# Homework Help: Probability distribution function / propagator

1. Mar 10, 2009

### raintrek

I have the following equation:

$$\frac{1}{2N^{2}}\int_{s} \int_{p} \left\langle (\textbf{R}_{s} - \textbf{R}_{p} )^{2} \right\rangle$$

which describes the radius of gyration of a polymer. (the term being integrated is the average position between beads p and s)

This is shown to be equivalent to:

$$\frac{1}{2N^{2}}\int_{s} \int_{p} \left| s - p \right| b^{2}$$
where b is the step size.

All my text book says is that the second equation has been found by using the propagator (probability density function) and two integrals:

$$G(\textbf{R}, N)=\left( \frac{3}{2\pi Nb^{2}}\right)^{3/2}e^{- \frac{3R^{2}}{2Nb^{2}}$$

$$\int^{\infty}_{- \infty} e^{-ax^{2}}=\sqrt{\frac{\pi}{a}}$$
$$\int^{\infty}_{- \infty} x^{2} e^{-ax^{2}}=\frac{1}{2a} \sqrt{\frac{\pi}{a}}$$

I have no idea how this "propagator" is used to reach the second equation. Is anyone able to shed any light on what's happened? Many thanks in advance!

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted