Insights What Exactly is Dirac’s Delta Function? - Insight

[Greg Bernhardt]

TL;DR Summary

Dirac introduced the delta function in 1930 as a continuum analog to the Kronecker delta.

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles.

In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra

Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/

by @jambaugh

 

[zerodish]

TL;DR Summary: Dirac introduced the delta function in 1930 as a continuum analog to the Kronecker delta.

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles.

In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra

Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/

by @jambaugh

Viewed as a mathematical object it is simply a function where the value is 1 at 0 and 0 every where else. The idea that you can take the derivative or intergal of this monster is interesting. I would say it is a degenerate function like a line segment could be viewed as a degenerate ellipse where one of the axis is 0. As to how it is used in quantum mechanics I have no idea.

 

[renormalize]

Viewed as a mathematical object it is simply a function where the value is 1 at 0 and 0 every where else.

At what value of $x$ does the Dirac delta function $\delta\left(x\right)$ equal to $1\,$?

 

[weirdoguy]

Viewed as a mathematical object it is simply a function

No it is not (it's functional) and I don't see why you try to make up your own definitions when this is a completly understood and formalized topic. I haven't read the insights but I guess it goes into details.