How Long Until a Two-Particle Quantum System Reverts to Its Initial State?

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Homework Statement



This is a quick one, which I apologize ahead of time for not writing this out more neatly. The parentheses denote subscripts. I have a system of two particles, which are in a superposition Psi(one) + Psi(two). The energy of particle one is E(1) and of particle two is E(2). How long does it take for the wave function of the system of two particles to return to what it was at t = 0?

Homework Equations



Perhaps the energy-time uncertainty principle.

The Attempt at a Solution



Well, alright. My first reaction is to say that because there are definite energies, it is in a stationary state and will not change with time. However, getting to the math of it, this only works if there is orthogonality between the two particles' initial states. When normalizing the time-dependent version, I end up with a cosine term at the end. Does the system return to the state of t = 0 when the term in the cosine = 2pi ?

I feel like I'm on the right track but it seems kind of messy.
 
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