What is the strength of a delta function.

Thread starter jk_zhengli
Start date Jun 1, 2012
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Delta Delta function Function Strength

In summary, a delta function is a mathematical concept used in calculus and physics to represent a point-like source or observation in a system. It is measured by its amplitude, which is typically infinite but can be normalized. In physics, it is used to represent an idealized point mass or charge and describe the behavior of a system under a single point force. It differs from regular functions by having a value of zero everywhere except at a single point where it has a value of infinity. The concept of a delta function can also be extended to multiple dimensions, with its strength still determined by its amplitude at the peak.

Jun 1, 2012

jk_zhengli

Hi all,

I read the following:

"If g(t) starts with a delta function of strength Y/2, then..."

I wonder what that means. Does it mean g(t) = 0.5Yδ(t) ?

Thanks

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Jun 1, 2012

micromass

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Yes. It means that

[tex]\int_{-\infty}^{+\infty} g(t)dt=\frac{Y}{2}[/tex]

So it coincides with [itex]\frac{Y}{2}\delta (t)[/itex].

1. What is a delta function?

A delta function is a mathematical concept used in calculus and physics to represent a point-like source or a point-like observation in a system. It is often denoted by the symbol δ and is also known as the Dirac delta function.

2. How is the strength of a delta function measured?

The strength of a delta function is measured by its amplitude, which is the value of the function at its peak. This value is typically infinite, but it can be normalized to a finite value by dividing it by the width of the function at its peak.

3. What is the role of a delta function in physics?

In physics, a delta function is used to represent an idealized point mass or point charge. It is also used to describe the behavior of a system when a force is applied at a single point.

4. How is a delta function different from a regular function?

A delta function is different from a regular function in that it has a value of zero everywhere except at a single point, where it has a value of infinity. This makes it a non-continuous function, unlike regular functions which have a defined value at every point in their domain.

5. Is the concept of a delta function limited to one dimension?

No, the concept of a delta function can be extended to multiple dimensions. In one dimension, it is represented by a spike or spike-like curve, while in higher dimensions it is represented by a spike or spike-like surface or volume. The strength of the delta function in higher dimensions is still determined by its amplitude at the peak.