Are Eigenkets with Eigenvalues Periodic for a Hamiltonian System?

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Hey,

A Hamiltonian has 3 eigenkets with three eigenvalues 1, sqrt(2) and sqrt(3) - will the expectation values of observables in general be period functions of time for this system?

I don't know how to procede?

Thnaks in advance
 
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To be periodic the three frequencies must be relatively rational.
 
sqrt(2) is not a rational number neither is sqrt(3). So when you say relative rational what do you mean?

Thanks in advance
 
That their ratio is a rational number.
 
So I thought - so with the eigenvalues posted they will not be periodic!

Thanks for the replies
 

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