- #1
rustyrusty
- 9
- 0
Homework Statement
I have a hamiltonian:
[tex] \begin{pmatrix}
a &0 \\
0&d
\end{pmatrix} + \begin{pmatrix}
0 &ce^{i w t} \\
ce^{-iwt}&0
\end{pmatrix}=\begin{bmatrix}
a & c e^{i w t} \\
c e^{-i w t}&d \\
\end{bmatrix}
[/tex]
Where the first hamiltonian can be labeled with states |1> and |2> corresponding to a and d.
Now it says that it is in state |2> at time zero. Find the state at time t.
Homework Equations
The Attempt at a Solution
I Found that looking at the first matrix ONLY, Its eigenstates are {{1},{0}} and {{0},{1}}
but when you look for the eigenstates at t=0 from the total hamiltonian, you have to use quadratic formula and quickly gets messy.
Im assuming I'm starting this all wrong