- #1
Mlisjak
- 6
- 0
Homework Statement
I have the matrix form of the Hamiltonian:
H = ( 1 2-i
2+i 3)
If in the t=0, system is in the state a = (1 0)T, what is Ψ(x,t)?
Homework Equations
Eigenvalue equation
The Attempt at a Solution
So, I have diagonalized given matrix and got the eigenvalues: 2+√6 and 2-√6. I am suspecting that these are not good, since I can't get eigenvectors I can use. When trying to calculate eigenvectors, I get:
a = 1 and b=(-1+√6)/(2+i). This is the one I got when I used 2+√6 but after that I didn't even try with the other eigenvalue since it will be similar.
I don't know what to do with those and don't know how to normalize them. Also, even if I knew how to get correct eigenvectors, I am not sure how to proceed and get Ψ(x,t). [/B]