Eigenvalues of the Hamiltonian with corresponding energies are:
Iv1>=(I1>+I2>+I3>)/31/2 E1=α + 2β
Iv2>=(I1>-I3>) /21/2 E2=α-β
Iv3>= (2I2> - I1> I3>)/61/2 E3=α-β
Write the matrix of the Hamiltonian in the basis of the orthonormalized vectors I1>, I2>, I3>
If in t=0, system is in the state I1>, what is the wave function in t?
Hij = <ilHlj>
The Attempt at a Solution
Although I know that energy is the eigenvalue of the Hermitian operator, I am not sure how to incorporate that in this certain problem. I have used mentioned equation for previous problems, but I always had the form of the operator. With only eigenvectors and eigenvalues I am stuck and don't even know how to begin solving this.