- #1
rockstar101
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Homework Statement
Let
( Eo 0 A )
( 0 E1 0 )
( A 0 Eo )
be the matrix representation of the Hamiltonian for a three state system with basis states
|1> |2> and |3> .
If |ψ(0)> = |3> what is |ψ(t)> ??
Homework Equations
The Attempt at a Solution
First I need to find the energy eigenstate of the system:
H|ψ> = E|ψ> and
(Eo 0 A , 0 E1 0, A 0 Eo)T ( <1|ψ> , <2|ψ>, <3|ψ>)T = E( <1|ψ> , <2|ψ>, <3|ψ>)T
so I got the equation (Eo - E)(E1 - E)(Eo-E) + A^2(E1-E) = 0
simplify, (Eo - E)^2 (E1 - E) + A^2(E1 - E) = 0
for this equation to be true, then E1 = E ... is this my eigenvalue??
From here, how do I find the energy eigenstate?
After that, what should I do to answer the question?
I would really appreciate any hint or help... thank you.