What is Gaussian: Definition and 771 Discussions

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. C

    Integrating exp(x^2) like gaussian integral?

    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.
  2. Born2bwire

    Gaussian to MKS Four-vector Conversion

    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...
  3. S

    Fourier transform of a gaussian

    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...
  4. L

    Gaussian Wave packet- Griffiths 2.22

    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...
  5. N

    Solve Linear System with Gaussian Elimination

    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...
  6. S

    Gaussian Units: Electric Field

    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?
  7. Q

    How Does Flux Distribute in a Gaussian Cube with a Corner Charge?

    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...
  8. S

    What is a non-linear gaussian?

    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...
  9. M

    Gaussian Wavepacket Tunnel Through double barrier

    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...
  10. F

    MATLAB Matlab - creating Gaussian noise

    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!
  11. P

    Division algorithm and unique Gaussian integers

    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...
  12. A

    How can the error function be used to solve this integral?

    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...
  13. G

    Generalized Gaussian integers

    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...
  14. Somefantastik

    Numerical Integration: Gaussian Quadrature

    \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.
  15. A

    How do I evaluate gaussian integrals with positive, real constants?

    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...
  16. J

    Joint Gaussian With Tensors

    For vectors we can define the Joint Guasian as follows: f_X(x_1, \dots, x_N) = \frac {1} {(2\pi)^{N/2}|\Sigma|^{1/2}} \exp \left( -\frac{1}{2} ( x - \mu)^\top \Sigma^{-1} (x - \mu) \right) Now what if (x - \mu) is a matrix A and \Sigma is an order four covariance matrix Q between ellements...
  17. D

    How to solve an integral of a gaussian distribution

    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...
  18. L

    Why Can't I Use My Indicated Vector ds on a Gaussian Surface?

    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.
  19. L

    Gaussian Surface: Electric Field & dA Visualization

    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...
  20. A

    Delta-Correlated Gaussian Noise

    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
  21. D

    Solve Gaussian Integral: A from \int^{-\infty}_{+\infty} \rho (x) \,dx = 1

    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...
  22. G

    QM: psi(x,t) for Gaussian Wave Packet

    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...
  23. B

    QM: Magnus expansion, Gaussian integral

    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...
  24. Saladsamurai

    Solving for x in a 3x3 Gaussian Elimination Problem

    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]...
  25. T

    Efficiently Solve Gaussian Integration with Expert Homework Help

    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...
  26. X

    Physics behind Gaussian Accelerator/ Magnetic Linear Accelerator

    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...
  27. N

    Understanding the Difference Between Gaussian Functions

    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?
  28. X

    Layperson's description of multivariate gaussian distributions?

    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...
  29. M

    Chi Square Test for Gaussian Distribution

    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...
  30. C

    Solve Gaussian Integral Homework: Even/Odd Cases

    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...
  31. C

    Solve Gaussian Integral: Even/Odd Cases

    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...
  32. H

    Gaussian Curvature: Use Gauss Map to Find Sphere/Cylinder Radii

    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.
  33. A

    Gaussian elimination in MATLAB

    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...
  34. O

    Gaussian pulse equation in Laser?

    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
  35. J

    What should be the intensity of receiving fibers for proper reception?

    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...
  36. Y

    Focusing gaussian beam using a lens

    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...
  37. F

    How Do You Calculate the Minimum Gaussian Beam Waist?

    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!
  38. T

    What's the significance of using a Gaussian wave packet in Quantum Mechanics?

    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...
  39. W

    The form factor of a radial gaussian charge distribution

    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...
  40. P

    Gaussian Integral Identity with Grassmann Numbers

    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...
  41. P

    Finding total flux on Gaussian surface

    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...
  42. A

    MATLAB - Gaussian Elimination with Partial Pivoting

    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...
  43. D

    Gaussian 03W Bonding: How Does It Work?

    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...
  44. S

    Finding PDF of Y if X is a Gaussian PDF

    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)...
  45. M

    Gaussian surface and net flux

    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...
  46. T

    What is the relationship between the Fourier transform and a gaussian function?

    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...
  47. N

    Gaussian Beam focused using a lens

    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)...
  48. T

    Time Evolution of Gaussian Wave packets

    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) =...
  49. A

    Finding Constants for a Gaussian PDF

    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...
  50. A

    Linear Gaussian parameter estimation

    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...
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