- #1
Happiness
- 679
- 30
Is the square of a Dirac delta function, ##(\delta(x))^2##, still a Dirac delta function, ##\delta(x)##?
A Dirac delta function peaks at one value of ##x##, say 0. If it is squared, it still peaks at the same value, so it seems like the squared Dirac delta function is still a Dirac delta function, ##\delta(x)##, or some multiple of it, ##k\delta(x)##, where ##k>1##, since the area under graph seems larger.
How about the square root of a Dirac delta function?
A Dirac delta function peaks at one value of ##x##, say 0. If it is squared, it still peaks at the same value, so it seems like the squared Dirac delta function is still a Dirac delta function, ##\delta(x)##, or some multiple of it, ##k\delta(x)##, where ##k>1##, since the area under graph seems larger.
How about the square root of a Dirac delta function?