- #1
quixi
- 3
- 0
Homework Statement
Homework Equations
The Attempt at a Solution
OK I have
[tex]
\left| \psi \right> = \alpha \left| 000 \right> + \beta \left| 001 \right> + ... + \theta \left| 111 \right>
[/tex]
which I need to normalise.
I know that
[tex]\left| \psi \right>^{*} = \left< \psi \right|[/tex]
and so have derived expression
[tex]
\left< \psi \right| = \alpha^{*} \left| 000 \right> + \beta^{*} \left| 001 \right> + ... + \theta^{*} \left| 111 \right>
[/tex]
which means each have 8 terms.. so now doing
[tex]
\left< \psi | \psi \right> = \alpha \alpha^{*} \left< 000 | 000 \right> + \alpha \beta^{*} \left< 000 | 001 \right> + ...
[/tex]
this multiplication will result in 64 terms!
then I know [itex] \left< 00|00 \right> = 1 [/itex] and [itex] \left< 00|11 \right> = 0 [/itex] which I assume I can apply to [itex] \left< 000|000 \right> = 1 [/itex] and [itex] \left< 00|11 \right> = 0 [/itex] ?
basically then end up with
[tex]
\left< \psi | \psi \right> = \alpha \alpha^{*} + \beta \beta^{*} + ..
[/tex]
I think that's along the right lines now? Its just the daunting 8x8=64 multiplication that I was unsure on!