Are Eigenkets with Eigenvalues Periodic for a Hamiltonian System?

[greisen]

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

 

[Meir Achuz]

To be periodic the three frequencies must be relatively rational.

 

[greisen]

sqrt(2) is not a rational number neither is sqrt(3). So when you say relative rational what do you mean?

Thanks in advance

 

[HallsofIvy]

That their ratio is a rational number.

 

[greisen]

So I thought - so with the eigenvalues posted they will not be periodic!

Thanks for the replies