- #1

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## 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! I don't know if that's right?! :uhh:

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!