Gaussian Definition and 772 Threads

Gaussian is a general purpose computational chemistry software package initially released in 1970 by John Pople and his research group at Carnegie Mellon University as Gaussian 70. It has been continuously updated since then. The name originates from Pople's use of Gaussian orbitals to speed up molecular electronic structure calculations as opposed to using Slater-type orbitals, a choice made to improve performance on the limited computing capacities of then-current computer hardware for Hartree–Fock calculations. The current version of the program is Gaussian 16. Originally available through the Quantum Chemistry Program Exchange, it was later licensed out of Carnegie Mellon University, and since 1987 has been developed and licensed by Gaussian, Inc.

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  1. I

    Electric field outside a gaussian surface

    Hello If we have a gaussian surface that is placed in a uniform electric field E and encloses 0 charge, what would the E-field at the gaussian surface be? I have assumed the gaussian surface to be cubic surface, and then I have found from Gauss's law that the electric field is zero at the...
  2. P

    Gaussian Elimination: Solving Homework Problem

    Homework Statement I started with the following equations : 3w+2x+3y+z=76 w+2x+2y+z=59 w/2+x+y+z/4=21 Homework Equations Gaussian elimination The Attempt at a Solution So I got the following after applying Gauss' method : 3w+2x+3y+z=76 -4x-3y-2z=-101 3/2z=51 which gives z=34 Then I get...
  3. CARNiVORE

    Net Charge within a Gaussian Cube

    Homework Statement The figure shows a closed Gaussian surface in the shape of a cube of edge length 1.80 m. It lies in a region where the electric field is given by E= (2.86x + 3.82)i + 7.18j + 8.36k N/C, with x in meters. What is the net charge contained by the cube? Homework Equations ε0...
  4. NATURE.M

    Showing a Distribution is Gaussian

    Homework Statement Consider f = wT x, where p(w) ∼ N (w|0, Σ). Show that p(f|x) is Gaussian. The Attempt at a Solution [/B] So there are apparently two approaches to this problem using either the linearity of f in terms of w or moment generating functions. But I'm having a lot of trouble...
  5. Einj

    Gaussian vs. non-Gaussian fluctuations

    Hello everyone, I know this is a very basic question but I was wondering, in the context of inflation, what does it mean to have gaussian or non-gaussian fluctuations. First of all, are we talking about the fluctuations of the inflation? Second of all, how is the nature of the fluctuations...
  6. A

    Does Applying a Function to Gaussian Variables Preserve Normality?

    Say I draw a set of numbers {x1,x2,x3,...} from a normal distribution and apply a function f(x) to these. Will the new set of numbers {f(x1),f(x2),f(x3),...} be gaussianly distributed? I guess it depends on f(x), since for example f(x)=x would certainly mean that the new set is gaussianly...
  7. R

    Is starlight a TEM00 gaussian beam or plane wave?

    I am simulating a radio telescope and confused on what kind of source should I setup to simulate a star. Should it be a TEM00 gaussian beam or simply a plane wave?Cheers, Robin
  8. avikarto

    LH vs Gaussian units in Biot-Savart Law

    I have a question regarding the relationship between the Biot-Savart formula in Gaussian and Lorentz-Heaviside units. In Gaussian, we have a ##\frac{1}{c}## outside the integral, but in LH units we have a ##\frac{1}{4\pi}\frac{1}{c}##. This does not make sense, considering the transformation...
  9. B

    What is Excess Kurtosis and Why is it Important in Financial Analysis?

    I heard a guy mention in a debate that some math calculation didn't obey Gaussian statistics. It was a debate re: the economy (not important here, though). I was curious what was meant by "Gaussian statistics" and would appreciate if anyone could offer a sort of layman's definition. Thanks...
  10. J

    Inequality involving probability of stationary zero-mean Gaussian

    Homework Statement Let $$(X(n), n ∈ [1, 2])$$ be a stationary zero-mean Gaussian process with autocorrelation function $$R_X(0) = 1; R_X(+-1) = \rho$$ for a constant ρ ∈ [−1, 1]. Show that for each x ∈ R it holds that $$max_{n∈[1,2]} P(X(n) > x) ≤ P (max_{n∈[1,2]} X(n) > x)$$ Are there any...
  11. J

    Integrating Gaussian Distribution (QM)

    Homework Statement I am struggling with one of the end of chapter questions in my QM textbook (see attachment as I don't know how to show calculus on PF). It has thrown me because the chapter introduces some of the key principles in QM by talking about probability but then it randomly chucks in...
  12. L

    Gaussian Beam Focusing: Find A(0) at Beam Waist

    A Gaussian beam has an intensity I(r,z), if the beam area at position Z is given by A(Z), then the beam gets focused by a lens of focal length f, what will the area of the beam be at the beam waist A(0) be? So I have been trying to figure this out for ages, I had to replicate an experiment in...
  13. A

    Determine the intensity profile and fwhm for gaussian beam.

    Homework Statement A beam of wavelength 600 nm has initially an intensity profile of Gaussian shape with a fwhm of 1 mm. Determine the intensity profile and fwhm 10 meter away.Homework Equations FWHM = λ/(2NA√(1 + I/Is)) The Attempt at a Solution [/B] FWHM1 = 1mm = 600 nm/(2NA√(1 + I/Is))...
  14. carllacan

    Wrong width when fitting a gaussian with SciPy

    Hi. Has anybody here any experience with SciPy? I'm trying to get SciPy to adjust a gaussian function to some data. For more details its the photopeak of Co60. This is what I do: import numpy as np from scipy.optimize import curve_fit # counts is a numpy array which...
  15. Chip

    Annihilation of shifted gaussian vs. nonshifted gaussian

    Maybe a picture will help. http://chipreuben.com/annihilation-of-shifted-Gaussian.jpg I get zero, both with the shifted and the non-shifted. Can anyone tell why the nonshifted should yield the ground state eigenfunction multiplied up by a constant? It seems the answer has to do with expanding...
  16. DeldotB

    Compute the G.C.D of two Gaussian Integers

    Homework Statement Hello all I apologize for the triviality of this: Im new to this stuff (its easy but unfamiliar) I was wondering if someone could verify this: Find the G.C.D of a= 14+2i and b=21+26i . a,b \in \mathbb{Z} [ i ] - Gaussian Integers Homework Equations None The Attempt...
  17. B

    Interaction of Gaussian Beams with Optics

    Homework Statement In a youtube video() it is explained how gaussian beams propagate through an optical lens. Using the complex parameter q \frac{1}{q} = \frac{1}{R} - \frac{j\lambda}{\pi n w^2} (with R the radius of curvature), one can use the ABCD matrix to calculate the effect of an optical...
  18. IvanSaurus

    Why Does the Outer Surface of a Conductor Reach 3/2 Q in Gaussian Law Problems?

    Hi there, I have following problem at hand: (any help would be appreaciated, I have a test tommorrow) 1. Homework Statement Homework Equations The Attempt at a Solution Above is obviously the teachers answer to the problem, what I don't get though; is, where does the 3/2 come from, at r...
  19. C

    Solving N Bead Gaussian Chain Partition Function

    Homework Statement Consider a system made up of joining together ##N## beads and ##N-1## springs. The positions of the beads is indicated by ##N## real numbers ##\left\{x_i\right\}_{i=1,...N}.## The Hamiltonian which characterises it is $$\mathcal H =...
  20. Destroxia

    Consider the Gaussian Distribution....?

    Homework Statement Consider the Gaussian Distribution ## p(x) = Ae^{-\lambda(x-a)^{2}} ##, where ## A ##, ##a##, and ##\lambda## are constants. (Look up any integrals you need.) (a) Determine ##A## (I only need help with this (a)) Homework Equations ##\int_{-\infty}^{\infty} p(x)dx = 1##...
  21. T

    Comparing gaussian distributions with Gumbel-like distribution

    Hi all, I study binding of analytes in a platform where I have 10.000 sensors. Theres is one binding event per sensor and I identify it as a sudden positive change in the signal. I do first a control experiment without analytes. I measure the maximum change in the signal for each sensor and I...
  22. K

    Gaussian wave packet in position space

    Hi all, The Gaussian wave packet is widely discussed in the text. I got the following expression for wave packet in momentum space ##\psi(p, 0) = A \exp\left[-(p-p_0)^2/ (2\sigma_p^2)\right]## with ##A=\sqrt{2\sigma_p/\sqrt{2\pi}}## As my understanding, the corresponding wave packet in...
  23. Adoniram

    Gaussian Integral: Converting from Cartesian to Polar

    Homework Statement I'm encountering these integrals a lot lately, and I can solve them because I know the "trick" but I'd like to know actually how the cartesian to polar conversion works: ##\int_{-\infty}^{\infty}e^{-x^2}dx## Homework Equations ##\int_{-\infty}^{\infty} e^{-x^2} = I##...
  24. Mnemonic

    Cylindrical Gaussian Surface around charged rod

    Homework Statement a) 21.4-nC of charge is placed on a 4.8-m long steel tube with a d = 5.9-cm diameter. What is the magnitude of the electric field as a radial distance of r = d / 3? b) What is the magnitude of the electric field as a radial distance of r = 20 d? I was able to determine the...
  25. B

    How can the difficult Gaussian integral be solved using standard tricks?

    Hi everyone, in the course of trying to solve a rather complicated statistics problem, I stumbled upon a few difficult integrals. The most difficult looks like: I(k,a,b,c) = \int_{-\infty}^{\infty} dx\, \frac{e^{i k x} e^{-\frac{x^2}{2}} x}{(a + 2 i x)(b+2 i x)(c+2 i x)} where a,b,c are...
  26. Aner

    Fortran [Fortran90]Problem with Gaussian distribution

    Hi, I have a problem in my program and I cannot figure it out. In the last post I had a problem about some arrays, I perfectly resolved it thanks to you, but now my problem is a little bit subtle. I have a subroutine(here I'll post it has a program )that generates random numbers in order to...
  27. T

    Is the Integration of a 2D Gaussian Over a Circle Similar to the 1D Case?

    This is a seemingly simple question, though I'm not exactly sure where I'm going wrong (if in fact I am going wrong). To start off: you have a 2D un-normalized Gaussian function centred at the origin and with a sigma of 4. If you integrate it over a circle of radius 4 also centred at the...
  28. QuantumCurt

    Fitting data to a Gaussian Distribution in Excel

    Hey everyone, I'm hoping I can get some input on this. As some of you may recall, I'm currently in an internship at Fermilab, and I've hit a snag in plotting my data. I'm measuring the intensity of the NuMI neutrino beam at multiple different points to look for discrepancies in the measured...
  29. M

    Integrating Gaussian in polar coordinates problem

    I have a 2D Gaussian: ## f(x,y) = e^{-[(x-x_o)^2 + (y-y_o)^2]/(2*{sigma}^2)}## which I converted into polar coordinates and got: ## g(r,θ) = e^{-[r^2 + r_o^2 - 2*r*r_o(cos(θ)cos(θ_o) + sin(θ)sin(θ_o))]/({2*{sigma}^2})} ## The proof for how this was done is in the attached file, and it would...
  30. H

    If X(t) is gaussian process, How about X(2t)?

    written as title, 1. If X(t) is gaussian process, then Can I say that X(2t) is gaussian process? of course, 2*X(t) is gaussian process 2. If X(t) is poisson process, then X(2t) is also poisson process?
  31. M

    Propagating uncertainties through Gaussian fit

    I'm doing an analysis where I have a set of random variables with some known uncertainties (the uncertainties are different for each random variable). The random variable is roughly Gaussian distributed. I'd like to get a meaningful characteristic value and uncertainty for the whole set. I can...
  32. B

    MHB Determinant using gaussian elimination

    I am attempting to find the determinant using gaussian elimination for the following matrix [4 3 2; 1 7 8; 3 9 3]. I have begun by attempting to form zeros below the diagonal. The answer should be -165, however i keep getting values up to -665. I have tried a variety of times and keep getting...
  33. ash64449

    What are these Gaussian coordinates?

    [Mentor's note: This post was moved from another thread as it raised a new question, off-topic in the originating thread] Albert Einstein in his book Relativity wrote " It is impossible to build up a system(reference body) from rigid bodies and clocks,which shall be of such a nature that...
  34. AwesomeTrains

    Derivation of orbital period - Hydrogen

    Hey everyone! 1. Homework Statement I've been giving the equation for a gaussian wave packet and from that I have to derive this formula: T_{Kepler}=2\pi \bar n ^3 by doing a first order taylor series approximation at \bar n of the phase: f(x)=f(\bar n)+\frac{df}{dx}|_{\bar n}(x-\bar...
  35. S

    Gaussian units vs Lorentz-Heaviside units

    The ##e^2## of Gaussian units becomes ##\frac{e^2}{4 \pi}## in Lorentz-Heaviside units. Is this the only difference between Gaussian units and Lorentz-Heaviside units?
  36. M

    Converting a 2D Gaussian in Cylindrical Coordinates

    Given the equation for a Gaussian as: ##z = f(x,y) = Ae^{[(x-x0)^2 + (y-y0)^2] /2pi*σ^2 }## , how would I go about converting this into cylindrical coordinates? The mean is non-zero, and this seems to be the biggest hurdle. I believe I read earlier that the answer is ~ ##z = f(r,θ) =...
  37. A

    Solve ∫xp e-x2 eix dx | Get Hints for Integration

    I need to evaluate ∫xp e-x2 eix dx from -∞ to ∞ Can someone please give me some pointers on how to do this? I am completely lost. I just need some hints or something.
  38. B

    MHB Help with finding the determinant using gaussian elimination

    I attempting to find the determinant using gaussian elimination for the following matrix [1 2 3; 3 2 2; 0 9 8]. I have begun by attempting to form zeros below the diagonal. My first row operation was to make row 2 equal to 3(row 1) - row 2. This gives me [1 2 3; 0 4 7; 0 9 8] . I think i am...
  39. A

    MHB Integral over gaussian pdf where parameters depend on integrand

    Hallo math helpers , i am trying to understand how one could solve the following integrall: $$\int_a^b \mathcal{N}(f(x_1,...,x_n,t),g(x_1,...,x_n,t)) dt$$, where $$\mathcal{N}$$ is the normal distribution, and $$f(x_1,...,x_n,t): \mathbb{R}^{n+1} \rightarrow \mathbb{R}$$, $$g(x_1,...,x_n,t)...
  40. AlanKirby

    Higgs mass - Why is it a Gaussian distribution?

    Hi, so my question is along the lines of the following: If I'm looking at the decay channel H=>ZZ=>4 Muons, why would the resultant distribution for the mass of the parent Higgs be a Gaussian? Is it a case of the peak is the actual value of the Higgs at rest; those of greater mass are Higgs...
  41. P

    How much charge inside a Gaussian surface?

    Homework Statement The electric field has been measured to be horizontal and to the right everywhere on the closed box shown in the figure. All over the left side of the box E1 = 80 V/m, and all over the right, slanting, side of the box E2 = 400 V/m. On the top the average field is E3 = 260...
  42. S

    Powell Lens Equations for Gaussian to Flat Top Beam Conversion

    I am a Post graduation student and I am doing a project on the conversion of a Gaussian beam into a flat top beam using optical components. I have found that the best component to do the same is a Powell lens. I would like to know more about the equations connecting the input beam diameter...
  43. H

    Where to place Gaussian surface

    Homework Statement I'm trying to calculate the electric field through two oppositely charged plates with the same magnitude: http://imgur.com/uXCQqtW Homework Equations Flux = ∫E⋅dA = Qenclosed/ε0 The Attempt at a Solution I understand how the electric field is calculated using S1 and S4...
  44. ognik

    How to choose N for Gaussian Quadrature

    Homework Statement Evaluate the definite integral below numerically (between limits -1 and 1) using a couple of numerical methods, including Gauss-Legendre quadrature - and compare results. Homework Equations $$ \int{(1-x^2)^\frac{1}{2}} dx $$ "Gauss quadrature yields the exact integral if φ...
  45. P

    Gaussian Integral with Denominator in QFT

    Hi all, so I've come across the following Gaussian integral in QFT...but it has a denominator and I am completely stuck! \int_{0}^{\infty} \frac{dx}{(x+i \epsilon)^{a}}e^{-B(x-A)^{2}} where a is a power I need to leave arbitrary for now, but hope to take between 0 and 1, and \epsilon is...
  46. ElijahRockers

    Convolution of gaussian functions

    Homework Statement Recall that we have defined the Gaussian ##f_s## by ##f_s (t) = \sqrt{s}e^{-st^2}## and shown that ##\hat{f_s}(\lambda) = \frac{1}{\sqrt{2}}e^{\frac{-\lambda^2}{4s}}##. Show that ##f_3 \ast f_6 (t) = \sqrt{\pi}f_{1/2}(t) = \sqrt{\pi/2}e^{-t^{2}/2}## The Attempt at a...
  47. G

    Can a Gaussian Surface Confirm Zero Electric Field Between Two Charges?

    1. We have two positive point charges (+q) at a distance from each other 2. Goal is to Find electric field at point A halfway between the point charges 3.By logic and summation of fields we should get ZERO 4. But how would I use a gaussian surface (sphere i assume ) to prove at point A...
  48. H

    Looking for an example of a Successive over-relaxation

    Hi I am working on a programming assignment that requires me to implement the successive over-relaxation algorithm. We are given the wikipedia page for this: http://en.wikipedia.org/wiki/Successive_over-relaxation. I have read through the wikipedia page for this numerous times but am still...
  49. V

    Complex Gaussian Integral - Cauchy Integral Theorem

    Homework Statement I have to prove that I(a,b)=\int_{-\infty}^{+\infty} exp(-ax^2+bx)dx=\sqrt{\frac{\pi}{a}}exp(b^2/4a) where a,b\in\mathbb{C}. I have already shown that I(a,0)=\sqrt{\frac{\pi}{a}}. Now I am supposed to find a relation between I(a,0) and \int_{-\infty}^{+\infty}...
  50. D

    Density Perturbations: Relation to c/H & Scale Invariance

    Why have the density perturbations of all lengths a relation to the constant radius c/H? I suppose this is the origin for scale invariance and gaussianity.
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