- #1
Denver Dang
- 148
- 1
Homework Statement
Find the probability, [itex]P_{2a}(t)[/itex], that a measurement of the quantity [itex]A[/itex] in
the state [itex]|\varphi (t)\rangle\right[/itex] will yield the value [itex]2a[/itex].
Homework Equations
[tex]\hat{A}|1\rangle\right = a(|1\rangle\right - i|2\rangle\right[/tex]
[tex]\hat{A}|2\rangle\right = a(i|1\rangle\right + |2\rangle\right[/tex]
[tex]\hat{A}|3\rangle\right = -2a(|3\rangle\right[/tex]
[tex]A = \[ \left( \begin{array}{ccc}
a & ia & 0 \\
-ia & a & 0 \\
0 & 0 & -2a\end{array} \right)\][/tex]
[tex]|\varphi (t)\rangle\right = \[ \left( \begin{array}{ccc}
cos(wt) \\
0 \\
-isin(wt) \end{array} \right)\][/tex]
The Attempt at a Solution
Well, I kinda suck at finding these probabilities. So I'm not sure what to do, since it asks for [itex]2a[/itex]. Is it just:
[tex]P(2a) = \left|\langle\psi_j|\Psi\rangle\right|^2,[/tex]
where [itex]\psi_j = \varphi[/itex] and [itex]\Psi = A|3\rangle\right[/itex], or am I just not getting it ?
Regards.