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The Dirac delta function

Anonymous Sun 24 Oct 22:17:19 2021 No.13786369 View Reply Original Report

Quoted By: >>13786405 >>13786526 >>13786591 >>13786687 >>13786690 >>13786716 >>13788985

>Make up a "function" on the spot
>It is not a function in the traditional sense, though
>But it is well-defined! Promise!
Why are mathematicians like this?

Anonymous

Anonymous Sun 24 Oct 2021 22:31:10 No.13786405 Report

Quoted By:

>>13786369
It is a measure which can be defined rigorously

Anonymous

Anonymous Sun 24 Oct 2021 22:35:52 No.13786420 Report

Quoted By: >>13786503 >>13786510

if the integral of the dirac delta function = 1, then its implied that infinity * dx = 1
is this allowed?

Anonymous

Anonymous Sun 24 Oct 2021 22:57:27 No.13786495 Report

Quoted By: >>13786510

It's a point measure.
Integration was discovered before functions. And also before measure theory. You need measures of space to integrate but not functions.

Anonymous

Anonymous Sun 24 Oct 2021 22:58:41 No.13786503 Report

Quoted By:

>>13786420
Yes. The probability of being somewhere in the space is 1.

Anonymous

Anonymous Sun 24 Oct 2021 23:00:25 No.13786510 Report

Quoted By:

>>13786420
>>13786495
What anon said, measure theory if I could put it into a few words is saying there are different ways to measure the value of the space that the integral sums over. The Dirac delta is one such measure that proves useful in QM.

Anonymous

Anonymous Sun 24 Oct 2021 23:02:29 No.13786526 Report

Quoted By:

>>13786369
>be witless student
>think they're hot shit
>confronted with ideas their tiny brain can't grok
>shit post about what a tard they are on 4gay
many such cases

Anonymous

Anonymous Sun 24 Oct 2021 23:22:22 No.13786585 Report

Quoted By: >>13786592

Mathlet here. Shouldn’t it be 1 at x=0, if the goal is to model the probability of particle with definite position

Anonymous

Anonymous Sun 24 Oct 2021 23:24:40 No.13786591 Report

Quoted By:

>>13786369
it is well defined, the definition is right there.

Anonymous

Anonymous Sun 24 Oct 2021 23:24:52 No.13786592 Report

Quoted By:

>>13786585
the integral of a function that is zero everywhere except at a finite number of points is zero. so no, this doesn't work.

Anonymous

Anonymous Sun 24 Oct 2021 23:42:53 No.13786636 Report

Quoted By: >>13786639 >>13786642 >>13786687 >>13786746

is measure theory a graduate school topic? where does it fit in?

Anonymous

Anonymous Sun 24 Oct 2021 23:44:13 No.13786639 Report

Quoted By:

>>13786636
undergraduate math

Anonymous

Anonymous Sun 24 Oct 2021 23:46:04 No.13786642 Report

Quoted By:

>>13786636
you can learn it immediately after learning set threory. see sigma algebra. it sounds scary but isn't

Anonymous

Anonymous Mon 25 Oct 2021 00:00:00 No.13786687 Report

Quoted By:

>>13786636
a good motivation for it is found in probability (im pretty sure it was developed there too) where we are concerned with finding probabilities by integrating distributions.

>>13786369
>make up a function
if you just took a second to read the image you posted, it says it can be thought of as one (or at least a limit of one), but it is really a distribution. the theory of distributions is developed by Schwartz and is mostly used in PDE's
https://en.wikipedia.org/wiki/Distribution_(mathematics)

Anonymous

Anonymous Mon 25 Oct 2021 00:02:03 No.13786690 Report

Quoted By:

>>13786369
>+infinity
this 'dirac' function became meaningless after this point

Anonymous

Anonymous Mon 25 Oct 2021 00:10:30 No.13786716 Report

Quoted By:

>>13786369
virgin measure theory-let vs. chad arrow

Anonymous

Anonymous Mon 25 Oct 2021 00:21:59 No.13786746 Report

Quoted By:

>>13786636
Yes it is generally a grad school topic. It's accessible if you have taken an undergraduate sequence in analysis. You usually taken functional analysis after measure theory.

Anonymous

Anonymous Mon 25 Oct 2021 16:55:22 No.13788985 Report

Quoted By:

>>13786369
>mathematicians
Dirac delta is a physics thing, desu. The sperg mathematicians literally strangle "dirac delta kek" physicists with there bare hands.

Anonymous

Anonymous Mon 25 Oct 2021 17:11:53 No.13789047 Report

Quoted By:

Is it common for mathematicians to think of the Dirac delta as a measure?
I'm a physishit and learned it in the context of distributions.

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