Homework Help: Two slit experiment - quantum theory - problem

1. May 15, 2007

dageki

Hi, I'm new and I'm from Poland.
I have problem with equation(average number of photons registered behind pinhole 1 in two slit experiment):
$$\bar{n}_1=\langle n|a_{1}^{+}a_{1}|n\rangle=\frac{\langle 0|(a^{+})^{n}a_{1}^{+}a_{1}(a^{+})^{n}|0\rangle}{n!}$$
using:
$$a^{+}=\frac{(a_{1}^{+}+a_{2}^{+})}{ \sqrt{2}}$$
and
$$a=\frac{(a_{1}+a_{2})}{\sqrt{2}}$$
and
$$|n\rangle=\frac{1}{\sqrt{n!}}(a^{+})^{n}|0\rangle$$
and using usual creation and destruction oprator properties, to give finally :
$$\bar{n}_1=\frac{1}{2}$$

I have no idea how to do it...
Big thnx

2. May 16, 2007

Milind_shyani

Welcome
Hi i think that you must specify that whether there is a detector or not at any of the slits and whether the other slit is open or not.Other wise refer volume three of feynman lectures

3. May 19, 2007

dageki

We have a stream of photons incident on a pair of identical pinholes. We assume that only a single mode of the cavity (cavity formed by the lens and the first screen) is excited, with photon creation and destruction operators

$$a^{+}$$

and

$$a$$

We suppose that the two piholes provide the only means for photons in the cavity.For pinholes of equal size, the incident photons are equally likely to be registered in mode 1 or 2.

Still I don't know how to prove it.
I will be grateful for help.