How Do You Compute the Adjoint of a Quantum State in Dirac Notation?

[spaghetti3451]

Homework Statement

1. Given that |ψ> = e^iπ/5|a> + e^iπ/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>?

Homework Equations

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.

 

[BruceW]

looks good to me. although 2)a) is only true when |a> is a normalised state vector. If you can assume that it is normalised, then its fine.