# Questions tagged [dirac-delta]

This tag is for questions involving the Dirac delta function, either in the informal sense, or in the distribution sense. The Dirac delta function is a mathematical construct which is called a generalized function or a distribution and was originally introduced by the British theoretical physicist Paul Dirac.

1,210 questions
Filter by
Sorted by
Tagged with
21 views

### Dirac Delta Evaluation of Function

I am struggling to understand what does the following expression evaluate to. "I am looking for general answer, not actual evaluation - i.e is dirac dealta making the integral center around h(x)? ...
60 views

### Why does the method using the Green's function for $\nabla^2 \Phi(\mathbf{x}) = \delta(x)\delta(y)$ not work?

I have the Poisson Equation (with $\mathbf{x}\in\mathbb{R}^3$) with the following form: $$\nabla^2 \Phi (\mathbf{x}) = \delta(x)\delta(y)$$ I used 2 methods for the resolution of this PDE. I am ...
21 views

### Laplacian and Dirac function gives contradictory result.

The following equation is correct for all non-negative real numbers: $$4\pi\delta^{(3)}(\mathbf{r})=\nabla\cdot\frac{\mathbf{r}}{r^{3}},$$ $$r\in[0,+\infty)$$ especially, when r=0, both sides give ...
30 views

### Show that $\sum\limits_{n=-\infty}^{\infty}\delta^{(|n|)}(x-n)$ diverges in S'

by Schwartz’s theorem, any generalized function from $S'$ has a finite singularity order. In this example, it is infinite and I want to show that the series $\notin S'$. ($g^{(l)}$ means $l$th ...
27 views

31 views

### How to prove the two formulas are equal in the sense of distribution

$1+2\sum_{n=1}^\infty \cos2n\pi x=\sum_{k=-\infty}^\infty \delta(x-k)$. I couldn't have an idea to prove it, maybe we can discuss how to get it clearly.
I'm relatively new to the concept of the Dirac Delta function have come across a problem in dealing with ODE with delta Solve the ODE: $$A''(y) - λ^2 A(y) = δ(y - ξ)$$ Subject to B.C (Hint: Use ...