Delta Definition and 1000 Threads

If we were to replace δ(x), the orginal Dirac Delta, with δ(sin(ωx)), what would be the result? Would we have an infinite spike everywhere on the graph of sinx where x is a multiple integer of π/ω? and 0 everywhere else? I apologize in advance if I had posted in the wrong category.

Homework Statement I am trying to derive the following relation using inner products of vectors: Homework Equations g_{\mu\nu} g^{\mu\sigma} = \delta_{\nu}^{\hspace{2mm}\sigma} The Attempt at a Solution What I have done is take two vectors and find the inner products in different ways with...

Hi again, another question. Please see the schematic below. It shows a wye-wye(n) with a delta tertiary winding. So this delta winding is inserted here so that we can achieve amp-turn balance with the zero sequence currents flowing on the secondary side. I know that zero sequence currents...

Homework Statement Find the uncertainty ∆y in y as a function of the uncertainties ∆u and ∆v in u and v for the following functions: y = 1/2(u+v) Homework Equations : Error propagation formula[/B] The Attempt at a Solution Don't know where to begin even. Help?[/B]

Homework Statement Homework Equations Power Triangle and 3-phase equations (listed in my solutions) The Attempt at a Solution Here are the instructor solutions: The instructor solutions just go straight into using equations, but I like to use the power triangle because it is more...

I made a few paper airplanes. I noticed that the common paper airplane (shown below) https://i.ytimg.com/vi/v29M7Oa1l-A/hqdefault.jpg flies much further/better than paper planes that look like standard 747s. Any know why ? I expected 747 like plane to be very efficient at generating the lift...

Currently, I am reading this article which introduces electromagnetism. It gives a function for the charge density as: $$\rho = q\delta(x-r(t))$$ The paper states that "the delta-function ensures that all the charge sits at a point," but how does it do that? Also, if ##r(t)## is the trajectory...

Hi, Consider this definition of the Dirac delta: $$\delta (x-q)=\lim_{a \rightarrow 0}\frac{1}{a\sqrt \pi}e^{-(x-q)^2/a^2}$$ First, this would make a normalized position eigenfunction $$\psi (x)=\lim_{a \rightarrow 0}\frac{1}{\sqrt{a\sqrt \pi}}e^{-x^2/2a^2}$$ right? If that is so, why do...

Homework Statement Prove the following '()( − ) = −′() ∫-∞∞δ'(x)*f(x-a) = -f'(a) Homework Equations ∫-∞∞δ'(x-a)*f(x) = f(a) The Attempt at a Solution [/B] ∫-∞ ∞δ'(x)*f(x-a) = ∫δ(x)*f(x-a)dx-∫f'(x-a)*δ(x)dx = f(-a) - f'(-a) Went from 1st to second by integration by parts Used...

Hey, everyone! I'm helping a friend through his calculus course and we've come across something that has stumped me (see: the title). When I learned calculus, our treatment of the epsilon-delta definition of the limit was, at best, brief. Anyway, here is the problem: Given ##\lim_{x \rightarrow...

Homework Statement I need to integrate this expression : P(k, w) = A * δ(w-k*v) * f(k, w) A is constant and δ, Dirac Delta.Homework Equations [/B] There is double integration : I = ∫0∞ dk ∫0∞ P(k,w) dw = A ∫∫0∞ δ(w-k*v) * f(k, w) dw dk The Attempt at a Solution [/B] I'm confused with...

Homework Statement Ultimately, I would like a expression that is the result of an integral with the sin(nx)/x function, with extra terms from the expansion. This expression would then reconstruct the delta function behaviour as n goes to infty, with the extra terms decaying to zero. I...

Is the square of a Dirac delta function, ##(\delta(x))^2##, still a Dirac delta function, ##\delta(x)##? A Dirac delta function peaks at one value of ##x##, say 0. If it is squared, it still peaks at the same value, so it seems like the squared Dirac delta function is still a Dirac delta...

Homework Statement Calculate ##\int_{r=0}^\inf δ_r (r -r_0)\,dr## Homework Equations ##\int_V \delta^3(\vec{r} - \vec{r}') d\tau = 1## The Attempt at a Solution $$\int_V \delta^3(\vec{r} - \vec{r}') d\tau = \int_V \frac {1}{r^2 sinθ}\delta_r(r-r_0) \delta_θ (θ-θ_0) \delta_Φ (Φ-Φ_0) r^2...

Homework Statement Homework Equations Continuity: $$\vert x-c \vert < \delta~\Rightarrow~\vert f(x)-f(c) \vert < \epsilon$$ $$\delta=\delta(c,\epsilon)$$ The Attempt at a Solution $$\vert f(x)-f(c) \vert <\frac{1}{2}f(c)~\Rightarrow~\vert x-c \vert < \delta_1$$ So i have this δ1 but what...

Homework Statement find a δ for a given ε for f(x)=x3 around c=5: $$\vert x-5\vert<\delta~\Rightarrow~\vert x^3-5^3 \vert < \epsilon$$ Homework Equations Continuity: $$\vert x-c \vert < \delta~\Rightarrow~\vert f(x)-f(c) \vert < \epsilon$$ $$\delta=\delta(c,\epsilon)$$ The Attempt at a...

I just want to make sure that I am understanding the Dirac Delta function properly. Is the following correct?: For two variables ##x## and ##y##: \begin{equation} \begin{split} \delta(x-y) f(x) &= f(y) \end{split} \end{equation} And: \begin{equation} \begin{split} \delta(x-x) f(x) &=...

Homework Statement I have a 2D integral that contains a delta function: ##\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}\exp{-((x_2-x_1)^2)+(a x_2^2+b x_1^2-c x_2+d x_1+e))}\delta(p x_1^2-q x_2^2) dx_1 dx_2##, where ##x_1## and ##x_2## are variables, and a,b,c,d,e,p and q are some real...

Homework Statement definition of εijk εijk=+1 if ijk = (123, 231, 312) εijk = −1if ijk = (213, 321, 132) , (1.1.1) εijk= 0,otherwise . That is,εijk is nonzero only when all three indices are different. From the definition in Eq. (1.1.1), show that...

I'm an undergraduate student, so I understand that it may be difficult to provide an answer that I can understand, but I have experience using both the Dirac delta function and residue calculus in a classroom setting, so I'm at least familiar with how they're applied. Whether you're integrating...

So if I have a logistic regression: ##log (\hat {odds})=\hat{\beta_{0}}+\hat{\beta_{1}}x##. How would I find a confidence interval for x if I am given ##odds=5## This is going in reverse, where if I have the outcome, I try to do inference on the predictor. We know that ##\hat{\vec{\beta}}##...

Trying to narrow down what type and size radiator and flow of both the water and air I should be looking at that would give me my best heat exchange efficiencies, if I want to input 50F water into a radiator that will have 100F air (60% RH) blowing through it and my goal here is the cooling down...

Homework Statement Homework EquationsThe Attempt at a Solution So cts approx holds because ##\frac{E}{\bar{h}\omega}>>1## So ##\sum\limits^{\infty}_{n=0}\delta(E-(n+1/2)\bar{h} \omega) \approx \int\limits^{\infty}_{0} dx \delta(E-(x+1/2)\bar{h}\omega) ## Now if I do a substitution...

Homework Statement In this problem we shall consider the scattering from repulsive δ-function potentials. We have already considered a single such potential. If the strength of the potential is V0, the transmitted and reflected fluxes may be represented by the transmission and reflection...

Homework Statement I just have a quick question about the delta function, I'm pretty confident in most other cases but in this simple one I'm not so sure. $$\int_{-\infty}^{\infty} \phi (x)\delta (-x)dx$$ Homework EquationsThe Attempt at a Solution [/B] $$\int_{-\infty}^{\infty} \phi...

Hi. I understand that in 1-D when E< V(minimum) there exist no physically acceptable solution to the Schrodinger Equation. I have been looking at delta potentials using Griffiths book. I follow his working for the delta potential well but when it comes to the potential barrier I don't understand...

TL;DR: My professor asked me to graph the probability that a particle would be excited from the ground state to a stationary state with a certain energy E (y-axis) verse the energy of that new state (x-axis). I need help finding this probability as a function of E. Probability=|<ΨE|P|Ψg>|2 P is...

Homework Statement True/False: If a particular delta has been constructed as a suitable response to a particular epsilon challenge, then any smaller positive delta will also suffice. Homework EquationsThe Attempt at a Solution The submitted solution is as follows: However, when I read this...

Thereis no proof for anything in us other than matter(and energy). Thermodynamics works everywhere. I think we live upto the time our system's Delta G (Gibbs free enery) remains negative. Please friends tell me if my undrstanding is justified.

I'm trying to use the Animate function on Mathematica to show a gaussian wave packet passing through a delta potential. I'm quite new to Mathematica and this is by far the hardest thing I've had to do so please bear with me. I effectively want to solve the integral: ## \phi_k(x) = \left\{...

Homework Statement I want to plot using Mathematica a wave packet entering a delta potential ##V(x) = s\delta(x) ## (s is the strength) but I need to get the physics right first and I'm having trouble with a a few parts. I need to compute the integral ## \int_{0}^{\infty} e^{-i\omega...

so, continuous signals as sums of weighted delta functions can be represented like this: if you switch order of some variables you get ∫x(τ)δ(-τ+t)dτ, and since,I presume, Dirac delta "function" is even I can write it like this ∫x(τ)δ(-(-τ+t))dτ=∫x(τ)δ(τ-t)dτ=x(t) and we got ourselves a...

The width of Δ resonances is around 110...120 MeV. All four of them. With modest differences. The difference in width between Δ0 and Δ++ is estimated from 5 to 9 MeV. Why? Δ+ and Δ0 resonances have two options to decay. Δ+→p+π0 Δ+→n+π+ and correspondingly Δ0→p+π- Δ0→n+π0 In contrast, Δ++ and Δ-...

Homework Statement \begin{equation} \int_V (r^2 - \vec{2r} \cdot \vec{r}') \ \delta^3(\vec{r} - \vec{r}') d\tau \end{equation} where: \begin{equation} \vec{r}' = 3\hat{x} + 2\hat{y} + \hat{z} \end{equation} Where d $\tau$ is the volume element, and V is a solid sphere with radius 4, centered...

Is square root of delta function a delta function again? $$\int_{-\infty}^\infty f(x) \sqrt{\delta(x-a)} dx$$ How is this integral evaluated?

I've come across the equation $$\int_0^1 dx \frac{dA(x)}{dx} + B = C = \text{finite}$$ in my readings on a certain topic in physics and, in both articles i have read, the following step is taken $$\int_0^1 dx \left( \frac{dA(x)}{dx} + (B-C)\delta(1-x) \right) = \text{finite}$$ For the...

I am quite new here, and was wondering if anybody knows how this 2D integral is evaluated. $$ \int_{-\infty}^\infty \int_{-\infty}^\infty \delta(k_1 x-k_2y)\,dx\,dy$$Any help is greatly appreciated! Thanks!

Homework Statement Using the equations given, show that the wave function for a particle in the periodic delta function potential can be written in the form ##\psi (x) = C[\sin(kx) + e^{-iKa}\sin k(a-x)], \quad 0 \leq x \leq a## Homework Equations Given equations: ##\psi (x) =A\sin(kx) +...

I am looking at an explanation of the gradient operator acting on a scalar function ## \phi ##. This is what is written: In the steps 1.112 and 1.113 it is written that ## \frac {\partial x'_k} {\partial x'_i} ## is equivalent to the Kronecker delta. It makes sense to me that if i=k, then...

We know, $$\delta(x) = \begin{cases} \infty & \text{if } x = 0 \\ 0 & \text{if } x \neq 0 \end{cases}$$ And, also, $$\int_{-\infty}^{\infty}\delta(x)\,dx=1$$ Using Fourier Transformation, it can be shown that, $$\delta(x)=\lim_{\Omega \rightarrow \infty}\frac{\sin{(\Omega x)}}{\pi x}$$ Let's...

Homework Statement I am trying to show that ## \int \delta (x-a) \delta (x-c) dx = \delta (-a-c) ## via integeration by parts, but instead I am getting ##\delta (c-a) ## (or ##\delta (a-c)## depending how I go...). Can someone please help me out where I've gone wrong: struggling to spot it...

Homework Statement I have ##\int dx \int dy \delta (x^{2}+y^{2}-E) ## [1] I have only seen expressions integrating over ##\delta## where the ##x## or the ##y## appear seperately as well as in the delta function and so you can just replace e.g ##y^2 = - x^{2} +E## then integrate over ##\int...

I want to calculate $$\langle x|XP|y \rangle$$ where X is the position operator and P the momentum operator, and the states are position eigenstates. But I get two different answers depending on if I insert a complete set of states. First way: $$\langle x|XP|y \rangle=x\langle x|P|y...

Hallo, I have a question which elements are responsible for the increase of tangent delta in a X Capacitor and the reduction of its insulation resistance?

Hi, I am studying transmission lines faults. There was a line that said In case of delta star transformer in transmission line, an Earth fault on star (grounded) side is seen as a line to line fault on delta side. There was no explanation. I tried to google solutions but couldn't find any...

The Green's function for a scalar field in Euclidean space is $$(2\pi)^4\delta^4(p+k) \frac{1}{p^2+m^2}$$ however when I continue to Minkowski space via GMin(pMin)=GE(-i(pMin)) there's seems to be a sign error: $$(2\pi)^4\delta^4(-i (p+k)) \frac{1}{-p^2+m^2}=(2\pi)^4\delta^4(p+k)...

My history of physics is all too rusty. Who first wrote that the work done by a conservative force is the negative of the change in potential energy? Was he/she also the one who first presented the equation?

Q's Let f,g ℝ→ℝ. Suppose that g is bounded. This means that its image is bounded or in other words there exists a positive real number B s.t. |g(x)| ≤ B ∀ x. Prove that if lim x→c f(x) = 0, then lim x→c f(x)g(x) = 0. Work. See the picture. I am really confused I can't seem to understand the idea...

Homework Statement During a .0050 second time period a rocket expels 1.000kg of gas at a velocity of 5000 m/s. Calculate the rockets average Thrust, as well as Impulse. http://imgur.com/a/uE9dVI am going to use this note for reference on a test and want to rock solid about it. 2. Homework...

Homework Statement A wooden pallet carrying a load of 600 kg rests on a wooden floor. (s= .28 and k= .17) a. A forklift driver decides to push it horizontally instead of lifting it. What force must be applied to just get the pallet moving from rest? b. After a bit of time, the driver pushes the...