Delta Definition and 1000 Threads

Homework Statement Prove that if ##\left |x-x_{0} \right | < \frac{\varepsilon }{2}## and ##\left |y-y_{0} \right | < \frac{\varepsilon }{2}## then ##|(x+y)-(x_0+y_0)| < \varepsilon ## and ##|(x-y)-(x_0-y_0)| < \varepsilon ##Homework Equations Postulate and proof with real numbers as well...

Why would we use delta sign such as Delta x but we can just call the missing part x rather than delta x, I mean what's the difference between using delta x and just x?

Homework Statement V(x) = \begin{cases} \infty & , & x<0 \\ -g*\delta (x-a) & , & x>0 \end{cases} \text{ }Write the wave function in the left side of x=a and right side of x=a (BOUND STATE) The Attempt at a SolutionIn the right side o x=a i would say that it is \psi...

Dear all, I just wondered whether there was any standard identity to help me solve this equation: $$ \int \delta(f(x))^{\prime\prime}g(x) dx $$ Thanks in advance for your help.

I know this probably belongs in one of the math sections, but I did not quite know where to put it, so I put it in here since I am studying Electrodynamics from Griffiths, and in the first chapter he talks about Dirac Delta function. From what I've gathered, Dirac Delta function is 0 for...

Greetings everyone! I have a question on how the delta-V required to reach different orbits is determined. I refer to lift-off delta-V. I'm curious to find the relationship between altitude and delta V required to get to the height. From what I have found out, the lift-off delta v to a...

So in the infinite square well, the eigenfunctions are ## \psi_n (x) = \sqrt{\dfrac{2}{a}} \sin \left( \dfrac{n \pi}{a} x \right) ## Each state is orthogonal to each other, and so ## \displaystyle \int \psi_m (x) ^* \psi_n (x) dx = \delta_{mn} ## Does this also hold if they were cosines?

Hi, I'm new to this forum but I've been aware of its existence for a while and it's pretty cool. I finally came up with a question to post so here i am :) I've read a few nice posts on this forum about this topic, but I couldn't find the answer to what I'm looking for. I'm familiar with the...

I've been reading through Spivak's calculus, and the problem is the answer key i have a hold of is for a different edition so it often doesn't answer the correct questions. Anyways, here they are: Chapter 5 problem 10 b. Prove that lim x-> 0 f(x) = lim x-> a f(x-a) c. Prove that lim...

Hi there, my version of Mathematica may be too old and I'm not finding this one by hand so any help would be appreciated: ψ''(z)=[k2/4 –M2 –kδ(z)]ψ(z), where δ(z) is the Dirac delta, k and M constants. i can solve the same equation without the M^2 term by exp(k|z|/2), but this one proves to...

Hello, For our final lab we will be given a box with three wires, the neuter is missing. In the box there is a Y or delta configuration and we can use everything to find out if it is a Y or a delta configuration. So, voltmeters or watt meters, or even something like tin foil. Can someone...

hi, the delta symbol as a tensor (in the minkovski space, in case one has to be specific), what is it exactly? is it \delta^a_b = \frac{\partial{x^a}}{\partial{x^b}} is it \delta^a_b = g^{ac} g_{cb}or is there some other definition?thanks

Hello, Two waves originated from point A and point B, waves are 'velocity-direction-dependent', can be treated as 'vectors', it took t2 time for the wave from point B to reach A, and it took time t2 for the wave from point B to reach A. Given the fact the two vectors have the same...

Homework Statement Two-electron Wavefunction: ψ(r1,r2,r12) = exp(-Ar1-Br2-Cr12), r12 = |r1-r2| A, B, and C are coefficients Calculate <ψ|δ(r12)|ψ> and <ψ|δ(r1)|ψ> Homework Equations NO The Attempt at a Solution <ψ|δ(r12)|ψ> = ∫∫dv1dv2ψ2(r1,r2,r12)δ(r12)...

Hi All, so I'm trying to tackle this DEQ: f''[x] = f[x] DiracDelta[x - a] - b, with robin boundary conditions f'[0] == f[0], f'[c] == f[c] where a,b, and c are constants. If you're curious, I'm getting this because I'm trying to treat steady state in a 1D diffusion system where...

A balanced 3 phase load is rated at S=10KVA and 500V. The device is operating at 90% nominal voltage and 100 % line current. The question is: if the load is delta connected, find the phase current in per unit and SI units. I calculated correctly that the per unit line current value is...

Speaking of delta and wye transformers and generators, why do we sometimes use one over the other? The WYE's seem easier to ground...but why pick a delta over a wye...or a wye over a delta in certain situations?

\nabla \cdot \frac{\mathbf{r}}{|r|^3}=4 \pi \delta ^3(\mathbf{r}) What's the proof for this, and what's wrong with the following analysis? The vector field \frac{\mathbf{r}}{|r|^3}=\frac{1}{r^2}\hat{r} can also be written \mathbf{F}=\frac{x}{\sqrt{x^2+y^2+z^2}^3}\hat{x}+...

I don't quite get the significance of the delta limit definition, if n>N and |sn−s|< ϵ , why does the limit converges does this simply means that there exist a number ε such that if n is great enough it will be greater than s by ε? But this doesn't make sense, because s is the value...

Prove that. \int_a^b f(x)g' (x)\, dx = -f(0) This is supposed to be a delta Dirac function property. But i can not prove it. I thought using integration by parts. \int_a^b f(x)g' (x)\, dx = f(x)g(x) - \int_a^b f(x)'g (x)\, dx But what now? Some properties: \delta...

In texts about dirac delta,you often can find sentences like "The delta function is sometimes thought of as an infinitely high, infinitely thin spike at the origin". If we take into account the important property of dirac delta: \int_\mathbb{R} \delta(x) dx=1 and the fact that it is zero...

This isn't really homework; It's just something that has been bothering me ever since I first learned calculus because I suck at epsilon-delta proofs. Homework Statement Show that 1/x is continuous at x=1 Homework Equations If |x-a|<δ Then |f(x)-f(a)|<ε The Attempt at a Solution...

Homework Statement In electrostatics it's useful to have ##\rho (\vec x )## written with Dirac's delta so that we can know the total charge by integrating the charge distribution over a region of space. Many problems/situations deal with point charges. In Cartesian coordinates for example...

What does the square of a Dirac delta function look like? Is the approximate graph the same as that of the delta function?

I'm trying to understand how the algebraic properties of the Dirac delta function might be passed onto the argument of the delta function. One way to go from a function to its argument is to derive a Taylor series expansion of the function in terms of its argument. Then you are dealing with...

is that star load will make unbalanced , delta will not? THX

Homework Statement I need to give scattering amplitude f(θ) in Born approximation to the first order in the case of delta function scattering potential δ(r). The problem is in spherical coordinate and I'll give major equation concerned.Homework Equations The equation for scattering amplitude is...

Hi, I try to prove, that function f_n = \frac{\sin{nx}}{\pi x} converges to dirac delta distribution (in the meaning of distributions sure). On our course we postulated lemma, that guarantee us this if f_n satisfy some conditions. So I need to show, that \lim_{n\rightarrow...

Hello, Is this correct: \int [f_j(x)\delta (x-x_i) f_k(x)\delta (x-x_i)]dx = f_j(x_i)f_k(x_i) If it is not, what must the left hand side look like in order to obtain the right handside, where the right hand side multiplies two constants? Thanks!

Hi there, I'm trying to comprehend Dirac Delta functions. Here's something to help me understand them; let's say I want to formulate Newton's second law F=MA (for point masses) in DDF form. Is this correct: F_i = \int [m_i\delta (x-x_i) a_i\delta (x-x_i)]dx Or is it this: F_i = [\int...

Hi, I'm working on a problem stated as: Expand the following expression and simplify where possible $$ \delta_{ij}\delta_{ij} $$ I'm pretty sure this is correct, but not sure that I am satisfying the expand question. I'm not up to speed in linear algebra (taking a continuum mechanics course) -...

Homework Statement I am trying to integrate the function \int _{-\infty }^{\infty }(t-1)\delta\left[\frac{2}{3}t-\frac{3}{2}\right]dt Homework Equations The Attempt at a Solution I think the answer should be \frac{5}{4} because \frac{2}{3}t-\frac{3}{2}=0 when t=9/4. then (9/4-1) = 5/4...

Homework Statement For a function ρ(x,y,z) = cδ(x-a), give the meaning of the situation and describe each variable. Homework Equations As far as units go, I know that: ρ(x,y,z) = charge density = C/ m^3 δ(x-a) = 1/m and if those two are correct, then b must have units of (C/m^2)...

Does the Dirac delta fuction have a residue? Given the close parallels between the sifting property and Cauchy's integral formula + residue theory, I feel like it should. Unfortunately, I have no idea how they tie together (if they do at all).

Homework Statement compute the integral: \int_ {-\infty}^\infty \mathrm{e}^{ikx}\delta(k^2x^2-1)\,\mathrm{d}xHomework Equations none that I have The Attempt at a Solution I don't actually have any work by hand done for this because this is more complex than any dirac delta integral I have...

Hi all, I'm familiar with the fact that the dirac delta function (when defined within an integral is even) Meaning delta(x)= delta(-x) on the interval -a to b when integral signs are present I want to prove this this relationship but I don't know how to do it other than with a limit...

hello, Please attached snapshot. Does the integral 7.9 equal to 0.5 \inthμσ dzμ/dτ dzσ/dτdτ ? I'm confused as to the fourth power of Dirac's Delta. Then where does the derivative on x go ? For more on this, see MTW pg180 thanks

How is that two hot phases can be put into a transformers and it not blow up? i have asked this question many different times to different engineers at work and I'm tired of hearing "just because". please explain in detail

I'm going through a list of 12 transformers and trying to determine if they are wye or delta. The schematics I have come across are for power engineering and don't go into too much detail other than the following: The transformers step down ~400V 60Hz AC (three-phase) to ~120V 60Hz AC (single...

Hi All, I have a problem in understanding the concept of dirac delta function. Let say I have a function, q(r,z,t) and its defined as q(r,z,t)= δ(t)Q(r,z), where δ(t) is dirac delta function and Q(r,z) is just the spatial distribution. My question are: 1. How can I find the time derivative...

Homework Statement When constructing an Epsilon Delta proof, why do we need to make a stipulation? For example, in most proofs for limits of quadratic functions, it is stipulated, for example, that δ≤1. Why is this needed anyway? This is my thought process for a quadratic: Prove that lim(x...

I have been wondering exactly how one would express the Dirac delta in arbitrary spaces with curvature. And that leads me to ask if the Dirac delta function has a coordinate independent expression. Is there an intrinsic definition of a Dirac delta function free of coordinates and metrics? Or as...

Homework Statement I have to integrate: \int_0^x \delta(x-y)f(y)dy Homework Equations The Attempt at a Solution I know that the dirac delta function is zero everywhere except at 0 it is equal to infinity: \delta(0)=\infty I have to express the integral in terms of function...

The Fourier series of a delta train is supposedly (1/T) + (2/T ) Ʃcos(nωt) ... where T is period and ω=2*Pi/T ...but when I plot this, it doesn't give me just a spike towards positive infinity, but towards negative infinity as well (see attached pic), so this does not seem to converge to the...

I am testing a cylindrical piece of steel dropping down steel pipe in a vacuum system, and came across a problem comparing the kinematic equation and a standard change in velocity over change in time to determine an acceleration. My derivation shows that the kinematic equation is exactly 2...

Homework Statement L[t^{2} - t^{2}δ(t-1)] Homework Equations L[ t^{n}f(t)] = (-1^{n}) \frac{d^{n}}{ds^{n}} L[f(t)] L[δ-t] = e^-ts The Attempt at a Solution My teacher wrote \frac{2}{s^{3}} -e^{s} as the answer. I got \frac{2}{s^{3}} + \frac{e^-s}{s} + 2 \frac{e^-s}{s^2} + \frac{2e^-s}{s^3}

Integrating the delta function: $$ \frac{4}{\pi^2}\int_0^{\pi}\int_0^{\pi}\delta(x - x_0,y - y_0)\sin nx\sin my dxdy $$ Would the solution be $\frac{4}{\pi^2}\sin nx_0\sin my_0$?

Homework Statement Evaluate the Laplace transform: L{δ(t-∏)tan(t)} Homework Equations The Attempt at a Solution L{δ(t-∏)tan(t)} = ∫ δ(t-∏)tan(t) dt evaluated from 0 to ∞ =tan(∏)e-∏*s = 0 Could someone check my work on this one? I'm suspicious that my transform is just zero...

Can you always put numbers directly into an expression which has the delta triangle against its variables? For example Faraday's Law is always shown with the delta triangle on top and bottom yet these are dropped when you use it for calculations; which leaves me wondering why they are there in...

Homework Statement Consider this situation, V(x)=λδ(x) ,-a<x<a. V(x)=∞,x>a or x<-a. How to find the eigenvalue and eigen wavefuntion of the Hamiltonian. Homework Equations i can only reder to stationary Schrodinger equation. The Attempt at a Solution when it is ouside the well(x>a...