Hi. I came across a problem in a book of mine that requires me to find the dual of a vector |x> = A |a> + B |b>. However, it's a bit sketchy about taking |x> to <x|. With a little algebra, I got(adsbygoogle = window.adsbygoogle || []).push({});

|x>_{i}= A |a>_{i}+ B |b>_{i}

So

<x|_{i}= |x>_{i}*

= (A |a>_{i}+ B |b>_{i})*

= (A |a>_{i})* + (B |b>_{i})*

= A* |a>_{i}* + B* |b>_{i}*

= A* <a|_{i}+ B* <b|_{i}

So, finally

<x| = A* <a| + B* <b|

I just want to double check I'm not making any mistakes, since I'm still getting used to this wacky notation!

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# Duals in Dirac Notation

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