Probability and probability amplitude

[phyky]

|A>=a|0>+b|1>
<A|A>=probability amp |<A|A>|^2=probability
If the state is same, so <A|A>= a^2+b^2=1. then i find the probability and no interference term in it!
so can i say <A|A>=|<A|A>|^2 and no square is needed? since if i square it become a^4+b^4=??
what wrong with it! and where should i place interference term?!

 

[Jilang]

|A> is the probability amplitude.
<A|A> is the probability.
Maybe you are confusing the situation with transition amplitudes where <A|B> is the amplitude of transition from A to B?

 

[phyky]

so if transition from A to B it need |<B|A>|^2 to find interference term? and <A|A> show only probability but nothing about interference? but its outer product |A><A| does show interference?

 

[phyky]

|A>=a|0>+b|1> so <A|A>=a^2<0|0>+b^2<1|1>+a*b<0|1>+b*a<1|0> where <i|j>=0 <i|i>=1. where the interference term?

 

[Jilang]

You looking for interference between orthogonal states then. Why would you expect there to be some?

 

[freshman123]

As for a normalized wave function |A>, a^2+b^2=1. However, <A|A>is not equal to a^2+b^2but a^2+b^2+a*b+ab* , generally speaking, the latter is not equal to 1. <A|A>=|A>|^2, would it help?