1. Given that |ψ> = eiπ/5|a> + eiπ/4|b>, express <ψ| as a linear combination of <a| and <b|.
2. What properties characterise the bra <a| that is associated with the ket |a>?
The Attempt at a Solution
1. <ψ| = e-iπ/5<a| + e-iπ/4<b|
2. a. The bra <a| when applied on the ket |a> will give 1.
b. The bra <a| is a linear function, which applied on the other elements of the vector space of |a> will give a complex scalar.
Comments are welcome.