Is that equal to finding the norm of the eigenvectors? For example, I have three eigenvectors: v1 = v2 = (1 0 0)† and v3=1/√2 (0 -i 1)†.
Would I write Ψo= 2*(1 0 0)†+1/√2 (0 -i 1)†?
To be precise, I don't understand how to get right coefficients to write Ψ(x,0) as a linear combination of the vectors I got. When i get that, I believe that I just have to add time dependence e-iEt/†
Do you get the same eigenvalues? I put it in the form:
( 1 2-i
2+i 3 ) * (a b)t = (2+√6) (a b)T
I'm sorry, I don't know to write it properly.
Then I got:
a+(2-i)b = (2+√6)a
That's where the expression comes from. And by using the second equation i got a=a in which cases we always put 1...
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...