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Questions tagged [dirac-delta-distributions]

Distributions are generalized functions, such as, e.g., the Dirac delta function.

DO NOT USE THIS TAG for statistical probability distributions, profiles, graphs, plots, etc.

Distributions are generalized functions, such as, e.g., the Dirac delta function.

DO NOT USE THIS TAG for statistical probability distributions, profiles, graphs, plots, etc.

793 questions
22
votes
5 answers

What is the square root of the Dirac Delta Function?

What is the square root of the Dirac Delta Function? Is it defined for functional integrals? Can it be used to describe quantum wave functions? \begin{align} \int_{-\infty}^{\infty} f(x)\sqrt{\delta(x-a)}dx \end{align}
linuxfreebird
  • 2,107
5
votes
1 answer

Physical meaning of the Jacobian in relation to Dirac delta function

Is there a physical meaning to the equation $$\delta(x-a)=\dfrac{\delta(\xi-\alpha)}{|J|} \, ?$$ In non-rectangular coordinate systems where the transformation is non-singular, what is the implication of dividing the Dirac delta function by the…
IRISistable
  • 51
4
votes
1 answer

Distributions (e.g., Dirac Delta): confused and unhappy

I am sorry that the following set of questions is very fuzzy and ill informed. I am a trained mathematician and now studying an undergraduate theoretical physics course. We use distributions. I have no clue of the How and Why, which makes me…
Jakob
  • 274
3
votes
2 answers

Delta Function of a Curve

I need to evaluate the integral \begin{equation} \int_0^1\mathrm dt\,f\left(t\right)\delta^{\left(3\right)}\left(\vec r\left(t\right)-\vec r_0\right) \end{equation} where there is only one $0\leq t_0\leq 1$ such that $\vec r\left(t_0\right)=\vec…
Chetan Vuppulury
  • 173
3
votes
1 answer

Interpretation of the Dirac-measure property

First and foremost, apologies in advance for using an abuse of notation by placing the Dirac measure inside an integral. But given the circumstances, I have no choice. This is essentially a word by word copy of an interpretation given on page 1 of…
BLAZE
  • 2,460
2
votes
1 answer

What is the correct cosine-like integral representation of Dirac delta?

exploring the integral representations of the Dirac delta I found this in terms of an integral of cosine function (from wolfram's database, https://functions.wolfram.com/GeneralizedFunctions/DiracDelta/07/01/01/…
Amadeus
  • 223
0
votes
2 answers

Physical picture of Dirac's delta impulses

In linear response theory, the response $A(t)$ is related to the impulse $g(t)$ by $$A(t) = \int_{-\infty}^{\infty}\chi(t-t^\prime)g(t^\prime)\, dt^\prime $$ A typical example is the case where $g(t)$ is the Dirac's Delta Function. i.e. $g(t) =…
user1420303
  • 372
-1
votes
1 answer

How is the Dirac delta distribution defined in product of two functions?

A Dirac distribution or Dirac $\delta$-distribution $\delta(p)$ is the distribution that is given by evaluating a function at a point $p$. That is, the Dirac $\delta(p)$ function is the distribution defined by $$\langle\delta(p),\phi…
amilton moreira
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