Gaussian Definition and 706 Threads

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 >...

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...

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

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 =...

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...

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...

|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...

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...

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...

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...

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...

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...

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...

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...

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.

-----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...

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...

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...

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...

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})|...

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...

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...

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...

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 -...

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}...

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!

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 =...

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

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...

[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^{-...

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...

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...

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!

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...

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?

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...

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...

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...

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...

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.

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...

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"...

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}...

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

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...

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...

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...

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?

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...

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.