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# 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.

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### What does Dirac delta function of a constant mean?

I have seen a formula that unit step function is the integration of Dirac delta function. $$H(x) = \int_{-\infty}^{x} \delta(t)~\mathrm dt$$ In evaluating the integral if we take the integral as ...
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### Where do the step function integral boundaries come from?

EDIT: I have a confusion about Heavyside step function. Suppose I have integral like $$\int_{0}^{\infty}dE_1\int_{0}^{\infty}dE_2\int_{0}^{\infty}dE_3 \delta(2- \gamma-E_1-E_2-E_3)$$ my first ...
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### $\int_{a-\epsilon}^{a+\epsilon} \delta(x - a)dx = 1$

$$\int_{a-\epsilon}^{a+\epsilon} \delta(x - a)dx = 1$$ I can see intuitively why this is so as $a$ is inside the the domain of integration and all other values in the domain contribute $0$ to the ...
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### What is the right way to calculate $\partial_z\frac{1}{\bar{z}}$?

In the appendix B of a physics paper arXiv: 1902.01434, it says $$\partial_z\frac{1}{\bar{z}}=\partial_{\bar{z}}\frac{1}{z}=2\pi\delta(z)\delta(\bar{z}),$$ same as 2-dimensional delta function (...
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### Using Green's function to solve 2d laplace equation

Consider a domain $D : {(x,y) : x>0 , y>0}$ Let $\mathbf{x}= (x,y)$ and $\mathbf{\xi}= (\xi_x, \xi_y)$. Then the Green's function satisfying $$\nabla^2G = \delta(\mathbf{x} - \mathbf{\xi} )$$ ...
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### Solution to ODE with Dirac Delta satisfies ODE

I am working on a problem where I have the following ODE. $$m\dot{v}+bv=\delta_I(t)$$ where $$\delta_I(t)=\begin{cases}0, & \text{for}&t\ne0\\ I, & \text{for} &t=0\end{cases}.$$ The ...
In a comment on Math.SE, I came today across the remark that the expression $\delta(f(x))$ has no meaning. Being a physicist, I have been surprised but I then remembered Schwartz distribution theory ...