What Exactly is Dirac’s Delta Function? - Insight

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Discussion Overview

The discussion revolves around the Dirac delta function, its mathematical properties, and its applications in quantum mechanics. Participants explore its definition, historical context, and the implications of its use in various fields, including physics and engineering.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants describe the Dirac delta function as a mathematical object that is 1 at 0 and 0 everywhere else, while others argue it is a distribution or functional.
  • A participant suggests that the Dirac delta function combines the distribution of values of a quantum variable into a single value.
  • There is a historical note that the delta function was not mathematically rigorous when introduced by Dirac in 1930, leading to criticism from pure mathematicians.
  • Some participants mention that the Dirac delta function is used in quantum mechanics for continuous eigenstates and completeness relations.
  • A later reply discusses the notation δx = ϕ(0) for test functions, questioning its clarity and historical usage.
  • There are disagreements regarding the interpretation of Dirac's notation and whether it has been properly clarified in the discussion.
  • One participant emphasizes the need for references to Dirac's original work to substantiate claims about the notation.

Areas of Agreement / Disagreement

Participants express differing views on the nature of the Dirac delta function, with some asserting it is a function and others insisting it is a distribution. The discussion remains unresolved regarding the clarity of Dirac's notation and its historical context.

Contextual Notes

There are limitations in the discussion regarding the rigor of the Dirac delta function's definition and the historical context of its introduction. Participants express uncertainty about specific references in Dirac's work.

  • #31
I'm going to leave you to your dusty echo chamber on the web. It's only there because people like me built it for you. Furthermore, a computer technician shouldn't have to point out to a Physicist and a Mathematician the foundational work Schwartz's Théorie des distributions written before they were born." Do it yourself. I'm out of here, account deleted.
 
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  • #32
You have become Idolaters of syntax and grammar, I'm dealing with priests of the page, not engineers of reality. And as for the Guessing machine you so rightly fear. Do you hear that sound the Ai makes?, its the sound of the 21st Century steam engine and you're the threshers of old. Science's reputation under siege like never before, and you not helping with this "Attitude".
 
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  • #33
TensorTronic-270 said:
cut something from a paper I thought looked useful.
TensorTronic-270 said:
OF COURSE, I wouldn't know, I cant ... I can no more tell you the correct syntax than i can tell you what the equation means! let alone its syntax!.
TensorTronic-270 said:
Do you hear that sound the Ai makes?, its the sound of the 21st Century steam engine and you're the threshers of old. Science's reputation under siege like never before, and you not helping with this "Attitude".
On PF, AI output is not considered to be a valid source, and this thread is an excellent example why. What you posted is an AI hallucination, and because you didn't know the material you didn't recognize it as a hallucination.

In my personal opinion, it is AI's reputation that is more in question today. The problem of hallucinations is becoming widely recognized. As AI technology advances, there may be some future fix to this issue, but today's AI's simply hallucinate too much to be reliable.

The thread is reopened, but I want to leave this exchange in place as a good example of why we currently have the policy that we do. We will continue to reevaluate the policy as new technology develops.
 
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  • #34
I was transported infront of a bodega watching a neighorhood whino chugg a 40 oz reading this thread.
 
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