Is f(x)δ(x) Equal to f(2)δ(x)?

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Homework Help Overview

The discussion revolves around the properties of the Dirac delta function, specifically in relation to the expression f(x)δ(x) and its potential equivalence to f(2)δ(x). Participants are examining the implications of substituting values into these expressions.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are questioning whether f(x)δ(x) can be equated to f(2)δ(x) based on the behavior of the delta function at specific points. Some are exploring the implications of substituting values and the resulting effects on integrals involving these expressions.

Discussion Status

The discussion is active, with participants providing differing viewpoints on the validity of the proposed equivalences. Some have raised concerns about the implications of their assumptions, particularly regarding the behavior of the delta function and the outcomes of integrals.

Contextual Notes

There is a focus on the properties of the delta function, particularly its value at points other than zero and how this affects the evaluation of integrals. Participants are also reflecting on the correctness of their previous statements and assumptions.

athrun200
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Homework Statement



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Homework Equations





The Attempt at a Solution



Can I write, say, [itex]f(x) \delta(x)=f(2)\delta(x)[/itex]?
Since [itex]\delta(x)[/itex] =0 for x[itex]\neq[/itex]0
 

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I think you can say [itex]f(x)\delta (x-2)=f(2)\delta (x)[/itex]
 
hunt_mat said:
I think you can say [itex]f(x)\delta (x-2)=f(2)\delta (x)[/itex]

Then if x=2, left hand side will become infinity and the right hand side 0.
Is it Ok?
 
So what's wrong with my post in #1?
 
athrun200 said:
So what's wrong with my post in #1?

The integral of [itex]f(x) \delta(x)[/itex] over x is f(0). The integral of [itex]f(2) \delta(x)[/itex] over x is f(2). So no, they aren't the same.
 

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