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Hello everyone,

I'm stuck on the question which I have provided below to do with Dirac notation:

In these questions |a>, |b> and |c> can be taken to form an orthonormal basis set

Consider the state |ξ> = α(|a> − 2|b> + |c>). What value of α makes |ξ> a normalised state?

I'm brand new to Dirac notation so I'm not too sure what to do? I was thinking that in order for |ξ> to be normalised, then (|ξ> )^2 = 1. But I don't know whether you can do (|ξ>)(|ξ>)? I've only ever seen something like <a|a> which equals 1 if you do <a|a> or 0 if you do <b|c>.

If you can square a ket, then would I be right in saying α is 1/ sqrt (3) because expressions like |a>|a> would be 1 and |a>|b> would be 0?

Any help will be greatly appreciated!

I'm stuck on the question which I have provided below to do with Dirac notation:

In these questions |a>, |b> and |c> can be taken to form an orthonormal basis set

Consider the state |ξ> = α(|a> − 2|b> + |c>). What value of α makes |ξ> a normalised state?

I'm brand new to Dirac notation so I'm not too sure what to do? I was thinking that in order for |ξ> to be normalised, then (|ξ> )^2 = 1. But I don't know whether you can do (|ξ>)(|ξ>)? I've only ever seen something like <a|a> which equals 1 if you do <a|a> or 0 if you do <b|c>.

If you can square a ket, then would I be right in saying α is 1/ sqrt (3) because expressions like |a>|a> would be 1 and |a>|b> would be 0?

Any help will be greatly appreciated!

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