Gaussian Definition and 706 Threads

Homework Statement I'm trying to solve the Gaussian integral: \int_{-∞}^{∞}xe^{-λ(x-a)^2}dx and \int_{-∞}^{∞}x^2e^{-λ(x-a)^2}dxHomework Equations I can't find anything online that gives the Gaussian integral of x times the exponential of -λ(x+(some constant))squared. I was hoping someone here...

Hello. I'm wondering if anyone has a table of transforms showing the result of an Abel transform on a Gaussian distribution. I have been unable to find the solution to this. Many thanks for any help. I'm reconstructing an an image from a picture that fits a Gaussian very well, hence I'm hoping...

why is the electric field zero , if the closed gaussian surface doesn't enclose any charges. but,, if the charges are present at a distance outside the conductor?? and why isn't the electric field zero inside the gaussian surface, if there are charges distributed on the surface of the...

Hi, Just wondering when using the Euclidean Algorithm to find gcd of 4+7i and 1+3i. Where does 2 and 2+i come from in the follwoing? 4+7i = 2*(1+3i)+(2+i) 1+3i=(1+i)*(2+i) +0? I know you didvide them to get (5-i)/2 and then take closest Gaussian integer then not sure where to go.

Homework Statement I am trying to compute an integral, as part of the expected value formula (using a Gaussian PDF) \int_{-∞}^{∞} (x)^2 p(x) dx Where p(x) is the Gaussian probability density function: \frac{1}{\sigma \sqrt(2 \pi)} \exp(\frac{-x^2}{2 \sigma^2}) My aim after this is...

Homework Statement I am asked to evaluate ##\displaystyle\int_{-\infty}^{\infty} 3e^{-8x^2}dx## Homework Equations I know ##\displaystyle\int_{-\infty}^{\infty} e^{-x^2}dx = \sqrt{\pi}## The Attempt at a Solution based on an example in the book it seems a change of variables...

[SIZE="4"]Definition/Summary A lens is most often used to focus light rays from an object to form an image. It can also be used to collimate light rays from an object, or to bring a collimated beam of light rays to a focus. [SIZE="4"]Equations See "Extended explanation" for definitions of...

[SIZE="4"]Definition/Summary A Gaussian beam is an electromagnetic wave, usually a laser beam, with a Gaussian cross-sectional irradiance pattern. The Gaussian irradiance profile results in minimal spreading due to diffraction effects. The spot size w represents the radius or half-width at...

Use Gaussian elimination with back substitution to solve the following system: x1+x2+x3=1, x1+2x2+2x3=1, x1+2x2+3x3=1. The answer is (1, 0, 0) and I know how to solve the problem but I just don't know if I should use bracket or the big parentheses for this type of problem when I solve...

Homework Statement A Gaussian Sphere with a radius of 1m surrounds an unknown charge at the center. At this surface a uniform outward directed electric field is 1 N/C. Use Gauss' Law to calculate the amount of charge enclosed by the sphere. Homework Equations E = q/4∏εor^2 The Attempt at a...

I am trying to simulate a Gaussian beam through an optical waveguide having a circular cross-section in matlab. I am familiar with the theory of modes in an optical fiber and can analytically calculate the evolution of the beam by breaking down the beam into a sum of infinite modes. However, I...

Hello everyone. I was yesterday asked in an interview to draw a gaussian curve. I drew. And then they asked in what region would this give rise to bound states? I am really confused how to conclude if a function gives bound state or not. Please help. Thanks.

So the problem statement is: A conducting solid sphere (R = 0.167 m, q = 6.63·10–6 C) is shown in the figure. Using Gauss’s Law and two different Gaussian surfaces, determine the electric field (magnitude and direction) at point A, which is 0.00000100 m outside the conducting sphere. (Hint: One...

Homework Statement When solving 2 equations using gaussian elimination, can we divide one equation by the other? Can you help me find where I went wrong? Homework Equations 4x + 2y = 14 2x-y=1 The Attempt at a Solution

I'm reading a book on Path Integral and found this formula \int_{-\infty}^{\infty }e^{-ax^2+bx}dx=\sqrt{\frac{\pi}{a}}e^{\frac{b^2}{4a}} I Know this formula to be correct for a and b real numbers, however, the author applies this formula for a and b pure imaginary and I do not understand why...

How do LQG regulators work? I have read the Matlab page about them, Wikipedia, and a few schools notes on them but it isn't either clear to me or they are not adequately explaining how they work. All see is that we want to control something giving a quadratic cost. Is there are more robust...

Water level assumed constant. Static state model \(P_0 = 1000\), system noise \(Q = 0.0001\), measurement noise \(R = 0.1\). I want to use Kalman filtering to solve this problem. I know how to do this but I need to generate \(\mathbf{y} = y\) using Gaussian random noise. \(P_0\) is also call...

Homework Statement This is the problem sheet that I am solving at the moment: 2. The attempt at a solution I have already solved 17. Here is my solution to 17: Now I am working on 18. I am trying to show that the probability density function is conserved. I.e the integral of the...

Is there a formula for this gaussian integral: $$int_{-\infty}^{\infty}{x^4}{e^{-a(x-b)^2}}dx$$ I've tried wikipedia and they only have formulas for the integrand with only x*e^... not x^4e^... Wolframalpha won't do it either, because I actually have an integral that looks just like that...

Hello, From an offset zener diode breakdown circuit, I have collected a set of bytes from an ADC. The values distribute normally as integers between 0 and 1024 with a mean of 512. I would like to use the data to create a set of random integers that distribute uniformly. So far, I have...

Is there a formula for Gaussian integrals of the form $$\int_{-\infty}^{\infty}{x^n}{e^{-a(x-b)^2}}dx$$ I've looked all over, and all I could find were formulas saying $$\int_{-\infty}^{\infty}{e^{-a(x-b)^2}}dx=\sqrt{\frac{\pi}{a}}$$ and...

I have a Gaussian distribution about t, say, N(t; μ, σ), and a a Dirac Delta Function δ(t). Then how can I compute: N(t; μ, σ) * δ(t > 0) Any clues? Or recommender some materials for me to read? Thanks!

Hi, I'm new to this subject and wondering if anything is known specifically on the zero-th Gaussian periods of type (N,r), where N is a product of distinct primes and r = p^s is a power of a prime. I know there are some very general results out there, but I haven't seen this so far. Thanks...

Hi guys, I have run multiple simulations on networks that are all slightly perturbed from each other. They produce slightly different curve outputs onto an x-y graph which I need to now analyse (it has been about 5 years since I did statistical analysis hence why I am here). A couple of the...

For a gaussian of the form: exp(-ax2) How is a related to the width of the graph? I can see that if I compare with a normal distribution a = 1/2σ2. Is that correct?

Hi :) I'm reading a didactic paper and the author defined the initial state ket as |\Phi_{in}> = {\int}dq\phi_{in}(q)|q> where q is a coordinate and \phi_{in}(q) = <q|\Phi_{in}> = exp\left[\frac{-q^{2}}{4\Delta^{2}}\right] I don't know if I'm missing something but isn't this definition a...

What is the difference between a Gaussian beam profile and an Airy disk? Both seem to be pretty much the same to me. An Airy disk looks like this: And a Gaussian beam profile looks like this: So they seem more or less the same. What is the difference between the two?

Suppose we have a quantity which can take discrete equally spaced values. Iteratively, we can increase or decrease this quantity by one quantum, splitting into two new worlds each time. After multiple iterations we have some indistinguishable worlds, as described by Pascal's triangle. As the...

Hi everyone, :) This is a question that one of my friends sent me. It is kind of open ended and I don't have any clue about the particular area of research he is undertaking. Therefore I am posting the question here with the hope that anybody knowledgeable in this area would be able to help...

I'm given a wavefunction (I think it's implied this is some sort of solution to the Schrodinger equation) in my quantum mechanics class, and I need to normalize it to find its constant coefficient. So I have $$\psi(x)=Ne^{-\frac{|x-x_o|}{2a}}$$ And the formula for normalizing this to find \(N\)...

Homework Statement A solid non conducting sphere of radius R=5.60 cm has a nonuniform charge ditribution ρ=(14.1 pC/m^3)r/R, where r is the radial distance from the spheres center. (a) What is the sphere's total charge? What is the magnitude E of the electric field at (b) r=0, (c) r=R/2.00...

Homework Statement An uncharged spherical thin metallic shell has a point charge q at its center. Find expressions for the electric field Inside the shell Outside the shell has the shell any effect on the field due to q? has the presence of q any effect on the shell? if a second point charge...

what is gaussian function?how this is related to gaussian distribution?

what is gaussian function?what are it's field of applicaton?how this function is derived,i mean what are the logical reason(approach) behind forming such function?

Hey, I am rather stuck on this gaussian integral... I have come this far, and not sure what to do now: [tex]\int dh_{01}(\frac{h_{01}}{\sigma})^{2}+\frac{\Delta k^{2}(t-x)^{2}h_{01}}{2}-ik_{0}(t-x)h_{01}[\tex] [tex]\int...

Homework Statement in the following figure, the dashed line denotes a Gaussian surface enclosing part of a distribution of four positive charges. a) which charges contribute to the electric field at P? b) is the value of the flux though the surface, calculated using only the...

Matlab rook here, Suppose I'd want to plot the Gaussian for 10 different values for n:function gauss(c,n) = plot_gaussian.m x=-1*c:0.1:c; gauss(x,j)=sqrt(j./pi)*exp(-1*j.*x.^2); for j=1:n plot(x,y) end And then I'll type gauss(3,10) to plot 10 curves in the interval [-3,3] Also, if I'd...

The problem asks to find a generator of the principal ideal <6+7i, 5+3i> in Z[i]. It is my understanding that such a generator must be a greatest common divisor of 6+7i and 5+3i. So, let's call this guy d, we should have d(a+bi)=6+7i and d(c+di)=5+3i. I'm not really sure how to find d. If I...

I know that \displaystyle \int_{-\infty}^{\infty}e^{-x^{2}}dx=\sqrt{\pi} (You calculate the square of the integral, combine both integrals, change variable to polar coordinates and you can finally integrate that with ease). But in this exercise I have the following statament: Let be P_{R} the...

Homework Statement The problem was to calculate the electric field inside an infinite length cylinder (with radius R) with a non uniform charge density. The charge density depended on r. Its easy enough to solve using a gaussian cylinder with r less than R. But what if I wanted to complicate...

Homework Statement Show in detail that: \sigma_{x}^{2} = \int_{-\infty}^{\infty} (x -\bar{x})^{2} \frac{1}{\sigma \sqrt{2 \pi}}e^{-\frac{(x-X)^{2}}{2\sigma^{2}}} = \sigma^{2} where, G_{X,\sigma}(x) = \frac{1}{\sigma \sqrt{2 \pi}}e^{-\frac{(x-X)^{2}}{2\sigma^{2}}} Homework Equations \int u...

In particular, i am solving part b. I pulled off a couple of formulas from a textbook, but I'm quite sure they are incorrect to apply here. Can anyone guide me? Below is my attempt.

I'm given a Gaussian function to apply a Fourier transform to. $$f(x)=\frac{1}{\sqrt{a\sqrt{\pi}}}e^{ik_ox}e^{-\frac{x^2}{2a^2}}$$ Not the most appetizing integral... $$g(k)=\frac{1}{\sqrt{2\pi}}\frac{1}{\sqrt{a\sqrt{\pi}}}\int_{-\infty}^{\infty}e^{ik_ox}e^{-\frac{x^2}{2a^2}}e^{-ikx}dx$$...

Consider the Gaussian Integral (eqn 2.64).. is anyone able to explain how the constant of normalization is rationalised?

Is it possible to obtain a sigma function or Taylor series function for the indefinite integral of a general Gaussian function? If not, why not, and if so, where can I find this infinite series solution? By general Gaussian function I mean f(x) = a \cdot e^{-\frac{(x-b)^2}{2c^2}} + d

Data "analysis", I don't understand why this isn't a Gaussian nor a Ma I have downloaded all the elo ratings of all active chess players in May of the FIDE and I have made an histogram. I have plotted the result on a graph rating vs number of people with this rating. I do not understand why...

How to prove that a gaussian random variable multiplied by a deterministic sinusoid also results in a random variable with gaussian pdf? Suppose here A is a guassian random variable and B is given as below where fc is the frequency of sinusoid and t is the time. B=A∗cos(2π fc t). Is random...

So I've been wondering.. from my previous post: https://www.physicsforums.com/showthread.php?p=4500082#post4500082 if we have a plane of infinite charge, then electric field does not depend on distance however, for a infinite line of charge: If we use a cylinder with radius 'r' as our...

In my course textbook it is written that "approximately 68% of the measurements from a normally distributed set lie within +-1 standard deviation of the mean value". What do they mean by standard deviation of the mean value? They give a definition for "the mean"(of a set of measurements(data))...

I was doing a problem: An infinite conducting plane has a uniform surface charge density of 30 μC m‾². Find the electric field strength 7.0 mm from the plane. so we can use a gaussian surface (e.g a cylinder), and come to the conclusion that E = 30 μ / ε but that got me thinking...