Delta Definition and 1000 Threads

If it's a dirac delta doesn't it mean it's infinite when x=y? Or is it a sort of kronecker where it's equal to one but the indices x and y are continuous? I'm confused.

Is it possible to take the variation of the Dirac delta function, by that I mean take the functional derivative of the Dirac delta function?

I saw this formula while studying Fourier Transform: [Sum of δ(t-lT) from l=-infinity to l= +infinity] = 1/T * [Sum Of exp(jlΩt) from l=-infinity to l=+infinity]. I am having trouble getting this into my head. How do I prove it or understand the physical meaning of this formula?

Hello I'm trying to figure out how to evaluate(in the distribution sense) \delta'(g(x)). Where \delta(x) is the dirac delta function. Please notice that what I want to evaluate is not \frac{d}{dx}(\delta(g(x))) but the derivative of the delta function calculated in g(x). If anyone could post...

Hi all, I read the following: "If g(t) starts with a delta function of strength Y/2, then..." I wonder what that means. Does it mean g(t) = 0.5Yδ(t) ? Thanks

OK, the Dirac delta function has the following properties: \int_{ - \infty }^{ + \infty } {\delta (x - {x_0})dx} = 1 and \int_{ - \infty }^{ + \infty } {f({x_1})\delta ({x_1} - {x_0})d{x_1}} = f({x_0}) which is a convolution integral. Then if f({x_1}) = \delta (x - {x_1}) we get...

hi I really need your help ... for linear time invariant system f(t) =f1(t) (convolution) f2(t) f(t) = ∫f1(t).f2 ( t-T) or f(t) = ∫f1(t-T).f2(t) where f1(t) = delta function = δ(t).δ(t-2) and f2(t) = sine wave = sin ( ∏t ) how i can solve this ... my problem is : how can i...

So far, all I understand is that the definition proves that there's a value of f(x,y) as f(x,y) approaches (x0,y0) which is sufficiently close to but not exactly the value at f(x0,y0). I am probably completely off... but I just don't understand the purpose of proving this. I also don't...

Really couldn't catch the concept on epsilon and delta in limits. Let ∂x=x2 - x1 In finding a gradient the value ∂y is taken at certain value. But in finding area using integral, the ∂y is seen to taken as zero. F(x2)=F(x1) Maybe one multiplication and the other is division.

Hello, I'm dealing with the following equation: A e^{jat} + B e^{jbt} = C e^{jct} \forall t \in \mathbb{R} My book says: given nonzero constants A,B,C, if the above equation yelds for any real t, then the a,b,c constants must be equal. The above statement is prooved by taking the Fourier...

Hello All, I am finding the hardest time in understanding how to work δ & ε Open Set Problems? Can someone please explain this approach to me? Thanks in Advance

hi! i have a question regarding the delta function. if i have a delta distribution with an argument that is a function of multiple arguments, somthimg like: ∫δ(E-p^{2}_{i}/2m)dp^{N}, ranging over +-∞ now, the argument of the delta function vanishes on a sphere. i can evaluate the...

I realize it's not a function in the classical sense, but how would one show that the delta dirac function is a distribution i.e. how do I show it's continuous and linear given that it's not truly a function?

Homework Statement Calculate the value of Go for the formation of 1 mol of phosphorus trichloride from its constituent elements: P2(g) + 3 Cl2(g) ---> 2 PCl3(g) The attempt at a solution I thought of trying delta G = delta H - T deltaS , but I'm lost on where to start...

Hi there, I am trying to integrate this: http://imm.io/oqKi I should get the second line from the integral, but I can't show it. This should somehow relate to the Heaviside step function, or I am completely wrong. Any ideas? Sorry about the url, I fixed it.

Hello team! I saw the other day in a textbook that the Dirac delta function of the form d(x-a) can be written as d(a-x) but the method was not explained. I was wondering if anyone know where this comes from. I've been googling but can seem to find it out. Any help would be appreciated...

Question: Which best describes the delta G for hydrolysis of creatine phosphate under cellular conditions in which the concentration of creatine phosphate, creatine, and phosphate all equal 1 mM at 25 degrees C. The delta G naught for the hydrolysis of creatine phosphate at 25 degrees C is...

Im really just searching for a general explanation! If you are solving a pretty standard left hand side differential equation, but a diracs delta function on the right hand side. I am abit confused about how to interpret this. If this is the case for the right hand side: r(t) = Diracs (t)...

The quark composition of the Δ0 is the same as that of neutron but much heavier and the quark composition of Δ+ is the same as that of proton but also much heavier, so what is the difference between the delta particles and the proton and neutron and where did that extra mass come from?

Homework Statement use the sifting property of the dirac delta function to evaluate the following integrals. a) integral from -inf to inf sin(t) delta(t-pi/2)dt b) integral from 0 to 2 e^(2t) delta(t-1)dt c) integral from 0 to pi e^tan(theta) delta(theta- 3pi/4)d(theta) d)...

I'm having a hard time grasping when I should use this little "function". I'm using Griffith's Intro to Electrodynamics and either he doesn't touch on it enough or I'm missing the point. From what I think I understand I'm to use it when there would be a singularity in a result or calculation(?)...

kron[m_,n_]:=\!\( \*SubsuperscriptBox[\(\[Integral]\), \(0\), \(2\)]\(\(Sin[ \*FractionBox[\(n\ \[Pi]\ x\), \(2\)]]\ Sin[ \*FractionBox[\(m\ \[Pi]\ x\), \(2\)]]\) \[DifferentialD]x\)\) This is the integral over x of sin(n pi x / 2) times sin(m pi x / 2) from 0 to 2. This is one way to...

Homework Statement I need to understand how to integrate \int_{0}^{t}\int_{0}^{s} \delta(\tau-\tau')d\tau d\tau' The solution is min(t,s) Homework Equations See aboveThe Attempt at a Solution min(t,s)

Homework Statement How can i prove this property of Delta, http://e1204.hizliresim.com/w/d/4bw2j.png Homework Equations This is my homework from John David Jackson's Classical Elektrodynamics book The Attempt at a Solution I can't an attempt. Some properties is proved at wiki and...

Homework Statement I just want to make sure I include all the steps in doing this: lim (6x-7) = 11 x->3 Homework Equations The Attempt at a Solution given ε>0, we need to find a δ>0, such that 0< lx-3l < δ then 0 < l (6x-7)-11 l < ε To prove this I need to make 0 < l...

Homework Statement http://gyazo.com/7b2a903b6b3165595b8766d3540f43d9 What is this really saying? I can see that a functino is the inverse Fourier transform of the Fourier transform... and it doesn't matter which way round you integrate. Is that all it's saying. What's the difference...

Homework Statement Use the law of conservation of energy to calculate the temperature increase expected from energy transferred to internal heat of the water. There is more than one way to do this. Consider a mass, m, of water which falls over the cascade. If you wish, you may take the mass...

Hey guys, I found this question and it started bugging me: find the _largest_ δ such that |x - 5| < δ => |1/x - 1/5| < 1/100. This is what I did to try solve the question: From |1/x - 1/5| < 1/100 : I got 1/x > 19/100 and so I wanted x < 100/19 plugging that back into the first...

Hi, Let Z be a r.v. from N(0, σ^2) and let Y = Z^2*exp(Z)/(1 + exp(Z))^2. What is the exptected value of Y, E(Y)? The delta method (Taylor expansion) doesn't work since the errors seem to accumulate. Any suggestions? This is a non-standard problem related to my research and I am totally stuck...

Homework Statement See http://mathworld.wolfram.com/DeltaFunction.html I want to show (6) on that page. I can show it using (7), but we aren't supposed to do that. I already proved (5), and my prof says to use the fact that (5) is true to get the answer. Homework Equations The...

I am doing an assignment about launching a rocket and at the moment I am looking for the delta V of the rocket. I have done a few researches and i found a method of finding the energy of the rocket and find the delta vee of it , but then i found this article and I am not sure if it is delta vee...

It is fairly easy to demonstrate that the Dirac delta function is the Fourier transform of the plane wave function, and hence that: \delta(x)=∫_{-∞}^{∞}e^{ikx}dk (eg Tannoudji et al 'Quantum Physics' Vol 1 p101 A-39) Hence it should be the case that ∫_{-∞}^{∞}e^{ik}dk = \delta(1) = 0...

I'm working on an online EECS course, and to be frank some of it is going straight over my head - but at the same time parts of it are far below my current knowledge, so I want to work and stick with it. The speaker is working through proving current and voltage - to arrive at Kirchoff's...

V(x) = |g| (δ(x+L)+δ(x-L) Consider scattering from a repulsive twin-delta function potential. Calculate R and T. I'm mostly confused about computing the T coefficients for multiple barriers. Would I compute the T coefficient for the barrier at x = -L and at x = L seperately? Then...

In my book the dirac delta is described by the equation on the attached picture. This realtion is derived from the Fourier transform, but I'm not sure that I understand what it says. If u=t it is clear that one gets f(u) in the Fourier inversion theorem. But why wouldn't u=t? In the derivation...

What's the reason that you write δ(x-x') rather than just δ(x') both indicating that the function is infinite at x=x' and 0 everywhere else? For me that notation just confuses me, and in my opinion the other notation is easier.

Hey All, I am trying to evaluate the limit: \lim_{x\to 0^{+}} \frac{\delta''(x)}{\delta''(x)} Where \delta'(x) is the first derivative of the dirac distribution and \delta''(x) is the second derivative of the dirac distribution. I thought about the fact that this expression...

1. Problem Statment: Sketch the sequence x(n)=\delta(n) + exp(j\theta)\delta(n-1) + exp(j2\theta)\delta(n-2) + ... 3. Attempt at the Solution: The angle theta is given in this case Can someone remind me of how to multiply a complex exponential by a delta function? This sequence represents...

Homework Statement I have to find this integral: \int \delta (( \frac{p^{2}}{2m} + Cz ) - E ) p^{2} dp dz where E, m, and C can be considered to be constants. Homework Equations I'm semi-familiar with delta functions, i.e. i know that: \int \delta (x - a) dx = 1 and that you can usually...

For part A, (described here: http://www.cramster.com/solution/solution/1157440) I don't understand why they say |x-2| < 1 and why \delta = min{1,ε/5} In case you can't view the page: lim x2+2x-5 = 3, x \rightarrow 2 Let ε > 0 and L = 3. |x2 + 2x -5 -3| < ε |x2 + 2x - 8| < ε |x+4||x-2| < ε...

A "simple" application of dirac delta "shift theorem"...help Homework Statement show that for a, b, c, d positive: δ(a/b-c/d) = bdδ(ad-bc) Homework Equations ∫f(x)δ(x-a)dx = f(a) The Attempt at a Solution Ok so I start with ∫δ(a/b-c/d)f(x)dx But I am not sure how to apply the shift...

What is delta ##Δ##, where and why do we use it ?

Hi! Thanks for your interest in this this post :D! So two reactions I performed were: A) Adding 50 cm3 water to 0.025 moles CuS04 and measuring ΔT. B) Adding 50 cm3 water to 0.025 moles CuS04.5H2O and measuring ΔT. Well turns out the calculations were wrong, since I apparently didn't get...

greetings . i have two questions regarding the sinc function in the week limit , where it can be used as a nascent delta function. the definition : \lim_{\varepsilon \rightarrow 0}\frac{1}{\pi }\int_{-\infty}^{\infty}\frac{sin\left(\frac{x-x_{0}}{\varepsilon}\right) }{x-x_{0}}...

Dear Forum Users, I have got more math question rather then the physics question. Does someone know if: \mid d(x)\mid^2 equals just d(x), here d(x) is just the Dirac delta ? best regards, nykon

Hello, I was under the impression that a dirac delta was a "legitimate" state for a particle: maybe not mathematically, but least physically. But I was recently told by a post-doc in QM that if your particle is in a dirac delta state at one moment, the very next moment the particle is...

Hello PF, When I was studying Quantum mechanics, I realized that this equality should be true, <{\psi}_{n} \mid {\psi}_{m}>=\int {\psi}_{m}^*{\psi}_{n}dx={\delta }_{mn} So {\psi}_{m}^*{\psi}_{n} must be equal to dirac delta function so that we provide the kronecker delta as a solution of...

If yes, how can we find it?

Well I don't understand this equality: A^{j}_{i}*A_{j}^{k}=\delta_{i}^{k} It is true because it is the result of a calculation. But assuming it is true ¿What happens if one of the A_{i}^{j} is zero?. Then it does not matter which is the value of the A_{j}^{k} the equality will be false...

consider a particle in one dimention. there is a dirac delta potential such as V=-a delat(x) the wave functions in two sides(left and right) are Aexp(kx) and Aexp(-kx) respectively. so the differential of the wave functions are not continious at x=0. what is the justification here?