A Beautiful Looking Gaussian Integral - Please HELP

In summary, the conversation discusses a Gaussian Integral and the attempts to numerically solve it using MATLAB. The problem arises when the system is inconsistent, despite knowing that a solution exists. The conversation also mentions an article that successfully solved the integral numerically, and the parameters and notation used in the equation. The conversation concludes with the individual sharing their own parameters and expressing curiosity about how the integral will be solved considering the need for varying parameters.
  • #1
n0_3sc
243
1
I have the following Gaussian Integral:

[tex] \int_{0}^{\infty}2\pi r\left |{\int_{-l/2}^{l/2}\frac{e^\frac{-r^2}{bH}}{(1+ix)(k^{''} - ik^{'}x)H}}dx\right |^2dr [/tex]

Where

[tex]H = \frac{1+x^2}{k^{''} - ik^{'}x} - i\frac{x - \zeta}{k^{'}}[/tex]

Assume any characters not defined are constants.

I agree it does look fantastic, and I'm currently trying to numerically solve it (duh..). I'm using MATLAB and I run into the problem:
"Warning: System is inconsistent. Solution does not exist."
Yet I know a solution exists because I'm looking at an article that solved it numerically.

Any Hints/Advice?
 
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  • #2
n0_3sc said:
I have the following Gaussian Integral:

[tex] \int_{0}^{\infty}2\pi r\left |{\int_{-l/2}^{l/2}\frac{e^\frac{-r^2}{bH}}{(1+ix)(k^{''} - ik^{'}x)H}}dx\right |^2dr [/tex]

Where

[tex]H = \frac{1+x^2}{k^{''} - ik^{'}x} - i\frac{x - \zeta}{k^{'}}[/tex]

Assume any characters not defined are constants.

I agree it does look fantastic, and I'm currently trying to numerically solve it (duh..). I'm using MATLAB and I run into the problem:
"Warning: System is inconsistent. Solution does not exist."
Yet I know a solution exists because I'm looking at an article that solved it numerically.

Any Hints/Advice?

whats the article? it doesn't say how they solved it? what notation are you taking for granted as known? for example is the zeta the riemann zeta fn ( i know not likely since it doesn't have arguments ) but yea if you tell em for what values of the constants you're trying to numerically integrate i'll put it into mathematica and tell you what i get.
 
  • #3
Hey ice109,
I've attached the article. You'll see the equation on page 1 and 2.
No it doesn't say how they solved it, they just quote the results.
For the notation:
zeta, k'', k' and everything else are just real numbers (constants). Well, for my current purpose they are.

I'm trying to (in a way) reproduce the results in this paper with my own parameters.
Ok, I havn't got all the parameters with me now, but tomorrow I'll grab them and post it here.
 

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  • #4
Here are my numbers:

l = 7e-3
b = 14.516e-6
k'' = 11.466e6
k' = 4.387e6
zeta is actually given by:
2*(z-f)/b
where z is a vector that varies from 0 to 10e-3, f is 2.51e-3. But you can try solving it for one particular value of z.

I am curious as too how you will solve this since I need to vary several parameters and obtain different results.
 

1. What is a Gaussian integral?

A Gaussian integral is a type of definite integral that involves the function e^(-x^2). It is named after the mathematician Carl Friedrich Gauss and is commonly used in probability and statistics.

2. Why is a Gaussian integral considered beautiful?

The Gaussian integral is often referred to as beautiful because of its elegant and symmetrical form, as well as its many applications in mathematics and science. It also has a rich history and has been studied by many famous mathematicians.

3. What are some real-world applications of Gaussian integrals?

Gaussian integrals are used in a variety of fields, including physics, engineering, finance, and signal processing. They can be used to calculate probabilities, solve differential equations, and analyze data.

4. Is it difficult to solve a Gaussian integral?

The difficulty of solving a Gaussian integral depends on the specific integral and the level of mathematical knowledge of the individual. Some Gaussian integrals can be solved using basic integration techniques, while others may require more advanced methods.

5. How can I learn more about Gaussian integrals?

There are many resources available for learning about Gaussian integrals, including textbooks, online tutorials, and courses. It is recommended to have a strong understanding of calculus before attempting to learn about Gaussian integrals.

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