepts of Epsilon Delta proofs and the logic behind them. I have read the definition and i realize for e>0 there is a d>0 such that... 0<sqrt((x-1)^2 - (y-b)^2) < d then f(x,y) - L <e (excuse my use of...

Homework Statement \[ \underset{\left|\underline{\xi}\right|=1}{\int}\delta_{0}\left(\underline{\xi}\cdot\underline{z}\right)dS_{\xi}=\intop_{0}^{2\pi}d\varphi\intop_{-r}^{+r}\delta_{0}\left(\varsigma\right)\frac{d\varsigma}{r}=\frac{2\pi}{r}\] The \delta_{0} is the dirac delta function.the...

Hi, I am not really sure whether its over the surface of the sphere or the Volume, the problem and the solution are given below, I want to know how it has been solved. The \delta_{0} is the dirac delta function. \[...

I have been reading papers for my research and I came across this equation twice: \lim_{\eta\to 0+}\frac{1}{x+i \eta} = P\left(\frac{1}{x}\right) - i \pi \delta(x) Where P is the pricipal part. It has been quite a while since I have had complex variables, but might it come from the...

Hi. How do we argue that \nabla^2\frac{1}{r} is a three dimensional delta function? I have seen some people do it using the divergence theorem, i.e. saying that \int_V \nabla\cdot\nabla\frac{1}{r}dv=-\oint_S \nabla\frac{1}{r}\cdot ds=-4\pi if S is a surface containing the origin, but I...

Homework Statement \int_{-\infty}^t (cos \tau)\delta(\tau) d\tau Evaluate the integral. I'm supposed to evaluate this for all t I believe, so I'm concerned with t<0, t=0, t>0. Homework Equations \int_{-\infty}^{\infty} f(x)\delta(x) dx = f(0) The Attempt at a Solution...

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...

Im trying to find the number of delta rays though a material and am having some trouble with the units, can anyone help? The number of delta rays through a material is given by N=epsilon(1/E1 - 1/Emax), where epsilon=[2*Pi*A^2*e^4*ne*x]/[m*c^2], where A is unitless, [ne]=cm^-3, and the...

Homework Statement The problem straight out of the book reads: Prove that the Kronecker delta has the tensor character indicated. Prove also that it is a constant or numerical tensor, that is, it has the same components in all coordinate systems. Without a context the first sentence...

Homework Statement Im having a lot of dificulties evaluating this function, I really need some easy to understand explanation about how to evaluate it by the given values, I would appreciate any help. -Problem one given the function: U(x) = 0 if x < 0 1 if 0 ≤...

I understand most of the logic behind the formal definition of a limit, but I don't understand the the logic behind an epsilon delta proof. The parts I'm having trouble with are these: 1. How does proving that, the distance between the function and the limit is less than epsilon whenever the...

Homework Statement I have to design a lab to calculate the delta H value of the enthalpy change of ice to liquid water. It has to stay at 0*C Homework Equations Needs to be in lab format but possible q=n(delta H) where n is the molarity The Attempt at a Solution I know the...

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

Hi guys. I play now a bit with EM fields and I have encountered some problems connected with Dirac delta. By coincidence I visited this forum and I thought I could find some help in here. The problem is that in order to get a potential in some point from a single charge you need to just...

The epsilon delta rule states \epsilon_{ijk}\epsilon_{pqk}=\delta_{ip}\delta_{jq}-\delta_{iq}\delta_{jp} I am constantly using this but get stuck when it is applied. For example \epsilon_{ijk}\epsilon_{pqk}A_{j}B_{l}C_{m}=(\delta_{ip}\delta_{jq}-\delta_{iq}\delta_{jp})A_{j}B_{l}C_{m}...

Hi, if I have the confidence interval for the point estimate of an option price A which was found through simulation, can I also find a confidence interval for delta (dA/dS), where S is underlying asset price, without further simulation? thanks, sl

Previously I posted a question on the Dirac delta function and was informed it was not a true function, but rather a distribution. However, I have to admit I still did not understand why its integral (neg inf to pos inf) is unity. I've thought about this and came up with the following...

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 A simple harmonic oscillator has a frequency of 3.4 Hz. It is oscillating along x, where x(t) = A cos(ωt + δ). You are given the velocity at two moments: v(t=0) = 1.8 cm/s and v(t=.1) = -19.3 cm/s. 1)Calculate A. 2)Calculate δ. Homework Equations w= 2pi*f = 21.36 rad/s...

Can someone give me quick refresher on what happens when you multiply the heaviside function with the unit impulse? Typically, the unit step function multiplied by anything simply delays it by the offset in the unit step function. The unit impulse function makes the value defined at only one...

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 http://i634.photobucket.com/albums/uu67/danilorj/circuito.jpg Above is the picture of the circuit I'm trying to solve. The problem asks to find the current over the resistor of 1 ohm. Homework Equations The Attempt at a Solution Well, I found the equivalent...

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.

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Homework Statement im not seeing a factorization for f(x)-L<e and and not sure how to proceed in this case

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}...

Is it possible to calculate Ksp at a certain temperature if you know Ksp at a different temperature and \Delta H?

well, that's the question. They both have the same queark structure. (udd). is it only their different bound states the differentiates them?? thus giving both different masses?

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...

Kronecker Delta expression Please, give me an example of this identity using a 3 dimensional matrix R (maybe representing a rotation). My difficulty lies in the indices manipulation. R_{ii'}R{jj'}\delta_{i'j'} = \delta_{ij} I know it is obvious, but I'm really stuck in my...