Gaussian Definition and 706 Threads

Googling this has only given me fairly detailed scientific papers and wikipedia (unusually) doesn't come up. Does anybody have a cheap and cheerful definition? Deducing these terms literally is not risk-free, but I suppose it involves a Gaussian probability distribution N(mu,sigma) where mu and...

Hello, I was trying to design a movie in Matlab. A Gaussian wave packet moves toward double barrier then some wave reflect and some pass out from the barrier . i design the double barrier in Matlab. but don't know how to make movie in Matlab with Gaussian wavepacket. can you help. Do u have...

Does anyone know how to create a matrix of complex Gaussian noise (with unit power = 1 and mean of zero)? I need to define a test sample for my algorithm, but I'm stuck at defining my test bench. Any help would be appreciated, thanks!

Homework Statement Theorem Let \alpha\neq0 and \beta be Gaussian integers. Then there are Gaussian integers \tau and \rho such that \beta=\tau\alpha+\rho and N\left(\rho\right)<N\left(\alpha\right) Problem Show that the Guassian integers \tau and \rho in the Theorem are unique if and only...

Greetings, I am a computer scientist revisiting integration after a long time. I am stuck with this simple-looking integral that's turning out to be quite painful (to me). I was wondering if one of you could help. The goal is to solve the integral \int_{0}^{\infty} e^{-(x - t)^2/2...

Homework Statement If \omega is and nth root of unity, define Z[\omega], the set of generalized Gaussian integers to be the set of all complex numbers of the form m_{0}+m_{1}\omega+m_{2}\omega^{2}+...+m_{n-1}\omega^{n-1} where n and m_{i} are integers. Prove that the products of generalized...

\int^{1}_{-1}f(x)dx = \sum^{n}_{j=-n}a_{j}f(x_{j}) Why does \sum_{j}a_{j} = 2 ? I know that the aj's are weights, and in the case of [-1,1], they are calculated using the roots of the Legendre polynomial, but I don't understand why they all add up to 2.

Homework Statement The book says to consider the gaussian distribution p(x) = Ae-m(x-a)2 where A, m, and a are all positive, real constants. I have no idea how to evaluate this! The book says to look up the relevant integrals. I see the integral of e-x2is pi1/2 but I don't know...

Homework Statement integrate \int_{-\infty}^\infty\! e ^{(x-a)^{2}}\, dx Homework Equations \int \! e^u\, du = e^u + C The Attempt at a Solution i just know that du = 2(x-a), but there is no x to make use of substitution, so I am confused on how to go about solving this since I...

folks, in my attached image, why can't i take the vector ds as indicated by me in pencil. i am confused. help will be greatly appreciated.

Homework Statement In the case of calculating electric field due to an infinitely long line charge, we assume cylinder to be a gaussian surface and electric field and small area element of the cylinder acts along the same direction at the curved surface and they act perpendicular direction at...

Hi What is \delta-correlated Gaussian noise? secondly, how is it that its correlation function is given to be 2\sigma^2\delta(t)? Thanks

Homework Statement Consider the gaussian distribution shown below \rho (x) = Ae^{-\lambda (x-a)^2 where A, a, and \lambda are positive real constants. Use \int^{-\infty}_{+\infty} \rho (x) \,dx = 1 to determine A. (Look up any integrals you need) Homework Equations Given in...

Homework Statement For a free particle, Given psi(x,0) = Aexp(-ax^2), find psi(x,t) Homework Equations phi(k) = 1/(sqrt(2pi)) times integral from -inf to +inf (psi(x,0)exp(-ikx))dx psi(x,t) = 1/(sqrt(2pi)) times integral from -inf to +inf (phi(k)exp(i(kx - (hk^2)t/2m)))dk my apologies...

Homework Statement The time-evolution operator \hat{U}(t,t_0) for a time-dependent Hamiltonian can be expressed using a Magnus expansion, which can be written...

Homework Statement Examine the solutions of \left[\begin{array}{c}x_1-x_2+x_3=c\\2x_1-3x_2+4x_3=0\\3x_1-4x_2+5x_3=1\end{array}\right] \text{when }c=1\text{ and }c\ne1 The Attempt at a Solution \left[\begin{array}{cccc}1& -1& 1& c\\2& -3& 4& 0\\3& -4& 5& 1\end{array}\right]...

Homework Statement Basically, i have to find the solution to: Int( x2 * exp (-(x-w)^2) , x= -infinity.. infinity) Homework Equations I realize this is connected to Gaussian Integration. So that if i have Int (exp(-x2), x=-infinity ... infinity) the answer is sqrt(Pi) Also, i...

Hi all. i have seen some videos on youtube and i am amazed by the videos of Gaussian accelerator/ Magnetic linear accelerator. As i have a physics project coming up i may consider using this for my project, however i need to ensure that this experiment is within my syllabus. i have basically...

I am having difficulty understanding the difference between the http://en.wikipedia.org/wiki/Gaussian_function" ? Which one would, say represent the line profile of a spectral line? Does anyone have a clue?

I am a Computer Science student who wants to implement the EM statistical clustering algorithm. I'm doing this on my spare time outside of any classes that I'm taking. I've been doing a lot of reading and understand almost everything I need to fully. However, I only understand univariable normal...

Hi there, I have very naive to statistics. I have a set of data points. that can be like 10, 12, 13, 14 ,15 , 15, 12, 13 17, 18, 19, 12, 19, 20 .... Now i need to know if these days points follows any gaussian distribution / normal distribution or not? IS chi -square test the right...

Homework Statement Solve: In = \int_{0}^{\infty} x^n e^{-\lambda x^2} dx Homework Equations The Attempt at a Solution So my teacher gave a few hints regarding this. She first said to evaluate when n = 0, then consider the cases when n = even and n = odd, comparing the even...

EDIT: meant to post this is the math forums, if you can remove this I'm going to switch it over Homework Statement Solve: In = \int_{0}^{\infty} x^n e^{-\lambda x^2} dx Homework Equations The Attempt at a Solution So my teacher gave a few hints regarding this. She first said to evaluate when...

I really need help answering these questions: use the gauss map to find the gaussian curvature of a sphere of radius r at any point. also, use the gauss map to find the gassian curvature of a cylinder of radius r at any point.

Homework Statement The point of this homework is to experiment with Gaussian elimination, and to develop an appreciation for partial pivoting. Questions 1 & 2 can be done with a calculator (though a computer is preferred). Question 3 requires a computer – you do not necessarily have to write...

I want to use a pulse current instead of continuous current in the Laser rate equation as input. What would be the equation for the Gaussian expression when I'll swap the continuous current with pulsed current in my equation and implement it in Matlab? please let me know the ans if u have any

I have a transmitting fiber and a receiving fiber. Now the transmitting fiber core diameter is 50 micrometer and I want to know how many receiving fibers should be used so all light from transmitted fiber is received properly. As suggested by some friends beam follows the Gaussian...

I am studying further about Gaussian optics. When Gaussian beam pass through a lens, the waist location is given by (z'-f) = (z-f)M^2 Where, z' is the waist location after lens, z is waist location before lens, f is the focal length of the lens M is the magnification. In Gaussian...

Physics students out there...how do you find the Minimum Beam waist after being given the beam waist and the focal length of a lens? Please help!

Hello, I have a question about basic Quantum Mechanics. In free particle study of Quantum Mechanics, why do we use the Gaussian wave packet always? I know that the Fourier Transform of it is also a Gaussian wave packet, but I was thinking, is that what we have selected? or is that what...

Homework Statement Compute the form factor of rho(r) = rho0 * exp[-ln2*r^2/R^2] where rho0 and R are constants. Homework Equations F(q) = 4pi/q \intsin(q*r)rho(r)rdr where the limits of integration run from 0 to \infty The Attempt at a Solution This is probably more of a...

Hi, I read the chapter "Anticommuting Numbers" by Peskin & Schröder (page 299) about Grassmann Numbers and now I would like to prove \int d \bar{\theta}_1 d \theta_1 ... d \bar{\theta}_N d \theta_N e^{-\bar{\theta} A \theta} = det A \theta_i are complex Grassmann Numbers...

Homework Statement Consider the uniformly charged sphere with radius R. Q is the total charge inside the sphere. Find the total flux passing through the Gaussian surface (spherical shell) with radius r. (r<R) Homework Equations I I tried solving for the Electric Flux by simply...

Homework Statement Let A be the nxn matrix with elements aij = -1 for i > j, aii = ain = 1, 1 <= i <= n, and zero everywhere else. Let b be a random vector. Solve the linear system Ax = b by Gaussian Elimination with partial pivoting. Use tril, eye, and ones to generate A, Generate b with...

I'm a new Gaussian 03W user and I have what I assume is a pretty basic question. How does Gaussian "know" how atoms are bonded to each other when a molecule is specified in an input file. An example molecule specification in Cartesian coordinates follows: 0 1 C 0.00 0.00...

A question which I amnot able to do...please help: Find the PDF of Y if X is a Gaussian PDF: fx(x) = (1e-x^2/2)/(2pi)^1/2 ; -infnity<x<+infinity Express your answer in terms of CDF of X gven by Fi(x) = Integral -infnty to + infnity((1e-x^2/2)/(2pi)^1/2) b) Sketch both the PDF, fY(y)...

In the figure below, the charge on a neutral isolated conductor is separated by a nearby positively charged rod. What is the net flux through each of the five Gaussian surfaces shown in cross section? Assume that the charges enclosed by S1, S2, and S3 are equal in magnitude. Surface 1...

The other day I was playing around with gaussian functions and I noticed that the Fourier transform of a gaussian function looked an awful lot like another gaussian function. I managed to find a single blurb about this fact in the Wikipedia article, and indeed, my hunch was correct. However, the...

Homework Statement Hello, I'm really confused about this one, =( Suppose I have a guassian beam that is colliminated (beam expanded) and then suppose i let it passed through a lens to focus it. Given an initial waist and focal length of the lens. How can i find the waist (or half width)...

Hi, I'm trying to derive a wave equation for a gaussian wavepacket for both the position (x) and the momentum (k), for a wave packet of width sigma, at some initial position x0 and with an initial momentum k0. Now I have worked out the initial wavepacket equation to be: psi(x) =...

Homework Statement The exam grades in a certain class have a Gaussian PDF with mean m and standard deviation \sigma. Find the constants a and b so that the random variable y=aX+b has a Gaussian PDF with mead m' and standard deviation \sigma'. Homework Equations The Attempt at a...

Hi, I have a multivariate linear-gaussian model and I am trying to estaimte a particular scalar set of parameters of the model. I know how to derive the MLE in order to find the matrices A and Q (linear transfer function and covariance respectively). I take the log of the joint...

Homework Statement A cylindrical shell of radius 7.00 cm and length 260 cm has its charge uniformly distributed on its curved surface. The magnitude of the electric field at a point 20.0 cm radially outward from its axis (measured from the midpoint of the shell) is 36.0 kN/C. Find values for...

Hello guys, I have got a homework for Advanced Quantum Mechanics, actually I've tried to solve it in many ways my own, but I'm always forced to use computer at the end (For infinite series or improper integrals), I want to solve it my self, so I can do it also in the class! The problem is...

Homework Statement I'm doing a problem on Gaussian functions (there are other constants to make it interesting, but I've removed them here): 1. \int_{0}^{x} e^{-x^2} dx 2. \int_{0}^{x} x e^{-x^2} dx 3. \int_{0}^{x} x^2 e^{-x^2} dx We know that erf(z) =...

If you imagine a string, the first part of the string (that the gaussian looking wave peak is moving along) has thicker mass density than the latter part of the string. (so it's essentially a thick bit of string going on to a thinner bit). What would happen when the wavepacket reaches the...

Hi, I have used some code that generates random numbers in a Gaussian distribution. when I plot say 100 numbers I don't get the bell curve although all the data seems to be around the correct mean value and changing the variance effects the spread. Am I wrong to expect the bell curve or am I...

3x+2y-z=5 -2x+2y+5z=2 x-2y+3z=11 Now we are required to solve these linear equations via Gaussian method. I put these in an echelon form and this how I did it: Switch L1 with L3 to make life easier. L1: x-2y+3z=11 L2:-2x+2y+5z=2 L3:3x+2y-z=5 Then I went to work to remove...

Que. 1 Consider a Gaussian PDF with µ = 20, σ = 30, a = 50 and b =80. Determine i)Probability that P(x>b) ii)P(x ≤ b) iii)P(x ≤ - b) iv)P(a ≤ x ≤ b) Que. 2 In a certain manufacturing process only shafts whose diameters are less than 1.5 inches can be used. Given the shaft diameters are...

hi i want to know why while dealing with any noise based application noise is assumed to be gaussian distributed? give me the explanation clearly please