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...
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...
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...
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...
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
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...
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...
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...
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...
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...
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...
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...