Dirac delta function with contineous set of zeros

In summary, the conversation discusses the use of the delta function in integrals and its behavior on a sphere. The question is whether there is a method to evaluate integrals with the delta function as in the case of discrete zeros, specifically in the context of statistical mechanics.
  • #1
klabautermann
34
0
hi!

i have a question regarding the delta function. if i have a delta distribution with an argument that is a function of multiple arguments, somthimg like:

∫δ(E-[itex]p^{2}_{i}[/itex]/2m)[itex]dp^{N}[/itex], ranging over +-∞

now, the argument of the delta function vanishes on a sphere. i can evaluate the integral by changing to spherical coordinates, but in general is there a similar method to evaluate something like this as in the case of discrete zeros? my question is in the context of statistical mechanics.

thanks!
 
Physics news on Phys.org
  • #2
klabautermann said:
hi!

i have a question regarding the delta function. if i have a delta distribution with an argument that is a function of multiple arguments, somthimg like:

∫δ(E-[itex]p^{2}_{i}[/itex]/2m)[itex]dp^{N}[/itex], ranging over +-∞

now, the argument of the delta function vanishes on a sphere. i can evaluate the integral by changing to spherical coordinates, but in general is there a similar method to evaluate something like this as in the case of discrete zeros? my question is in the context of statistical mechanics.

thanks!

Check out http://en.wikipedia.org/wiki/Dirac_delta_function#Composition_with_a_function
 

Related to Dirac delta function with contineous set of zeros

1. What is the Dirac delta function with a continuous set of zeros?

The Dirac delta function is a mathematical function that is defined as zero everywhere except at a single point, where it has an infinite value. When a continuous set of zeros is added to the Dirac delta function, it remains zero at all points except for a countably infinite set of points, where it has an infinite value.

2. How is the Dirac delta function with a continuous set of zeros used in physics?

In physics, the Dirac delta function with a continuous set of zeros is used to model point-like particles or impulses, such as in the case of electric charges or gravitational forces. It also has applications in signal processing and quantum mechanics.

3. Can the Dirac delta function with a continuous set of zeros be graphed?

No, the Dirac delta function with a continuous set of zeros cannot be graphed as it is a theoretical concept that does not have a physical representation. However, it can be represented visually as a spike at the point where it has an infinite value.

4. How does the Dirac delta function with a continuous set of zeros relate to the Kronecker delta function?

The Dirac delta function with a continuous set of zeros and the Kronecker delta function are both types of delta functions, but they have different properties. The Kronecker delta function is discrete and takes on a value of 1 when the input is 0 and a value of 0 for all other inputs. On the other hand, the Dirac delta function with a continuous set of zeros is continuous and has an infinite value at a countably infinite set of points.

5. What is the integral of the Dirac delta function with a continuous set of zeros?

The integral of the Dirac delta function with a continuous set of zeros is equal to 1, as it represents the area under the curve of the function. This property is known as the sifting property and is important in many applications of the Dirac delta function.

Similar threads

I Dirac delta function confusions
    • Calculus
Replies
25
Views
1K
I Probability: why can we use the Dirac delta function for a conditional pdf?
    • Set Theory, Logic, Probability, Statistics
Replies
12
Views
3K
A Prove a formula with Dirac Delta
    • Calculus
Replies
3
Views
1K
Writing the charge density in the form of the Dirac delta function
    • Advanced Physics Homework Help
Replies
5
Views
3K
A Dirac delta function confusion
    • Calculus
Replies
2
Views
2K
I Square of Dirac delta function
    • General Math
Replies
3
Views
25K
Question on Dirac Delta function in Griffiths
    • Classical Physics
Replies
7
Views
4K
A Calculate the distribution of energies from momenta
    • Classical Physics
Replies
17
Views
1K
Solve $$\int_{∞}^{∞}dxf(x)\delta((x-x_1))$$: Dirac Delta Function
    • Calculus and Beyond Homework Help
Replies
7
Views
2K
Dirac delta function of a function of several variables
    • Advanced Physics Homework Help
Replies
3
Views
2K

Hot Threads

Recent Insights

Back
Top