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## Homework Statement

Eigenvalues of the Hamiltonian with corresponding energies are:

Iv

_{1}>=(I1>+I2>+I3>)/3

^{1/2}E

_{1}=α + 2β

Iv

_{2}>=(I1>-I3>) /2

^{1/2}E

_{2}=α-β

Iv

_{3}>= (2I2> - I1> I3>)/6

^{1/2}E

_{3}=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?

## Homework Equations

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.

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