- #1
Bacat
- 151
- 1
Homework Statement
Consider a quantum system described by a basis [tex]\mid 1 \rangle[/tex] and [tex]\mid 2 \rangle[/tex].
The system is initially in the state: [tex]\psi_i = \frac{i}{\sqrt3} \mid 1 \rangle + \sqrt{\frac{2}{3}} \mid 2 \rangle[/tex].
(a) Find the probability that the initial system is measured to be in the state: [tex]\psi_f = \frac{1 + i}{\sqrt 3} \mid 1 \rangle + \frac{1}{\sqrt{3}} \mid 2 \rangle[/tex]
Homework Equations
The basis is assumed to be orthonormal, hence [tex]\langle 1 \mid 1 \rangle = \langle 2 \mid 2 \rangle = 1[/tex]
Probability is calculated as [tex](\langle \psi_f \mid \psi_i \rangle)^2[/tex]
The Attempt at a Solution
Calculating this, I get a complex answer. I'm not sure but I think a probability (a real observable) should be a real number. Is that right?
The answer I get is [tex]\frac{2 + 2\sqrt{2}}{9}(1+i)[/tex].