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. D

    Gaussian Cylinder Electric Field and Net Charge Calculation

    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...
  2. S

    Gaussian process & Brownian motion

    Homework Statement Let \{ B(t) \}_{t \geq 0} be a standard Brownian motion and U \sim U[0,1] and {Y(t)}_t\geq0 be defined by Y(t) = B(t) + I_{t=U}. Verify that Y(t) is a Gaussian process and state its mean and covariance functions. Is Y(t) a standard Brownian motion?Homework Equations The...
  3. T

    Fourier Transform of Gaussian Function

    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...
  4. B

    Integrating Gaussian functions with erf

    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) =...
  5. H

    Gaussian Wave Packet: Reflection & Transmission

    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...
  6. A

    Calculate Gaussian Beam Radius for FRAP Diffusion Coefficient

    I'm doing FRAP(fluorescence recovery after photobleaching) Diffusion coefficient is what I want to calculate. t=w^2*f/(4D) t:halftime of recovery fluorescence w:radius of the focused circular laser beam at the e^(-2) intensity f : correction factor for the amount of bleaching D:diffusion...
  7. R

    Generated random data how can I check if it is a Gaussian?

    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...
  8. K

    How to Solve Linear Equations Using Gaussian Reduction

    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...
  9. A

    Gaussian PDF: Probability of P(x), Usable Shafts %

    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...
  10. C

    Why is noise always assumed to be Gaussian in noise-based applications?

    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
  11. T

    Getting Started with Gaussian Wavepackets & Uncertainty Principle

    I'm starting a project on Gaussian Wavepackets, and the evolution of the Uncertainty principle with time, however after the summer I'm a bit rusty :s, so I have a few questions, if anyone could help that would be great. Ok, first of all I see (and largely understand) that delta-x delta-p >...
  12. A

    Electric Field in Gaussian Spheres: Equilibrium and Charge Distribution

    Homework Statement Consider a metal sphere and spherical shells. The innermost one is solid with radius R_1. A spherical shell surrounds the sphere and has an inner radius R_2 and an outer radius R_3. The sphere and shell are again surrounded by a shell of inner radius R_4 and outer radius...
  13. J

    Electric Field Inside a Cylindrical Gaussian Surface: Exploiting Symmetry

    What is the electric field inside a cylindrical Gaussian surface in terms of volume charge density?
  14. T

    Linear algebra - gaussian elimination

    Homework Statement Use Gauss-Jordan elimination to solve this sys of linear eqs 2w+3x-y+4z =0 3w-x+z =1 3w-4x+y-z=2 The Attempt at a Solution I wrote 9 tablabeaus and ended up with three arbitrary solns. I just want to know if there anything wrong, here they are: 225a/121 =...
  15. G

    Filter out Gaussian noise from data curve

    What is the best way to filter out Gaussian noise from points in a data curve? (i.e. each point of the x-y-graph is displaced in y by a random amount) A simple running mean does it, but on the other hand it also changes the shape of the underlying real curve. Is it possible to use the...
  16. B

    Dirac Delta as the limit of a Gaussian

    Show that \stackrel{lim}{\alpha \rightarrow \infty} \int^{\infty}_{-\infty}g(x)\sqrt{\frac{\alpha}{\pi}}e^{-\alpha x^2} dx = g(0) where g(x) is continuous. To use the continuity of g(x) I started from \left|g(x)-g(0)\right|<\epsilon and tried to put it in into the integral...
  17. K

    Solving Augmented Matrices with Gaussian Method

    |1 -5 2 |-5 |3 -14 3 |-8 |4 -18 8 |-8 above is a augmented matrix of a 3 equations. now i know that you can solve these via simul. equations however, my textbook solves them via some gaussian method but doesn't mention how it's done. it just shows - 1 -5 2 |-5 0 1 -3 |7 0 0...
  18. maverick280857

    Fourier Transform of a Gaussian

    Hi everyone I am trying to prove that if a signal g(t) is its own Fourier Transform (so that G(f) = g(f), i.e. they have the same functional form), then g(t) must be a Gaussian. I know that the Fourier Transform of a Gaussian is a Gaussian, so that's not the point of the exercise. Simon...
  19. B

    Solving Gaussian Integral with Integration by Parts

    I see that the formula for this general integral is \int^{+\infty}_{-\infty} x^{2}e^{-Ax^{2}}dx=\frac{\sqrt{\pi}}{2A^{3/2}} However, I am not getting this form with my function. I transformed the integral using integration by parts so that I could use another gaussian integral that I knew at...
  20. N

    A Beautiful Looking Gaussian Integral - Please HELP

    I have the following Gaussian Integral: \int_{0}^{\infty}2\pi r\left |{\int_{-l/2}^{l/2}\frac{e^\frac{-r^2}{bH}}{(1+ix)(k^{''} - ik^{'}x)H}}dx\right |^2dr Where H = \frac{1+x^2}{k^{''} - ik^{'}x} - i\frac{x - \zeta}{k^{'}} Assume any characters not defined are constants. I agree...
  21. V

    Deriving Gauss' Law for Gravity from Newton's Law

    Homework Statement How would I derive Gauss' law for gravity from Newton's law?Homework Equations \mathbf{g}(\mathbf{r}) &=& -G\frac{m_1}{{\vert \mathbf{r}\vert^2}}\hat{\mathbf{r}} to \nabla\cdot\mathbf{g} = -4\pi G \rhoThe Attempt at a Solution I have no reference material outside the wide...
  22. D

    Derivation of Gaussian Distribution

    Homework Statement Derive the equation for the Gaussian distribution. Homework Equations The probability density function for the Gaussian distribution: f(x) = \frac{1}{\sigma \sqrt{2\pi} } e^{ -\frac{(x-\mu)^2}{2\sigma ^2} } The Attempt at a Solution It is my understanding that the...
  23. P

    How Does Charge Density Affect Electric Field Inside a Cylindrical Insulator?

    Homework Statement A long cylindrical insulator has a uniformcharge density of 1.46uC/m3 and a radius of 6cm.a-What is the electric field inside the insulator at a distance of 2cm and 12cm? Answer should be in N/C. b-How much work must you do to bring a q=0.086uC test charge from 12cm to 2cm...
  24. D

    Solving Gaussian Distribution Problem: Find (Δx)^2 and Uncertainty δp

    Problem Let us define a wave function \phi = A \exp \(\frac{-(x-x_0)^2}{4a^2}\) \exp \(\frac{i p_0 x}{\hbar}\) \exp(-i \omega_0 t). Show that (\Delta x)^2 = a^2. Also, calculate the uncertainty \delta p for a particle in the given state. Attempt at a solution I honestly have no idea as to...
  25. A

    Formally Proving the Invariance of Solutions in Gaussian Elimination

    I've been doing Gaussian Elimination in a Linear Algebra class, but I have a question: How do I formally prove that elementary row operations do not change the set of solutions to a system of linear equations? Thanks.
  26. S

    Gaussian infinite line charge, find force

    -----problem------- an infinite line of charge produces an electric field of 20N/C at a point that is 3 meters from the line. the electric field points toward the line of charge what is would be the force (magnitude and direction) on a negative 6 microcoulomb charge that is located 6m from the...
  27. S

    Gaussian infinite sheet, electric field

    Homework Statement three thin charged sheets are placed parallel to each other as shown: far left sheet, charge density = +10C/m^2 middle sheet, charge density = -25C/m^2 far right sheet, charge density = -10C/m^2 |<--2m (A) -->|<-----4m (B) ------>| a) what is the electric field in regions...
  28. B

    How to Resolve Convergence Failures in Gaussian NH3+ Calculations?

    Homework Statement I am using gaussian to calculate the potential energy surface for NH3+, but I have been having troubles with convergence failures. I did some searching on the internet and found that using SCF=qc can sometimes help with convergence failures since it instruct the program to...
  29. P

    Solving Complex Gaussian Integral Problems

    Homework Statement We know that \int_{-\infty}^\infty e^{-ax^2}dx = \sqrt{\pi \over a}. Does this hold even if a is complex? Homework Equations The Attempt at a Solution In the derivation of the above equation, I don't see any reason why we must assume that a be real. So I...
  30. F

    Gaussian Curvature of (x^2+y^2+1)^-2

    1. Homework Statement Is the gaussian curvature at a point on the surface \frac{1}{(x^2+y^2+1)^2}? 2. Homework Equations shape operator: S(\textbf{x})=-D_\textbf{x}\hat{\textbf{n}}=\frac{\partial (n_x, n_y)}{\partial (x,y)} Gaussian Curvature = |S(\textbf{x})|...
  31. F

    Gaussian Curvature: Calculating for g(x,y)=xy\frac{1}{(x^2+y^2+1)^2}

    Homework Statement Is the gaussian curvature at a point on the surface g(x,y)=xy \frac{1}{(x^2+y^2+1)^2}?Homework Equations shape operator: S(\textbf{x})=-D_\textbf{x}\hat{\textbf{n}}=\frac{\partial (n_x, n_y)}{\partial (x,y)} Gaussian Curvature = |S(\textbf{x})| \hat{\textbf{n}}=\frac{\nabla...
  32. B

    MATLAB Please help me with Gaussian Distribution and central limit theorem in matlab

    please help me with Gaussian Distribution and central limit theorem in matlab! :cry:I am trying to generate a random variable with a approximate gaussian distribution using the rand function and central limit theorem, got stuck when trying it. Please help me. Also want to know how to produce a...
  33. P

    Solve System of Equations: Gaussian Elimination

    Solve the following system of equations using Gaussian elimination: 3w+10x-2y+3z=55 w+12x-11y-z= 69 -3w-6x-5y-10z=-47 -3w+9x+5y+4z=-1 Here's what I did so far: swap R1 and R2 (row 1 and row 2) -3R1+R2 (multiply row 1 by -3 and add row 2 to that product) 3R1+R3 3R1+R4 Now, after...
  34. D

    MATLAB Plotting a 3D Gaussian in MATLAB

    Homework Statement Hi all! I'm trying to solve the following problem but I'm not too sure of a few things. Write Matlab instructions to plot a three dimensional Gaussian: A = A0exp((x^2 + y^2 + z^2)/w^2) choosing appropriate values for A0,w and range of coordinates. Homework...
  35. W

    MATLAB 5-point Gaussian Quadrature using constructed approximant in Matlab

    Homework Statement 6.3.b highlighted in attachment. Have solved part a (which gives the approximant used in part b) and problem 3.8 (which gives the original function). 3.8 was definitely solved correctly. Part a could be wrong, but the solution seems OK. a = acreage y = yield from 3.8 -...
  36. N

    How Do Quantum Operators Affect Position and Momentum Expectations?

    I'm trying to evaluate the expectation of position and momentum of \exp\left(\xi (\hat{a}^2 - \hat{a}^\dag^2)/2\right) e^{-|\alpha|^2} \sum_{n=0}^\infty \frac{\alpha^n}{\sqrt{n!}} |n\rangle} where \hat{a},\hat{a}^\dag are the anihilation/creation operators respectively. Recall \hat{x}...
  37. H

    Solve Physics Problem: Gaussian Distribution

    Hello, I am attaching what was an extra credit question in my physics class which I didn't understand at all. The topic isn't in the book and all the internet searchs I read confuse me. I was hoping someone might give me a walk through. Thanks!
  38. I

    Solving Gaussian Integration: 0.513e-5i Wrong Answer?

    I'm trying to integrate the Gaussian distribution between arbitrary limits, but I'm not having a lot of luck. As far as I can see I've done it right, but the answer I get is imaginary, which is obviously wrong, since it's supposed to represent a probability :confused: Homework Statement a =...
  39. H

    Understanding Gaussian Equation - Practical Uses

    Hi every body, I need help how to understand the Gaussian equation. For what we can use it i practise. I saw it in many things used but I have a problem to understand it. Thanks
  40. Z

    Solving the Gaussian Cube Question: Understanding E = 7.35i - 5.63(y2 + 9.74)j

    http://img255.imageshack.us/img255/8083/47252155dr7.jpg Okay I totally don't understand this problem at all. There is an example in the book also, but I just don't understand how to do it. Like the whole concept of how the E is written. I don't understand what this means: E = 7.35i - 5.63(y2...
  41. S

    How do I integrate Gaussian form equations without prior knowledge?

    [SOLVED] Gaussian Form Integration Homework Statement http://img153.imageshack.us/img153/9489/001km6.jpg I'm trying to do the last part. Homework Equations Stated in the question. The Attempt at a Solution For (iii) i know the probability density is: A^2e^{-...
  42. tony873004

    Generating a random gaussian number

    I want write a short block of computer code that allows me to generate a random gassuian number. For example, if the inputs are mean = 100 and sd = 10, if I generage 1000 random numbers, I'd like 67% of them to be between 90 and 110, 98% of them to be be between 80 and 120. But I only know...
  43. V

    Why Is My Gaussian Quadrature Implementation Inaccurate?

    I'm trying to make a generalized quadrature method and I seem to be running into some bizarre errors. For n=2 my answer is twice what it should be and for n greater the innaccuracy increases (answer/n is close but worse than answer/2 with n=2). My general algorithm is: p = nth legendre...
  44. A

    Does Gauss' Law Hold for Infinite Gaussian Surfaces?

    Hi, From what I understand the proof of Gauss' law applies only to finite surfaces. Can anyone give an example of a charge distribution and an infinite Gaussian surface, where the total flux on it is not proportional to the enclosed charge? Thanks!
  45. F

    Solving Gaussian Integral with Complex offset

    Homework Statement Given f(x) = e^{-ax^2/2} with a > 0 then show that \^{f} = \int_{-\infty}^{\infty} e^{-i \xi x - ax^2/2} \, \mathrm{d}x = \surd\frac{2}{a} = e^{-\xi^2/2a} by completing the square in the exponent, using Cauchy's theorem to shift the path of integration from the real axis...
  46. B

    Can Gaussian Elimination Solve a System with Identical Equations?

    2x+3y+3z=7 2x+3y+3z=7 2x+3y+3z=7 Using Gaussian Elimination... is it possible to find the value of x,y,z with three similar equation?
  47. M

    Cant understand Gaussian surface

    Homework Statement Can someone please explain what use gaussian surfaces have, in really simple terms? I don't really understnd the point of wrapping an imaginary surface around a charge, when we can just do the calcs without the imaginary surface. Also if there are preset gaussian surfaces...
  48. F

    Solving Matrix with Gaussian Elimination: Find Solutions

    I used Gaussian elimination on a matrix to find the soultions. I know that there is either no solutions or infinatley many, but the matrix is confusing me. The only definition I have of when a matrix has infinatley many solutions is when a zero row is equal to zero, and no solutions when a zero...
  49. C

    Electric flux through gaussian cube

    Homework Statement I have a cube with four faces parallel to the field and two perpendicular. The field is non uniform, given by E = 3 + 2x^2 in the +x direction. The Attempt at a Solution So I get \phi = \int \vec{E} \cdot d\vec{A} = \int EdA = A \int E = A \int (3+2x^2) But how do I...
  50. I

    Electric Field from Gaussian Pillbox of Thickness 2d & Uniform Charge Density ρ

    The question states that there is an infinite plane slab of thickness 2d that has a uniform charge density rho. Find the electric field as a function of y, where y=0 at the center. inside plane: \int E da = 2EA = \frac{\rho A y}{\epsilon_o} outside plane: \int E da = 2EA = \frac{\rho A...
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