Gaussian Definition and 706 Threads

Hi, We know that the Gaussian integral is \int_{-\infty}^{+\infty}e^{-\frac{x^2}{a^2}}dx=a\sqrt{\pi} However, if the gaussian function is discrete in x, what is the result of \sum_{n=0}^{+\infty}e^{-\frac{n^2}{a}} = \\? where n is natural number, that is n=0,1,2,3....

http://upload.wikimedia.org/math/1/9/8/1983171154842b0b061fc42aa5eb7642.png" How to rewrite this 2D Gaussian eqn in terms of x? i need to calculate the x and y values. let x0=0 and y0=0. is it complex?

Hi there, I'm trying to reconstruct the ESP charges that have been determined in a paper using a Gaussian-like quantum chemistry program. While I understand the basic notion of the iterative procedures to approximate the wavefunctions etc., I'm not a chemist and so I'm having problems with...

Hi, I understand how to get the electric field between two spheres of uniform charge, \vec{E} = \frac{\rho \vec{d}}{3 \epsilon_0} which is simplified because at a point \vec{r}, the vectors from each charge center combine to give the distance, \vec{d}, between centers (since \rho's can...

Hello, I am new in computational chemistry. I was calculating by "DFT and HF theory" (using GAUSSIAN 03W) molecular parameters of "2D coordination polymer, [Cd(μ-pydc)(2-mim)]n (pydc = pyridine-2,3-dicarboxylate, 2-mim = 2-methylimidazole)" . I have Crystallographic data are belong to this...

Can you please give me formulas which give intersection of two gaussian function f(x, mu, sigma) = 1/sqrt(2*pi*sigma^2) * exp(-(x-mu)^2 / (2*sigma^2)) for the case variances are different. (Note: I think it is time I learn how to use "tex" tags, do you know a good tutorial?)

Hi everyone. The problem I have to face is to perform a taylor series expansion of the integral \int_{-\infty}^{\infty}\frac{e^{-\sum_{i}\frac{x_{i}^{2}}{2\epsilon}}}{\sqrt{2\pi\epsilon}^{N}}\cdot e^{f(\{x\})}dx_{i}\ldots dx_{N} with respect to variance \epsilon. I find some difficulties...

Homework Statement Looking through this proof in my DTI(diffusion tensor imaging) book and they don't show the work on how to compute this integral (and I'll need to know it for a presentation): \int cos(\gamma G\delta x) * e^{-x^{2}/4D\Delta}dx I haven't really gotten anywhere yet...

Homework Statement I need to introduce Gaussian errors to a set of velocity measurements. The errors should have mean zero and standard deviation .2. v = [4.6 3.8 7.2 9.7 6.4]; The Attempt at a Solution I tried to use Matlab's imnoise command (J=imnoise(v,'gaussian',0,.04), but...

Hey everyone, I know, lots of threads and online information about Gaussian integrals. But still, I couldn't find what I am looking for: Is there a general formula for the integral \int_{\mathbb{R}^d} d^d y \left|\vec{y}\right| \exp(-\alpha \vec{y}^2) where y is a vector of arbitrary...

Hello, If we are given a gaussian function which is continuous in x we know that: \int_{-\infty}^{+\infty}e^{-x^2}dx=\sqrt{\pi} What if the gaussian function is discrete in x? What is the result of \sum_{x=-\infty}^{+\infty}e^{-x^2} = \\? where x\in \mathbb{Z}

Hi, I have a gaussian of the form exp[-\frac{\pi*x^{2}}{A^2}]. I know that the FWHM=0.939A, but I cannot prove it. I Let exp[-\frac{\pi*x^{2}}{A^2}=0.5 (i.e. the half maximum part) taking natural logs I get rid of the exponential, but then which bit represents the full width?

We finally started modern quantum mechanics. I'm definitely feeling a bit lost or fuzzy, especially in the more rigorous book Quantum Physics by Gasiorowicz. At any rate, we have two more problem sets before the last exam. As for the problem, I'm not sure what to. Is it asking to calculate...

Homework Statement Evaluate this integral (in essence the Fourier transform of the Gaussian): \int_{-\infty}^{+\infty} e^{-ax^2} e^{ikx}\, dx 2. The attempt at a solution One way is to complete the square, so that -ax^2 + ikx = -a(x-ik/2a)^2 - (k/2a)^2 so the integral becomes...

Hello, I was looking at the explanation for Gaussian smoothing found here: http://homepages.inf.ed.ac.uk/rbf/HIPR2/gsmooth.htm" Now, figure 3 shows a discrete Gaussian kernel approximation. I have 2 questions: 1: Why is there a scaling factor (1/273)? Is it so that the sum of the discrete...

Q. (Something), (Something) and (Something) is at the centre of distribution.(bell curve) The mean? And i don't know - I've read through my maths book(s) and several other sources of information and can not find any information. Thanks.

Hello :smile: I have a homework question regarding Gaussian Elimination, where I am supposed to use information in a block of text to get equations, and form an augmented matrix. There are 4 unknowns, but I can only seem to get 3 equations and 3 "checks", to see if the values I get are...

Homework Statement A thin cylindrical shell of radius R1 = 5.0 cm is surrounded by a second cylindrical shell of radius R2 = 9.0 cm, as in the figure. Both cylinders are 5.8 m long and the inner one carries a total charge of Q1 = +4.2 µC and the outer one carries a total charge of Q2 = -2.4...

can some one tell me how to go about solving the gaussian integral e^(-x^2) I know it has no elementary integral . but i was told the improper integral from -inf to positive inf can be solved and some said that i haft to do it complex numbers or something and help would be great , this...

Homework Statement The Gaussian Elimination with Partial Pivoting algorithm when applied to the following matrix A[-3 0 4; 5 2 -6; 0 0 1] Will construct matrices P, L, and U 1- What are the defining properties of the matrices P, L and U? 2- What relation do P, L, U and A always satisfy...

This is probably a stupid question, but here goes: based on the covariance function of some (centered, stationary) Gaussian process - how can one determine non-degeneracy (here I mean for any choice of a finite number of sampling times, the resulting RV is AC). Ideas?

Hi all, when I have a Gaussian beam passing through a circular aperture: What should be the far field (Fraunhoffer's) distribution? Thanks in advance, Yoni

This is a University quantum physics problem but I'm posting it in this section as what I'm having trouble with is the integration. Homework Statement Homework Equations Normalisation condition: \int ^{\infty}_{-\infty} \left| \psi(x)^2 \right| dx = 1 The Attempt at a Solution...

My linear algebra teacher is strange. This is proof, he wants us to write a 4 page essay about the strengths and weaknesses of the Gaussian Elimination method to solve systems of equations covering these four areas: accuracy, student understanding, preparation for higher-level mathematics...

Our professor said that when a metallic body or a conductor is inserted inside a gaussian sphere, it will not experience anykind of electric force? But i don't understand why? Any help will be appreciable.

Homework Statement http://img.rflz.net/problems.jpg Homework Equations The Attempt at a Solution Question 1 x4 = 1 + 4x5 but from there I am not sure where to go or if there is even a solution? Question 2 I eventually got the matrix down to this: 1 2 -3 1 4 1 0 1 1 0...

Here is an interesting problem that I've been thinking about for a while: Let p be a prime s.t. p = 4m+1 for some integer m. Show that p divides n^2 + 1, where n = (2m)! It comes from a section on principal ideal domains and unique factorization domains. It is well-known that p is the...

Homework Statement Find coefficients a,b,c and d so that the curve of a circle in an xy plane, with points (-4,5), (-2,7) and (4,-3), is given by the equation ax2 + ay2 + bx + cy + d = 0. Not even sure where to start. Can anyone help me with this?

In the book "Fundamentals of Photonics", the form of the Gaussian beam is written as I(\rho,z) = I_0 \left(\frac{W_0}{W(z)}\right)^2\exp\left[-\frac{2\rho^2}{W^2(z)}\right] where \rho = \sqrt{x^2 + y^2} However, in some books (I forgot which one), the author use the following form I(R) =...

Gauss' Law only figures out the the total charge enclosed by the Gaussian surface and on it, I treid this in a few cases where charges were placed only inside the surface, and my answers were correct. But, when I tried imagining how to do this if there were charges present outside...

Homework Statement \int e^{-\frac{1}{2}(ax^{2}+\frac{b}{x^{2}})} dx from -\infty to \infty Homework Equations it says to solve this, given that, again from -\inftyto \infty: \int e^{-\frac{1}{2}x^{2}}}dx = \sqrt{}2\pi and suggests that the substitution u =...

The probability distribution for some thermodynamic variable x is given by P = N e^{-A(x)/KT} where A(x) is the availability, which can be replaced by Hemlholtz free energy F, Gibb's free energy G, etc depending on the conditions imposed. N is just some normalization constant. A(x) can be...

Hello! If I have the gaussian function, but x is a loarithmic scale. Can I infer that, if x was plotted using a regualr scale, that the function would be 'fairly' linear? At least initially? As the rate of change gradually increases befor slowing down again. I think this is reasonable... I...

I need to fit a tail-heavy "Gaussian" curve Hi, it's been a long time since I've been around PF. Homework Statement This isn't a homework problem per se, but I've been trying to fit some scattering data using a Gaussian function using a least squares approach and it's not working so...

Simple question: can a chi-squared be represented as a gaussian distribution? I'm wondering if I can take some chi-squared numbers that I have and represent them as increasing/decreasing widths of FWHM of a gaussian. Can I?

Forgetting about spin and polarity for the moment, do individual identical particles of the same type (electrons, photons, etc.) really have their own individual wave functions (Gaussian packets)? The mathematical definition of probability (relative frequency, etc.) has meaning only at the...

Hello everyone, I am trying to understand situations under which Gaussian distribution would apply. For example, I read somewhere that if you have some ink drop on a porous paper, then the distribution of the displacement of ink particles is approximately gaussian. I am trying to figure...

Hi, I am trying to recreate the naive gauss elimination method in fotran 95 but am having a few problems with it. The idea is to read in a nxn matrix of equations, so you can type in any number when u start the program and then the program will ask you to enter the relavant amount of...

Hi, Energy density of the ith annular section of a Gaussian pulse is written as F(r_i, r_i+1)=2*totalEnergy/[(r_i+1^2-r_i^2)*w^2]*integral(r*exp(-r^2/w^2),from r_i to r_i+1) where r spans from r=0 to r=r_n (theoretically infinity) in n steps, w is the waist size of the beam. This...

Homework Statement draw the field lines of a simple hydrogen atom model. A case is given where a proton is surrounded by an electron cloud. Without getting into quantum mechanics how would represent the field lines of this mini sphere inside and out. Homework Equations gauss's law The...

Hi I have fitted Gaussian function to some data in matlab. Now MATLAB gives me this: General model Gauss1: f(x) = a1*exp(-((x-b1)/c1)^2) Coefficients (with 95% confidence bounds): a1 = 2633 (2628, 2637) b1 = 1824 (1824, 1824) c1 =...

In Section XXV of Relativity we are introduced to Gaussian Co-ordinates. I can't seem to find much about this on the internet, perhaps there is another name? Can anyone link some background behind why this system was initially derived, and most importantly does anyone know the derivation of...

I have a set of data for an absorption spectra that I plot the firtst derivative of and it gives me a gaussianish plot, I then want to fit it with a gaussian and what I've been doing so far is calculating the mean and variace of the spread and then using them in the equation. Although this does...

Integrating exp(x^2) like gaussian integral?? Hi, I can't solve this integral \int^{1}_{0}\\e^{x^2}\\dx Can I solve this integral like gaussian integral? Please help me Thanks.

Is there a straightforward way to determine a given four-vector in MKS units? Our system of units is MKS but I need to use some results from special relativity and of course all the sources use Gaussian units. Jackson has a simple chart in his appendix on converting between the two systems...

fourier transform of the gaussian (1/\sqrt{2 pi \sigma}) e ^ (^{x^2/2\sigma^2}) now the Fourier of a gaussian is said to equal another gaussian as shown by equation (4) here: http://mathworld.wolfram.com/FourierTransform.html but when i also did it using equation (1) here...

Homework Statement Hi, The problems asks to calculate multiple things for a Gaussian wave packet. Steady state function: psi(x,0)=A*exp(-ax^2).My problem is that I'm stuck at calculating <p^2>.Homework Equations <p^2>=Int(|psi|^2*(-1*h^2*d^2/dx^2))dx or...

Homework Statement Hey everyone! I was handed this question in class without being taught how to do it! The text is supposed to be helpful but it is just confusing. Using Gaussian elimination and 3-digit rounding arithmetic, solve the following linear system: 3.3330x_1 +15920x_2...

I am stuck with Gaussian units. If the field in vacuum is E = \frac{Q}{r^2} Is the field in a dielectric E = \frac{Q}{\epsilon_r r^2} , or is it unchanged?

Homework Statement A particle charge of q is placed at one corner of a Gaussian cube. What multiple of q/\epsilon_0 gives the flux though each cube face not making up that corner? The solution is amazing - stack up eight cubes around the corner and find the flux through each individual cube...