- #1
dageki
- 2
- 0
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):
[tex]\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!}[/tex]
using:
[tex]a^{+}=\frac{(a_{1}^{+}+a_{2}^{+})}{ \sqrt{2}}[/tex]
and
[tex]a=\frac{(a_{1}+a_{2})}{\sqrt{2}}[/tex]
and
[tex]|n\rangle=\frac{1}{\sqrt{n!}}(a^{+})^{n}|0\rangle[/tex]
and using usual creation and destruction oprator properties, to give finally :
[tex]\bar{n}_1=\frac{1}{2}[/tex]
I have no idea how to do it...
Big thnx
I have problem with equation(average number of photons registered behind pinhole 1 in two slit experiment):
[tex]\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!}[/tex]
using:
[tex]a^{+}=\frac{(a_{1}^{+}+a_{2}^{+})}{ \sqrt{2}}[/tex]
and
[tex]a=\frac{(a_{1}+a_{2})}{\sqrt{2}}[/tex]
and
[tex]|n\rangle=\frac{1}{\sqrt{n!}}(a^{+})^{n}|0\rangle[/tex]
and using usual creation and destruction oprator properties, to give finally :
[tex]\bar{n}_1=\frac{1}{2}[/tex]
I have no idea how to do it...
Big thnx