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. R

    Gaussian Integers and Pythagorean Triplets

    It is well known that 4n(n+1) + 1 is a square if n is an integer but if n is a Gaussian integer i.e., 4n(n+1) + 1 = A + Bi, then the norm (A^2 + B^2) is always a square! The proof is quite easy since A = u^2 - v^2 and B = 2uv.
  2. A

    Creating a histogram and then applying a gaussian fit. Help

    Ok, I need to take the data: D1 D2 6.5 3 6 4 6.7 5.5 7 3.8 6.3 4.5 8.6 5.8 5.5 4 7 3.5 7 4.5 7 5 6.5 4 6.8 3.2 7 3.6 6 4.5 6 2.8 and make a histogram (centered around 0 -- i.e. 0 will not be an edge of a bin) of the data...
  3. J

    How Do You Calculate the Electric Field Inside a Bored Insulating Cylinder?

    Hi all - I reposted this here, as I posted in the advanced forum on accident: Here's the problem I am having trouble with: A very long, solid insulating cylinder with radius "R" has a cylindrical hole with radius "a" bored along its entire length. The axis of the hole is a distance "b"...
  4. M

    Calculate $\hbar \ln$ Gaussian Path Integral w/Einstein Summation

    Einstein summation convention employed throughout We want to calculate \hbar \ln \int D x_i \exp[\frac{1}{32 \pi^3} \int ds \int d^3 r x_i(-is,r) M_{ij}(s,r) x_j(is,r)] The answer is \hbar \int \frac{ds}{2\pi} \ln \det[M_{ij}\delta^3(r-r')] I know that \int d^3 x_i e^{\frac{1}{2}x_i B_{ij}...
  5. J

    One integral (square root and gaussian peak)

    An integral \int\limits_{-\infty}^{\infty} \sqrt{1+x^2} e^{-Ax^2+Bx} dx is the problem. Anyone knowing the solution?
  6. E

    Another Way to do the Gaussian Problem

    Shankar page 155 Homework Statement Use the propagator equation for a free particle U(t) = \exp\left(\frac{i}{\hbar}\left(\frac{\hbar^2t}{2m}\frac{d^2}{dx^2}\right)\right) = \sum_{n=0}^{\infty}\frac{1}{n!}\rleft(\frac{i\hbar t}{2m}\right)\frac{2^{2n}}{dx^{2n}} The initial state of...
  7. E

    Time Evolution of the Gaussian packet

    Homework Statement Can someone give me a general idea (I do not need and probably will not understand the rigorous mathematics) of how you can use the propagator equation \psi(x,t) = \int{U(x,t;x',t')\psi(x',t')dx'}, the equation for a Gaussian wave packet, \psi(x',0)= e^{i p_0...
  8. L

    Is a gaussian distribution 'like a sine wave'

    So I was having a conversation with the guy I share an office with and I brought up the gaussian distribution to show the probability distribution of energies of electrons generated by a filament. He mentioned that it 'looks like a sine wave', and I said 'sorta, but it's not a sine wave'. He...
  9. M

    Mathematica Gaussian integral in Mathematica

    How can I evaluate something like \int^{\infty}_{-\infty} d^3 \mathbf{x} f(\mathbf{x}) e^{t g(\mathbf{x})} in Mathematica, where x is a vector in 3D?
  10. M

    Gaussian integral as an average

    OK so we have: \int f(z) e^{a g(z)} dz^3 integerated over all space. Now there is a identity for this integral as an average, or something like that, right? What is it? Or perhaps you have suggestions where I could read up on that kind of thing? (I'm not looking for the integral in...
  11. P

    Gaussian Functions: Summation of Infinite Variations

    Is the summation of an infinite number of different (not just different by constants ) Gaussian functions still a gaussian function? I think not because you can becuase you can just pull an e^(ax^2) from the series where a is any value as small as needed.
  12. R

    Sets of numbers and Gaussian distribution

    Are there any sets of numbers that represent numbers of sets? Any sets of numbers that follow a Gaussian (normal) distribution?
  13. cepheid

    Understanding Gaussian Wave Packets: Momentum, Width, and Amplitude Explained

    Hi, I've got the right answer in this problem, but I'm not sure if I've got the correct reasoning Homework Statement A Gaussian wave packet travels through free space. Which of the following statements about the packet are correct for all such wave packets? I. The average momentum...
  14. K

    Fourier transform of a Gaussian

    Homework Statement I need to have the Fourier transform of a Gaussian Homework Equations The Attempt at a Solution ∫(exp[-ax^2])(exp[-ikπx]) dx I tried by braking the last exponential into sine and cosine terms.The sine term is odd and it cancels.Then,I cannot evaluate the...
  15. N

    Gaussian Surface Derivations

    For the following Eo is epsillon zero Homework Statement 41. A solid nonconducting spere of radius R has a uniform charge distribution of volume charge density p = kr/R where k is constant and r is the distance from the center. Show the (a) the total charge on the sphere is Q =...
  16. T

    Gaussian Geometry: Finding Resources Online

    Can any resources on gaussian geometry be found on line?
  17. S

    Solving Gaussian Elimination Problem: 3x - y + z = 1

    Question: solve by using gaussian elimination: 3x - y + z = 1 2x + 2y – 5z = 0 5x + y – 4z = 7 what i did: step 1: new row 1 = old row 1 – row 2, I got: x – 3y + 6z = 1 2x + 2y – 5z = 0 5x + y – 4z = 7 step 2: new row 2 = old row 2 – (2 * row1) and new row 3 = old row 3 –...
  18. G

    Help Solving a Problem Involving Gaussian & Spherical Balloon Charge

    I can't figure out how to get started on this problem. Maybe you guys can help. A spherical balloon carries a total cahrge Q(1C) uniformly distributed over the surface. At t=0, r=r(sub 0), at t=30s, r=2r(sub 0). Find what is the electron field at 90 s at a distance of .5m from the balloon...
  19. Q

    What is an orthogonal chart in the context of Gaussian Normal Coordinates?

    What are Gaussian Normal Coordinates?
  20. H

    Comp Sci I want code (program) to solve Gaussian Elemination by C++

    Hi, can anyone help me ? I want code (program) to solve Gaussian Elemination by C++ . Please Help me and I will really appreciate your time and effort in helping me in my assignment. Thanks.
  21. H

    Solving Gaussian Elimination with C++

    Enter Here!? Hi, can anyone help me ? I want code (program) to solve Gaussian Elemination by C++ . Please :cry: :cry: very important:cry:
  22. T

    Proving Average Value of Gaussian Function as k_0

    The question says show that the average value of k is k_0 for the function A(k)=\frac{1}{\sqrt{2\pi}a}e^{\frac{-(k-k_0)^2}{2a^2}. I know that this is a gaussian function and that the center is k0 but i am not sure how to show this is the average value of k, what equation for average value...
  23. K

    Evaluating a infinite-dimensional Gaussian integral

    Hello,.. that's part of a problem i find in QFT (i won't explain it since it can be very tedious), the question is that i must evaluate the Multi-dimensional Gaussian Integral. \int_{-\infty}^{\infty}d^{n}V exp(x^{T}Ax)exp(ag(x)) for n\rightarrow \infty of course if the integral is...
  24. P

    Gaussian Integral Solving: Physics III Tips & Resources

    Can you direct me to any websites or papers on how to solve these? We've been coming across them in Physics III, and I really want to know how to solve them. lol, It's getting annoying not knowing how to solve them or differential equations (finally taking it next semester).
  25. L

    Evaluating the Gaussian integral

    Hi, I'm trying to evaluate the standard Gaussian integral \int_{-\infty}^{\infty} e^{-x^2} dx = \sqrt{\pi} The standard method seems to be by i)squaring the integral, ii)then by setting the product of the two integrals equal to the iterated integral constructed by composing the two...
  26. S

    Electric Field and Gaussian Pillbox

    check whether this result of this problem is consistent with this statement \vec{E_{above}} - \vec{E_{below}} = \frac{\sigma}{\epsilon_{0}} \hat{n} an infinite plan carries a uniform surface charge sigma. Find its electric field Solution: Draw a Gaussian Pillbox extending above and below the...
  27. M

    Calculating Sum of Three Correlated Gaussian Distributions

    I have three sets of data that I’ve used to create three Gaussian distributions which have different means and standard deviations. The data sets are also correlated as the data is dependent on time. I want to compare the sum of two distributions with the sum of three distributions to find which...
  28. F

    Need Help with Gaussian Surface Problem: Electric Flux Calculation

    I just realized that I accidentally didn't post this in the homework help section...if any mods can move this, I'd appreciate it. Sorry for the trouble! Hello. I need help solving the following problem: Consider a spherical Gaussian surface and three charges: q1 = 1.60 μC, q2 = -2.26 μC, and...
  29. RogerPink

    Heisenberg Uncertainty Principle and Gaussian Distributions

    I was reading about the derivation of the Heisenberg Uncertainty Principle and how Heisenberg used Gaussian Distributions to represent the uncertainty of position and momentum in his calculation. Why is it that Gaussian Distributions were used? There are many different types of distributions...
  30. N

    Gaussian Beam Optics Experiment: Measuring Beam Waist & Rayleigh Range

    I am doing a Gaussian Beam Optics Experiment - where I observe how lasers have a gaussian intensity profile. I've measured the beam radius at several points from the Laser in the far-field (ie. position 'z' >> Rayleigh Range). I want to know why is there a beam waist inside the laser. How...
  31. D

    What are some helpful math websites for understanding the Gaussian distribution?

    Hi i need a good math site (easy to read) so i can find the gaussian distribution
  32. M

    Solving Gaussian Surface Problems - Get Help Here!

    hi I have problems with gaussian surface.:cry: is anybody who tell me here?:shy: help me please,thanks :tongue2:
  33. M

    Probability: ranges in Gaussian approximation

    Hello everyone, I got stuck on a probability question and would be very thankful if someone could give me a hint: An Opaque bag contains 10 green counters and 20 red. One couner is selected at random and then replaced: green scores 1 and red scores zero. 1) Calculate the probability of...
  34. G

    MATLAB Filtering Gaussian noise with Matlab

    I’m generating a 1 kHz square wave and adding Guassian noise to obtain a SNR of 0 dB (using Matlab6.5). The task is to design a filter that will filter out as much noise as possible from the square wave plus noise signal. The sampling frequency is 100kHz. Noise signal: 100.0*randn(1...
  35. B

    Evaluate Gaussian Integral with Complex $\mu$ and $\sigma$

    Evaluate: \frac{1}{\sqrt{2\pi} \sigma} \int_{-\infty}^{\infty} \, dx \, exp\left[-\frac{(x - \mu)^2}{2\sigma^2}\right] \, , where $\mu$ and $\sigma$ are complex numbers. I tried writing \begin{align} \sigma &= s_1 + is_2 \,\\ \mu &= m_1 + i m_2 \, . \end{align} The integral...
  36. B

    Solve System of Equations Using Gaussian Elimination

    use gaussian elimination to solve the following system of equation: 2x + y - 3z = 3 4x - y + 2z = 25 -3x + 2y + 4z = -9 ok so first i rearranged them so the inital numbers were in decending order (for the pivot) R1 -> 4x - y + 2z = 25 R2 -> -3x + 2y + 4z = -9 R3 -> 2x + y - 3z = 3...
  37. D

    Maple Maple gaussian reduction multiplying rows

    Hello, I am using maple for gaussian reduction. I have to do it row by row for 1 part > g:=swaprow(f,1,2); [ 0. 3.5 3.5 3.5] [ ] g := [ 2 -1 -5 -7] [ ]...
  38. M

    The Magic of the Gaussian Function

    In academics, you hear so much about the Gaussian function, whether it be in statistics, physics, or even social sciences! The Gaussian function takes the general form of: f(x) = Ae^\frac{-(x-b)^2}{c^2} Further yet, the antiderivative of this function is the famous error function...
  39. S

    Gaussian Quadrature Explained: Example Included

    Anyone care to explain the concept of gaussian quatrature? I've tried some websites but they're a little over my head. An example would be appreciated, thanks!
  40. J

    Help with Gaussian Elimination

    S = Columns 1 through 3 1.0000 0 0 0 1.0000 0 0 0 1.0000 Columns 4 through 5 0.2750 -0.2786 -0.1750 0.5929 0.2250 0.1357 Which is the rref of A = 2 9 9 1 6 2...
  41. B

    2D Integral, Gaussian and 2 Sinc Functions

    I am looking for help with the following integral A = \int dx \int dy \exp(-a (x+y)^2 +ib(x-y)) sinc(cx+dy) sinc(dx+cy) where sinc(x) =\sin(x) / x for x \neq 0 and sinc(0) = 1 (pls forgive my poor latex) Either in the indefinite form or with the upper/lower limits at...
  42. T

    Solution: Solve Gaussian Elimination | 2x1 + 1x2 = 4

    2 1 1 | 4 -1 2 1 | 3 7 6 5 | 19 Need a little help please
  43. M

    Identifying Inconsistent Systems of Linear Equations with Gaussian Elimination

    Any help on this one would be greatly appreciated. Due to that I can't find much of a connection (due to lack of inconsistent set of linear equations), and the fact that I'm unable to explain it properly, can someone please help me? Here's the question: If a system of linear equations is...
  44. G

    Gaussian Integral Using Residues

    I am trying to to the Gaussian integral using contour integration. What terrible mistake have I made. I = \int_{-\infty}^\infty \mathrm{e}^{-x^2} \mathrm{d}x I consider the following integral: \int_C \mathrm{e}^{-z^2} \mathrm{d}z where C is the half-circle (of infinite...
  45. P

    Complete EM Field of Gaussian Beam: References & Pointers

    Does anyone have any references or pointers to the complete electromagnetic field of a "Gaussian Beam"? By Gaussian, I mean that for a beam propagating in the z direction, a cross-section of the beam in the x-yplane has |E| = k exp( -(x^2+y^2)/w^2 ) see for instance...
  46. C

    Proving Linear Filtering of Gaussian Process Still Gaussian

    How to prove the output of Linear Filtering a Gaussian Process is still Gaussian? It has been stated in many books I read, but none of them actually prove it. One even stated that "The technical mechinery to prove this property is beyond the scope of this book..." By definition, a Gaussian...
  47. M

    Problem with a gaussian integral.

    Hey, I've been learning about gaussian integrals lately. And I'm now stuck in one part. I am now trying to derive some kind of general formula for gaussian integrals \int x^n e^{-\alpha x^2} for the case where n is even. So they ask me to evaluate the special case n=0 and alpha=1. So its...
  48. C

    Gaussian Random Variables Question

    How do you show that a linear combination of two Gaussian Random Variables is again Gaussian?
  49. F

    Gaussian surface, and uniform charge density

    28. The problem is stated as: A long, thin wire carrying 5.6nC/m runs down the center of a long, thin-walled, hollow pipe with radius 1.0cm carrying -4.2nC/m spread uniformly over its surface. (a)Find the electric field 0.50 cm from the wire. (b)Find the electric field 1.5 cm from the wire...
  50. A

    Solving Gaussian Elimination Algorithm Problems (Matrices)

    I tried to solve this Gaussian elimination algorithm problem (matrices) but for some reason when I plug in the x variables it doesn't work. The problem is: Alright so the first thing I did was divide the 1st row by 1/3 (scaling). Then I made the entries below the first pivot equal to 0...
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