Recent content by cahill8

I'm trying to compare fits to data in a certain way. I start with the initial data and fit and compute the \chi^2 value for example: x: 1 2 3 4 y: 2.1 3.9 6.0 10.1 I get the linear fit, \chi^2 value and degrees of freedom=3. Now with what I'm working with, I don't actually know the...

When a stars radial velocity is measured in search for a planet, the planet imparts a radial velocity shift proportional to m\sin i\text{ where }i is the orbital inclination of the planet with respect to our line of sight and m is the planet mass. I've heard that even though the inclinations are...

I'm dealing with a histogram and want to use poisson errors for each bin. For example, having 7 items in a bin gives that bin an error of sqrt(7). I'm comparing four different data sets, each with different sizes. I'm scaling everything in terms of probabilities so the four data sets can be...

Well another part of the question says the mean of one component of velocity, \bar{v_x^2} = \sigma^2 could I simply continue and say \bar{v_x^2}=\beta\int^\infty_0 v_x^2\hspace{2pt} exp\left[-(\sqrt{v_x^2+v_y^2+v_z^2})^2/2\sigma^2\right] dv= \beta\int^\infty_0 v_x^2\hspace{2pt}...

Thanks for the reply. That is the answer given (from the textbook galaxy dynamics, problem 4.18) Your right those answers were wrong, I calculated them using mathematica when writing this topic but inputted the equation wrong. The first can be done by making a u substitution...

Homework Statement A group of stars in a Maxwellian distribution have a one-dimensional velocity dispersion \sigma. The number of objects within an element d^3v is dN=F(v) d^3 v=\beta\hspace{2pt}Exp[-v^2/2 \sigma^2]d^3v where \beta is a constant Find that the mean speed...

Homework Statement I'm at the last step of an integral but can't seem to get the right answer. Homework Equations After many substitutions I finally have \int^1_0 arctan(w)dw which from wiki is a standard integral, =[w \text{ arctan}(w)-1/2 \text{ ln}|1+w^2|]^1_0 The Attempt at a...

Homework Statement I'm trying to solve a second order ODE for y(x) to show that the solution is y(x)=sin(x)/x. We've been told to use the substitution y(x)=h(x)/x. I've got to the stage of solving for h(x), arriving at h''(x)=-x. Using the general solution, h(x)=A sin(x) + B cos(x) and...

Homework Statement I am inquiring about Braggs Law 2 d\sin\theta = n\lambda . The question I'm working on gives me the first four Bragg angles (\theta values) and I have also calculated the wavelength of the light. I want to solve for d but I am unsure what value to use. Homework Equations...

I figured out the case when the slit has some width: T(x,y)=rect\left(\frac{x}{L}\right) \left[rect\left(\frac{y+d}{t}\right)+rect\left(\frac{y-d}{t}\right)\right] where t is the thickness. However I'm looking for the case where t is "infinitely narrow" What I want is to replace...

Homework Statement I have to find the transmittance function T(x,y) of two narrow slits of length L and separated by a distance 2d.Homework Equations [PLAIN]http://being.publicradio.org/programs/quarks/images/youngexperiment.gif This is what I'm talking about. In my case the x-axis runs in...

Homework Statement I'm trying to go through something shown in a lecture and the part I'm stuck on is shown here. \frac{\partial}{\partial t}\int^t_0 \mbox{du }e^{i \omega(t-u)}\hat{b}(u)=\hat{b}(t) \hat{b}(u) is an annihilation operator The Attempt at a Solution Can someone explain how this...

Homework Statement I need this to answer a question, its not a homework question itself. Can this be simplified? u(t-2)u(t-a) where u is the unit step function. Homework Equations - The Attempt at a Solution I know the answer is u(t-2) if a <= 2, u(t-a) otherwise. But is there a...

A photon can spontaneously produce an electron-positron pair (see pair production)

You can walk outside and point to a planet in the sky. Are you saying the planet isn't exactly there or are you talking about mathematical predictions being wrong?